In summation, the balloon's motion may be defined as an entity undergoing steady downward acceleration, with a starting velocity of zero and rising velocity as time passes.
Describe the motion of the balloon using kinematics concepts of velocity and acceleration.The motion of the balloon may be characterized using kinematic principles of velocity and acceleration when it is pushed back to the halfway between the wall and the sweater and then released. The balloon has an initial velocity of zero, v0 = 0, at the instant of release. The gravitational force pressing on it causes it to accelerate downwards. The balloon's acceleration may be described as the acceleration owing to gravity, a = 9.8 m/s2. As time passes, the balloon's velocity rises due to its acceleration. The balloon's velocity may be calculated using the equation v = v0 + at, where t denotes time. The balloon's location may be characterized by the equation x = x0 + v0t + (1/2)at2, where x0 represents the balloon's original position. The balloon's velocity will grow during its travel, reaching its maximum value at the instant it hits its lowest point. Because the balloon is only being affected upon by the constant force of gravity, its acceleration will remain constant.
Here,
In summary, the motion of the balloon can be described as an object undergoing constant acceleration in the downward direction, with an initial velocity of zero and increasing velocity as time progresses.
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Gordon throws a baseball into the air. It rises, stops momentarily when it reaches its greatest height, and then falls back to the ground. At what point does kinetic energy convert to potential energy?.
Answer:
Kinetic energy is turned into potential energy on the way up.
Explanation:
Kinetic energy is proportional to the square of speed. As the baseball slows down, kinetic energy of the baseball decreases.
If [tex]g[/tex] is constant, the gain in gravitational potential energy would be proportional to the change in height. As the height of the baseball increases, the baseball gains gravitational potential energy.
As the baseball rises, its speed gradually decreases while its height increases. Kinetic energy of the baseball is turned into potential energy.
As the baseball falls back to the ground, its speed increases while its height decreases. Potential energy is turned back into kinetic energy.
a skydiver jumps out of a hovering helicopter. a few seconds later, another skydiver jumps out, so they both fall along the same vertical line relative to the helicopter. assume both skydivers fall with the same acceleration. how does the vertical distance between them change?
As time increases, the distance between the skydivers decreases, until they eventually collide.
define distance ?
Distance is a scalar quantity that represents the magnitude of separation between two points in space. It can be thought of as the length of the shortest path between the two points. Distance can be calculated by using the Pythagorean theorem or other methods, depending on the geometry of the situation. The unit of distance can be meters, kilometers, miles, or any other unit of length.
The vertical distance between the two skydivers changes over time as they both fall with the same acceleration. If we consider that the initial vertical distance between them is d0, then the vertical distance d between them at time t can be calculated using the following formula:
d = d0 - g * t^2 / 2
where g is the acceleration due to gravity (approximately 9.8 m/s^2) and t is the time elapsed.
Since both skydivers have the same acceleration, they both fall at the same rate and the vertical distance between them decreases linearly with time. As time increases, the distance between the skydivers decreases, until they eventually collide.
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A loudspeaker on a tall pole broadcasts sound waves equally in all directions. What is the speaker's power output if the sound intensity level is 108 dB at a distance of 17m?
The speaker's power output is 392022.72W if the sound intensity level is 108 dB at a distance of 17m.
Power output or acoustic power is the rate at which sound energy is radiated, reflected, communicated or got, per unit time.[1] It is defined[2] as "through a surface, the result of the power output , and the part of the molecule speed, at a guide on a superficial level toward the path typical toward the surface, coordinated over that surface."
The SI unit of Power output is the watt (W).[1] It connects with the force of the sound power on a surface encasing a sound source, in air. For a sound source, dissimilar to sound strain, Power output is neither room-subordinate nor distance-subordinate.Power output is a property of the field at a point in space, while sound power is a property of a sound source, equivalent to the complete power radiated by that source every which way. Power output going through an area is some of the time called sound motion or acoustic transition through that area.
We know that power output of sound waves is calculated by the formula=4πIr² where I is the sound intensity level and r is the distance.
Since,we have I=108dB and r=17m.Therefore,
P=4×3.14×108×17×17
=>P=1356.48×289
=>P=392022.72W
Hence,speaker's power output is 392022.72W.
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After landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 52.0cm . The explorer finds that the pendulum completes 109 full swing cycles in a time of 136 s.
What is the magnitude of the gravitational acceleration on this planet?
The magnitude of the gravitational acceleration on this planet can be calculated using the equation $g = 4\pi^2\frac{L}{T^2}$, where $L$ is the length of the pendulum in meters and $T$ is the time in seconds it takes for the pendulum to complete one full swing cycle.
In this case, the length of the pendulum is $52.0 \textrm{ cm}$, which is equal to $0.52 \textrm{ m}$, and the time it takes to complete one full swing cycle is $136 \textrm{ s}$.
Plugging these values into the equation gives us $g = 9.8 \textrm{ m/s}^2$. Therefore, the magnitude of the gravitational acceleration on this planet is $9.8 \textrm{ m/s}^2$.
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Classify each measurement as a scaled or vector a 20 books on a shelf
Scalar is the measurement of a unit strictly in magnitude. Vector is a measurement that refers to both the magnitude of the unit and the direction of the movement the unit has taken.
Classify each measurement as a scaled or vector a 20 books on a shelf?
a-scalar
b-vectot
c-scalar
d-vector
e-vector
f-scalar
g-scalar
h-scalar
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The fastest server in women's tennis is sabine lisicki, who recorded a serve of 131 mi/h (211 km/h ) in 2014. Suppose that the acceleration of the ball was constant during the contact with the racket.
The acceleration of the ball is - 25764.47 m/s.
What is velocity?
The direction of a body or object's movement is defined by its velocity. In its basic form, speed is a scalar quantity. In essence, velocity is a vector quantity. It is the speed at which distance changes. It is the displacement change rate.
Given that sabine lisicki recorded a serve of 131 mi/h (211 km/h ) in 2014.
Now convert the unit 211 km/h into m/s
211 km/h
= 211km/ 1 h
= (211×1000)m/ 3600s
= 1055/12 m/s
The initial velocity of the ball is 1055/12 m/s. The final velocity of the ball is 0 m/s. The ball covers 0.15 m.
The formula of motion is v² - u² = 2as
0² - (1055/12)² = 2 × a × 0.15
0.30 a = - (1055/12)²
a = -1113025/(144 × 0.30)
a = -25764m/s
The negative sign indicates that it is deceleration.
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an object moves in one dimension, according to the position versus time graph. express your answers in m/s.
Calculate the slope of the graph at a particular moment in time to determine the velocity of an item moving in one dimension from its location against time graph.
The slope reflects the rate of change of the object's location and consequently its velocity. If the object's location is shown on the y-axis and time is drawn on the x-axis, the velocity may be determined as the position's derivative with respect to time.For example, if the object's location is provided by a mathematical function p(t), its velocity at each moment t may be determined as follows: v(t) = dp(t)/dt The velocity units would be the location units divided by the velocity units. the units of time, which in this case is meters per second (m/s).
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a car is moving along a straight line with an initial velocity of 8.33 . its acceleration is . determine the stopping distance.
The stopping distance is 8.33.
Let's use the equation s = v0t + 1/2at^2 to solve for the stopping distance.
s = 8.33t + 0.5(0)(t^2)
s = 8.33t
Since the acceleration is 0, the stopping distance is equal to the total distance the car traveled while its velocity was 8.33.
What is distance?
Distance is the amount of space between two points. It can be measured in various units such as miles, kilometers, feet, and meters. Distance can also be used to describe the length of time or amount of effort it takes to reach a certain point. Distance can be used in reference to physical space or to abstract concepts.
Therefore, The stopping distance is 8.33.
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find the electric field at x = 5.00 cm in figure 18.52(a), given that q =1.57 µc.
The electric field at x=5.00 cm in Figure 18.52(a) can be found using the formula for the electric field due to a point charge: 5.62 x 10⁵ N/C
E = k × q / x²,
where k is the Coulomb constant, q is the charge, and x is the distance from the charge. Substituting the given values, we get: E = (8.99 x 10⁹N m²/C²) ×(1.57 x 10⁻⁶ C) / (0.05 m)² = 5.62 x 10⁵ N/C
When charge is present in any form, a point in space has an electric field that is connected to it. The value of E, often known as the electric field strength, electric field intensity, or just the electric field, expresses the strength and direction of the electric field. Without any precise information of what generated the field, simply knowing the value of the electric field at a certain location is sufficient to predict what would happen to electric charges nearby.
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Brandy has built a computer model of a weather system. She has included information about bodies of water, the sun, and the atmosphere. In her model, brandy doubles the size of an inland sea. How will this likely affect temperatures in areas along the sea's coast?.
Increasing the size of a sea in a computer model of a weather system is likely to affect temperatures along the coast of that sea. In general, larger bodies of water can have a moderating effect on temperatures, leading to more stable and milder temperatures compared to areas further away from the water. This happens because water has a higher specific heat capacity than land, which means it takes longer to heat up and cool down. As a result, coastal areas near a large sea may experience less extreme temperature fluctuations and a more moderate overall climate compared to areas further inland.
You observe a ball that moves (33.6 +0.2) cm in (11.49 +0.02) s. What is the observed speed of the ball (best estimate and most probable uncertainty)? (speed = distance/time) A. (2.92 +0.01) cm/s B. (1.62 +0.01) cm/s C. (2.92 +0.02) cm/s D. (1.619 +0.008) cm/s E. (1.739 +0.005) cm/s.
The observed speed of the ball is (2.92 ± 0.02) cm/s
Speed is calculated as follows: speed = distance/time.The most often used measure of speed in daily life is the kilometre per hour (km/h), or miles per hour in the US and the UK. The SI's unit of speed is the metre per second (m/s) (mph). We may determine the ball's actual speed using the values provided by computing the following:
[tex]distance = 33.6 ± 0.2 cm[/tex]
[tex]time = 11.49 ± 0.02 s[/tex]
speed = distance / time
[tex]=\frac{ (33.6 ± 0.2) cm } {(11.49 ± 0.02) s}[/tex]
We may calculate the speed calculation's uncertainty as follows by using the most likely uncertainty (0.5 times the smallest uncertainty):
distance uncertainty = 0.2 cm
uncertainty in time = 0.02 s
Speed uncertainty is equal to (distance uncertainty) / (time uncertainty) 0.5 * (smallest uncertainty)
[tex]=\frac{{ (0.2) }} {(11.49) }}{± 0.5 * (0.02)}[/tex]
[tex]=0.01744 ± 0.01 cm/s[/tex]
Therefore, the observed speed of the ball is (2.92 ± 0.02) cm/s.
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permeability is a measure of a material's ability to:
Permeability is a measure of a material's ability to: transmit the fluids.
What is meant by permeability?Measure of the ease of flow of a fluid through a porous solid is known as permeability. Rock may be extremely porous, but if pores are not connected, it will not have permeability.
Permeability is determined by applying head and determining depth of penetration or the amount of liquid or gas passing through sample.
Widely used are permeability μ = B0/H0 (B0 is the magnetic flux density B at the point P and H0 is the magnetic field H ) and differential permeability μd = dB/dH.
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on individual intelligence tests such as the stanford-binet and wechsler scales, an iq of 100 indicates that the test taker
According to a test taker's average test score is indicated by an IQ score of 100 on the Stanford-Binet and Wechsler intelligence test.
A common IQ test, like the Stanford Binet IQ test or the Wechsler Intelligence Scale, is used to gauge a person's level of intellectual functioning. 100 is the global average. Low IQ scores refer to those with scores below 70. Professionals assess the person's adaptable behaviour as well.
The average result for all test takers of the same age is 100.
a test that is given to each person individually to assess their level of intelligence by testing their ability to solve problems, develop concepts, reason, pay attention to detail, and do other intellectual tasks.
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Find the Parametric Equations for the Curve. The line passing through (2, 6) and (3, 9).
Parametric equations are commonly used in kinematics, where the trajectory of an object is represented by equations depending on time as the parameter.
What is Parametrics?The application, a single parameter is often labeled t; however, parameters can represent other physical quantities (such as geometric variables) or can be selected arbitrarily for convenience.
Parameterizations are non-unique; more than one set of parametric equations can specify the same curve.
The same curve can be specified by more than one set of parametric equations because parameterizations are not unique.
Therefore, Parametric equations are commonly used in kinematics, where the trajectory of an object is represented by equations depending on time as the parameter.
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your dog is running around the grass in your back yard. he undergoes successive displacements 3.62 m south, 8.10 m northeast, and 14.6 m west. what is the resultant displacement? (take the x direction to be east.)
Answer:
The displacement can be represented as vectors in the x and y direction.
The displacement 3.62 m south can be represented as a vector of magnitude 3.62 m and direction -90°.
The displacement 8.10 m northeast can be represented as a vector of magnitude 8.10 m and direction 45°.
The displacement 14.6 m west can be represented as a vector of magnitude 14.6 m and direction -180°.
We can find the x and y components of each displacement vector, and then add those components to find the x and y components of the resultant displacement.
x component of the first displacement: 3.62 * cos(-90°) = 0 m
y component of the first displacement: 3.62 * sin(-90°) = -3.62 m
x component of the second displacement: 8.10 * cos(45°) = 5.65 m
y component of the second displacement: 8.10 * sin(45°) = 5.65 m
x component of the third displacement: 14.6 * cos(-180°) = -14.6 m
y component of the third displacement: 14.6 * sin(-180°) = 0 m
The x and y components of the resultant displacement are the sum of the x and y components of each individual displacement:
x component of the resultant displacement: 0 + 5.65 - 14.6 = -8.95 m
y component of the resultant displacement: -3.62 + 5.65 + 0 = 2.03 m
We can use the Pythagorean theorem to find the magnitude and direction of the resultant displacement:
resultant displacement = √(x^2 + y^2) = √(-8.95^2 + 2.03^2) = 9.06 m
direction = tan^-1(y/x) = tan^-1(2.03/-8.95) = 125.3°
So, the resultant displacement is 9.06 m at an angle of 125.3° with respect to the x-axis (east).
Explanation:
What is an experimental factor?
A study that uses two sets of variables and a scientific methodology is called experimental research. You use the first set as a reference point to calculate the differences between the second set. For instance, quantitative research techniques involve experimentation. You can specify and set your own experimental parameters. The highest temperature to which a solution can be heated, for instance. Although classification factors cannot be defined or set, they can be recognized, and your samples can be chosen in accordance with them. such as a person's gender or age. True experiments must include manipulation, control, random assignment, and random selection. The most important aspects are the manipulation and control of these elements. The Experimental Psychology Method by Using an experimental strategy, one variable is changed to see if it has an impact on another. In order to test a hypothesis, this strategy employs controlled research methods and random subject selection. T Therefore, any variable in a research project that is actually kept constant is referred to be a control variable. Despite not being a study-relevant variable, it is controlled anyway because it might have an impact on the results. 01-Mar-2021
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An experimental factor (also known as an independent variable) is a variable that is manipulated by the experimenter in order to observe its effect on the outcome of the experiment.
What is experimental factor?Experimental factors are variables that are controlled and manipulated by a researcher during an experiment. These factors can be either independent variables, which are the conditions the researcher changes, or dependent variables, which are the behaviors or outcomes that are observed and measured as a result of changing the independent variables. Experimental factors are important in determining the results of an experiment, and it is important for researchers to have an understanding of the potential effects of different combinations of factors.
It is the variable that the researcher changes or controls in order to measure the effect it has on the dependent variable, which is the variable being measured.
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what is the acceleration with which a 50 kg person can slide down a rope without the rope breaking, if the maximum tension the rope can withstand as the person slides down is 400 newtons?
The acceleration with which a 50 kg person can slide down a rope without the rope breaking if the maximum tension the rope can withstand as the person slides down is 400 N is 2m/s².
The maximum tension that the rope can withstand, is T= 400N. The mass of the person,m= 50kg. So the upward force on the rope is 400N. And the downward force is 50g N and an acceleration also acts downwards as the person climbs down the rope. So, the net force downwards is 50(g+a). Now the acceleration of the person which the rope can withstand is, a=( 50g-400)/50 = (50×10 -400)/50= (500-400)/50 =100/50=2 m/s². So, the acceleration with which a 50 kg person can slide down a rope without the rope breaking is 2m/s².
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a spring gun is compressed 15 cm to launch a 200 g ball on a inclined, frictionless surface. the ball had a speed of 2.0 m/s before the contact with the spring. find the spring constant of the gun
The spring constant of the gun 80 N/m.
The formula for finding the spring constant is
k=(2mv^2)/x
where m is the mass of the ball, v is the speed of the ball, and x is the distance the spring is compressed.
In this case, m=200 g, v=2.0 m/s, and x=15 cm.
Plugging these values into the formula, we get
k=(2*(200g)*(2.0m/s)^2)/(15 cm)
k=(2*0.2 kg*(4 m^2/s^2))/(0.15 m)
k=80 N/m
What is mass?
Mass is an amount of matter or energy that an object contains. It is measured in kilograms, grams, or pounds. Mass is different from weight, which is a measure of the force an object exerts on the environment due to gravity.
Therefore, The spring constant of the gun 80 N/m.
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When a positively charged particle enters into a uniform magnetic field with uniform velocity, its trajectory can be
(i) A straight line
(ii) A circle
(iii) A helix
A(i) only
B(i) or (ii)
C(i) or (iii)
DAny one of (i), (ii) and (iii)
The correct option D .Any one of (i), (ii) and (iii): Any of them might be the trajectory of a positively charged particle that enters a uniform magnetic field at uniform velocity.
Explain the path of positively charged particle in magnetic field?We are aware that: F=q(vB) describes the magnetic force acting on such a moving charge in such a magnetic field.
Where q represents the particle's charge.V represents the particle's speed.The magnetic field is B.The magnetic field's strength, velocity, and direction all affect the particle's course. Given the direction of all these values, there are three possible scenarios.
Case I: Equation holds true when the particle travels in the magnetic field's direction.
(1) changes to F=0.
As a result, the particle travels along the into because in a straight line.
Case ii. The force develops perpendicular towards the direction of magnetic field when the particle travels perpendicular to it.
As a result, the particle's route is circular.
Case iii) The parallel component of the velocity direction tends to drive the particle all along direction of the magnetic field when the velocity direction has both parallel as well as perpendicular components to it. The particle is moved in a circular motion by the perpendicular component.
As a result, the particle's route is helix-shaped.
Consequently, a positively charged particle's trajectory can be a straight line, a circle, or a helix when it enters a uniform magnetic field having uniform velocity.
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what is the jogger's velocity at t = 35 s ?
The jogger's velocity at t = 35 s is [tex]v=-5m/s[/tex]
For [tex]t=35s[/tex]
consider the following:[tex](t_{1} ,x_{1})=(30,50)[/tex] and [tex](t_{2} ,x_{2})=(40,0)[/tex]
Speed is the rate at which something is moving, usually expressed in terms of distance travelled per unit of time. The average jogger typically runs at a velocity of 5 to 8 miles per hour. This is equivalent to 8 to 12 kilometers per hour.Velocity is the rate and direction of something's movement. It is the speed of an object in a particular direction.The speed of the jogger at that particular position is determined by the graph's slope.
[tex]v=\frac{x_{2}-x_{1}}{t_{2}-t_{1}}\\\\[/tex]
[tex]=\frac{0-50}{40-30}\\\\=-5m/s[/tex]
Consequently, the jogger's speed at time [tex]t=35s[/tex] the velocity is [tex]v=-5m/s[/tex]
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a. How does lightning form?
b. Why does lightning form?
c. How is lightning released?
d. What type of electricity is lightning?
e. What is Nature's light show?
f. What is static electricity?
Lightning is an electrostatic discharge which occurs naturally within the storm. The electrostatic discharge is due to electrically charged regions in the storm.
What is Lightning?Lightning can be defined as the naturally occurring electrostatic discharge during which two electrically charged regions positive and negative, both in the same atmosphere or with one on the ground, and other at a certain distance which temporarily neutralize each other, causing the instantaneous release of an average of about one gigajoule of energy from the effect.
The electric field within the storm is not the only field which develops. Below the negatively charged storm base in this region, positive charge begins to pool within the surface of the earth. This positive charge will then shadow the storm whichever direction it goes, and is responsible for the cloud-to-ground lightning.
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A roller coaster starts from rest at its highest point and then descends on its (frictionless) track. Its speed is 40 m/s when it reaches ground level.
Its speed when its height was half that of its starting point is 28.28 m/s
v = 36 m/s is the roller coaster's final speed.
applying the fundamental motion equation;
V² = U² + 2gh
where;
V is the roller coaster's final speed.
U is the roller coaster's starting speed, which is 0
h is the height achieved at a specific speed.
40² = 0 + (2 x 9.8)h
1600 = 19.6 h
h = 1296/19.6
h = 81.63 m
h₂ = 1/2 h when its height was half that of its beginning point.
h₂ = ¹/₂(81.63 m) = 40.81 m
At h = 40.81 m, V = ?
V² = U² + 2gh
V² = 0 + 2 x 9.8 x 40.81
V² = 800
V = √800
V = 28.28 m/s
As a result, it moved at a speed of 28.28 m/s when its height was half that of its starting point.
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what happens if you disconnect a circuit from its positive terminal?
If you disconnect a circuit from its positive terminal, the electrons stop flowing, and the current stops. The power source would no longer provide a flow of electrons.
The flow of electrons and current ceases if the positive terminal of a circuit is cut off. The flow of electrons would stop coming from the power source. It is safer for you if the negative is eliminated first, which is why they advise doing so. In all contemporary automobiles, the negative cable is fastened to the chassis. Therefore, if you use a wrench to loosen the negative post and the wrench impacts the chassis, nothing happens.
After removing the negative cable, you can proceed with the positive without any concerns. Because the battery is already disconnected, nothing happens if the wrench strikes the chassis once more.
A large spark, and possibly more, will occur if you remove the positive first and then touch the chassis with your wrench. Since there is currently no fuse in the system, a wrench handle can draw a significant amount of electricity. The sparks could be hot enough to throw molten metal fragments, possibly even weld the wrench to the automobile, and cause a dead short to kill the battery. As a result, doing the negative first is significantly safer. However, if you took the positive first without the wrench striking and there were no sparks, everything was OK.
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An electron's position is given by r with arrow = 2.00ti hat − 7.00t2j + 5.00k, with t in seconds and r with arrow in meters. (a) In unit-vector notation, what is the electron's velocity v with arrow(t)? (Use the following as necessary: t.) v with arrow(t) = m/s (b) What is v with arrow in unit-vector notation at t = 9.00 s? v with arrow(t = 9.00) = m/s (c) What is the magnitude of v with arrow at t = 9.00 s? m/s (d) What angle does v with arrow make with the positive direction of the x axis at t = 9.00 s? ° (from the +x axis)
The angle v with arrow makes with the positive direction of the x axis at t = 9.00 s is -86.23° degrees from the +x axis.
What is the electron's speed?
One of the subatomic particles with mass is the electron. The kinetic energy of any moving object is equal to 1 / 2 mv ², where m is the object's mass and v is its velocity. Electron speed V = 1 / 2 mqv ² is an electromagnetic equation.
Evaluating :a) v with arrow(t) = dr with arrow/dt
= 2.00i + (-14.00t)j + 0k
b) v with arrow (t = 9.00) = 2.00i + (-14.00 9.00)j + 0k
= 2.00i - 126.00j
c) the magnitude of v with arrow (t = 9.00)
= √(2.002 + (-126.00)2)
= 126.00
d) tan(theta) = vy/vx
= -126.00/2.00
= -63.00,
θ = atan(-63.00)
= -86.23° degrees.
So, the angle v with arrow makes with the positive direction of the x axis at
t = 9.00 s is -86.23 degrees from the +x axis.
In an electric field, what happens to an electron?Because of its negative charge, an electron will move in the opposite direction of the electric field. As a result, it will move to the left. The electron might also be thought of as being drawn to the positively charged plate.
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Three identical metallic conducting spheres carry the following charges: q1 = +7.8 μC, q2 = −1.4 μC, and q3 = −4.0 μC. The spheres that carry the charges q1 and q2 are brought into contact. Then they are separated. After that, one of those two spheres is brought into contact with the third sphere that carries the charge q3. What is the final charge on the third sphere?
0.8 μC is the final charge on the third sphere
Define electric charge
The physical quality of matter—its electric charge—is what causes it to feel a force when exposed to an electromagnetic field. You can have a positive or negative electric charge (commonly carried by protons and electrons respectively, by convention). Unlike charges attract one another while like charges repel one another. Neutral refers to an object that carries no net charge.
Since the 3 objects are similar and conductors, charge can move freely among them. Since the four objects are identical, the overall charge disperses among them as equally as possible.
q1, q2, q3 are same
Q/3 will be value of q
Q is 7.8-1.4-4.0 i.e. 2.4 μC
q will be 2.4/3 i.e. 0.8 μC
The charge q is positive so we have defecit of electrons
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find the rotation speed for a person at latitude 72 ∘n . express your answer in kilometers per hour using three significant figures.
Rotational speed refers to the number of rotations an object completes in a given time period. The rotation speed for a person at latitude 72°N is approximately 522 km/hour.
Explanation:
Given,
Latitude = 72°N
The rotation speed can be calculated using the following formula:
V = ω × R
where:
V is the rotation speed,
ω is the angular velocity,
R is the radius of the Earth at the given latitude.
The angular velocity of the Earth can be approximated as the rotation rate of the Earth, which is 360 degrees per 24 hours or 2π radians per 24 hours.
ω = (2π radians) / (24 hours × 3600 seconds/hour) ≈ 7.292 × 10⁻⁵ radians/second
The radius of the Earth at latitude 72°N can be approximated as the product of the equatorial radius (6,378 km) and the cosine of the latitude (cos(72°)).
R = (6,378 km) × cos(72°)
V = (7.292 × 10⁻⁵ radians/second) × (6,378 km) × cos(72°)
V = (7.292 × 10⁻⁵ radians/second) × (6,378 km) × 0.309
V = 0.145 km/second
To convert the rotation speed from km/second to km/hour, multiply by 3600 (the number of seconds in an hour):
V = 0.145 km/second × 3600 seconds/hour
V = 522 km/hour
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a box is knocked off a 1.4 m high table and then strikes the floor 2.7 m from the edge of the table. assume that wind resistance is negligible. the acceleration of gravity is 9.81 m/s 2 . what was the speed of the box when it slid off the table?
The speed of the box when it slid off the table is 9.47 m/s².
What is Projectile Motion?
A particle that is flung obliquely toward the surface of the earth travels along a curved route with constant acceleration that is pointed in the direction of the planet's center. Such a particle's motion and trajectory are both referred to as projectile motion.
The only force acting on a particle when it is launched into the air at some speed is the acceleration due to gravity (g). The downward motion of this acceleration is vertical. The horizontal direction does not experience any acceleration, hence the particle's horizontal velocity stays constant.
It is given that a box is knocked off a 1.4 m high table and then strikes the floor 2.7 m from the edge of the table.
[tex]\implies \triangle x_{y}=-1.4m[/tex] and [tex]\triangle x_{x}=2.7m[/tex]
Here, the acceleration of gravity, g = a = -9.81 m/s²
Under projectile motion, the vertical motion equations corresponding to the given problem is:
[tex]\triangle x_{y}=\frac{1}{2}at^{2}+V_{iy}t[/tex]
Since, [tex]V_{iy}=0[/tex], we get t as
[tex]t=\sqrt{\frac{2 \triangle x_{y} }{a} }[/tex]
Substituting the given values, we get
[tex]t=\sqrt{\frac{2(-1.4)}{-9.81} } \\\implies t=\sqrt{\frac{-2.8}{-9.81} }\\\implies t=0.285s[/tex]
Also, we know that, [tex]\triangle x_{x}=V_{ix} \times t[/tex]
Now, calculating the speed, we get
[tex]V_{ix}=\frac{\triangle x_{x} }{t} \\\implies V_{ix} =\frac{2.7}{0.285} \\[/tex]
[tex]\implies V_{ix}=9.47 m/s^{2}[/tex]
Hence, the speed of the box when it slid off the table is 9.47 m/s².
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What is 8 degree celsius in F?
The equivalent of 8 CELSIUS in F is 46.4 F. In 8 C, the majority of individuals dress warmly and wore jackets. You are one of those folks who can endure the cold without the need of a jacket. Freezing is 8 C.
What is in CELSIUS in reality?MetaPlus®, a patented mixture found in CELSIUS, activates thermogenesis to quicken metabolism and raise caloric burn. Your metabolic rate is increased by Green Tea, EGCG, Tadalafil, Guarana Seed Extract, Taurine, and Ginger Root Extract in combination with other nutrients in CELSIUS.
What does CELSIUS aim to achieve?The Celsius scale is often used to measure the temperature The Celsius scale was developed by Swedish astronomer Anders Celsius. The water temperature (°C) on a thermometer is the melting point liquid clear water at standard pressure and sea level.
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Two of the interior angles of a triangle are equal. The third interior angle is 68.0 degrees. What are the other two interior angles?
theta=_______ degrees
The other two interior angles are calculated to be both 56.0 degrees.
What are interior angles?The inner of the two angles formed where two sides of a polygon come together are called interior angles.
Given if two of the interior angles of a triangle are equal, then the third interior angle must be different. Let's call the equal angles "x". The sum of all interior angles of a triangle is 180 degrees, so:
x + x + 68.0 = 180
2x + 68.0 = 180
Subtracting 68.0 from both sides,
2x = 180 - 68.0 = 112.0
x = 56.0
So, the other two interior angles are both 56.0 degrees.
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What will be the acceleration of a skydiver when air resistance is half the weight of the skydiver.
4.9m/s^2 will be the acceleration of a skydiver when air resistance is half the weight of the skydiver
What is acceleration?
The rate at which velocity changes is called acceleration. Acceleration typically indicates a change in speed, but not necessarily. An item that follows a circular course while maintaining a constant speed is still moving forward because the direction of its motion is shifting.
Acceleration occurs in the direction of the velocity change, which is the same direction that the circular path's center of rotation points. The centripetal acceleration typically has a negative sign in vector form. This is due to the centripetal acceleration, which is along the radius vector pointing toward the center of the circular motion, being in the opposite direction to that of the radius vector.
Let m be the mass of the skydiver.
The acceleration due to gravity is g = 9.8m/s^2
W = mg
W -Fr = ma
Fr = W/2
W/2 = ma
mg/2 = ma
a = g/2
a = 9.8/2 = 4.9m/s^2
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