The speed of the objects after collision, given that they stocked together is 5.4 m/s
How do I determine the speed of the objects after collision?We'll beging by listing out the given parameters from the question. This is given below:
Mass of object moving east (m₁) = 2.0 KgSpeed of object moving east (u₁) = 4.0 m/sMass of object moving west (m₂) = 5.0 KgSpeed of object moving west (u₂) = 6.0 m/sSpeed after collision (v) =?The speed after the collision can be obtained as shown below:
Momentum before = momentum after
m₁u₁ + m₂u₂ = v(m₁ + m₂)
(2 × 4) + (5 × 6) = v(2 + 5)
8 + 30 = v × 7
38 = v × 7
Divide both sides by 7
v = 38 / 7
v = 5.4 m/s
Thus, the speed after collision is 5.4 m/s
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If a train going 60 m/s hits the brakes and it
takes the train 1 minute and 40 seconds to
come to a complete stop, what is the train's
acceleration?
Answer with Explanation:
We can use the formula for acceleration to find the train's acceleration:
acceleration = (final velocity - initial velocity) / time
In this case, the initial velocity of the train is 60 m/s (since that's how fast it was going before it hit the brakes), the final velocity is 0 m/s (since the train comes to a complete stop), and the time it takes for the train to stop is 1 minute and 40 seconds, or 100 seconds.
So, plugging in the values we have:
acceleration = (0 m/s - 60 m/s) / 100 s
acceleration = -60 m/s / 100 s
acceleration = -0.6 m/s^2
Note that the negative sign indicates that the train is decelerating (slowing down), as opposed to accelerating (speeding up).
Problem 6
Frank, a San Francisco hot dog vender, has fallen asleep on the job. When an earthquake strikes, his 300-kg hot-dog
cart rolls down Nob Hill which is 50 m high.
A. What is the PE of the cart at the top of Nob hill?
B. What is the Kinetic Energy of the cart at the bottom of the hill?
C. What is the speed of the cart at the bottom of the hill?
an intersection that has signals or signs to assign the right of way is called
a. a registered intersection.
b. an unregistered intersection.
c. a controlled intersection.
d. an uncontrolled intersection.
A controlled intersection is one that contains signals or signs to designate the right of way.
Describe signal.An electrostatic or electric current known as a signal is used to transfer information from one device or networks to another. Although it can sometimes take other dimensions, such as current, a signal in electronics frequently consists of a time-varying temperature that is also a electromagnet carrying information.
What characteristics do signals have?They can be deterministic or random, deterministic or agnostic, continuous or continuous time, both analog and digital, periodic or nonstationary, finite or infinite. They can also be separated into groups based on the causality and symmetry of those groups. An optimum impulse signal is one that is 0 everywhere else but infinitely high at the origin.
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two cyclists, 144 mi apart, start riding towards each other at the same time. one cycles twice as fast as the other. if they meet 3 hr later, at what average speed is each cyclist traveling?
The required speed of the cyclist 1 is 16 mile per hour and the speed of the cyclist 1 is calculated to be 32 mile per hour.
Distance between cyclists is given as 144 miles.
If v is the speed of one bicycle, the speed of the other cyclist is twice as fast.
Speed of second cyclist = 2 × v
Time taken by them to meet each other is 3 hr
The relative velocity between them as they approach one another is given by
Relative speed is equal to v + 2v = 3v.
We have,
Distance = Time × Velocity
144 = 3 × 3 v
9v = 144
v = 16 mile per hour
Thus, speed of cyclist 1 is v = 16 mile per hour, speed of cyclist 2 is 2v = 32 mile per hour.
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an excimer laser produces radiation at 157 nm, and optics with a numerical aperture of 1.4 is available. what is the smallest size of feature you could make in a resist? how might smaller final features be made in the underlying silicon with the same optics?
A 157 nm exim laser emits light, and 1.4 numerical aperture optics are provided. What would be the smallest feature you could create?
Radiation definition?Electromagnetic waves or particles are emitted as energy. Radium, cosmic rays from space, medical x-rays, or energy released by a radioactive unstable version of a chemical substance that emits radiation because it begins to break down and becomes more unstable are a few common sources of radiation.
hazardous external risk. "Beta burns" can result from beta particles partially penetrating skin. Alpha rays cannot pass through healthy skin. A human can be penetrated by gamma and x-rays, which harm the cells in the path.
Describe cosmic rays?They are energetic particles that travel through space at velocities close .
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How does the ocean floor preserve evidence of past magnetic reversals.
(A) The ocean floor is uniformly old, preserving the Earth's 4. 6 billion history.
(B) Isotopic analysis of ocean core sediments help determine sea floor age and this can be used to infer past magnetism.
(C) Magnetic particles in basalt orient with the magnetic field in force at the Curie Point.
(D) Mantle hot spots are always oriented to the magnetic field
(B) and (C) both describe methods that are used to study past magnetic reversals on the ocean floor.
Isotopic analysis of ocean core sediments can help determine the age of the sea floor and reveal information about past magnetic fields.
Magnetic particles in basalt can also be used as a record of past magnetic fields, as they orient with the magnetic field at the time of solidification.
The ocean floor is not uniformly old, but rather new sea floor is constantly being formed at mid-ocean ridges and spreading away from these locations, preserving a record of Earth's magnetic history.
Mantle hot spots are not always oriented to the magnetic field, but rather are thought to be associated with the movement of large mantle plumes that are not directly controlled by the magnetic field.
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can someone tell me what herman branson was recognized or awarded for their work
Answer:
The Pauling-Branson Award recognizes the contributions of Herman Russell Branson, (1914-1995), one of the first African American physicists to make crystallography the focus of his research.
a man weighs 600 n while on the surface of earth. if he is transported to the planet mythos, which has the same mass as earth but a radius that is five times larger than earth's, his weight would be group of answer choices
Human body weight is equal to 600 N. Gravitational acceleration on earth: g = 10 m s 2 Man's weight on Earth is 600 kg. 10 sq . ft = 60 kg Since mass is consistent everywhere, we are aware of this.
What does gravity mean?
The attraction of items by the earth is known as gravitation. The earth's gravity causes objects that are hurled upward to reach a specific height before falling to the ground. 2. Space objects may be drawn to one another by gravity. the attraction force between the sun and the other planets.
Gravitational interaction: What is it?
The weakest of the four basic forces of nature, attraction between physical things having mass or energy is a natural phenomena. also known as gravity. the process or act of moving while being drawn to something. check out gravitational interaction. a movement in the direction of a source of desire: the middle classes' attraction.
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what is the fastest speed at which you can go around the curve without the book sliding? the coefficient of static friction between the book and the seat is 0.40.
The highest G force this may produce is 0.80e n = 0.8 (9.8 m/sec2) = 7.84 m/sec2 since the friction factor is 0.80. The issue then claims that stopping takes three seconds.
Is g-force a basic force?
Despite its name, g-force is not a fundamental force; rather, it is a specific kind of acceleration that may be detected by an accelerometer. Any g-force can be thought of as "weight per unit mass" because g-force amplitudes indirectly produce weight
Is the g-force a scalar or a vector?
Despite the fact that acceleration is indeed a vector variable, g-force accelerations (abbreviated "g-forces") are frequently written as a scalar, with good g-forces pointing below (signifying upward acceleration) and minus g-forces pointing upward. A g-force is indeed a vector of velocity as a result.
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A semicircle of radius a is in the first and second quadrants, with the center of curvature at the origin. Positive charge +Q is distributed uniformly around the left half of the semicircle, and negative charge −Q is distributed uniformly around the right half of the semicircle in the following figure.(Figure 1) Figure1 of 1A semicircle of radius a is in the first and second quadrants of the xy plane, with the center of curvature at the origin. Charge +Q is distributed uniformly around the left half of the semicircle and charge -Q is distributed uniformly around the right half of the semicircle. A semicircle of radius a is in the first and second quadrants of the xy plane, with the center of curvature at the origin. Charge +Q is distributed uniformly around the left half of the semicircle and charge -Q is distributed uniformly around the right half of the semicircle. Part A What is the magnitude of the net electric field at the origin produced by this distribution of charge? Express your answer in terms of the variables Q, a, and constant k.
The magnitude of the net electric field at the origin produced by this distribution of charge is zero.
The magnitude of the net electric field at the origin produced by the charge distribution described in the problem can be calculated using Coulomb's law. According to Coulomb's law, the electric field created by a point charge Q at a distance r from the charge is proportional to the magnitude of the charge and inversely proportional to the square of the distance.
In this problem, the net electric field at the origin is the vector sum of the electric fields created by each half of the semicircle. The electric field created by the left half of the semicircle with charge +Q is in the positive x-direction and the electric field created by the right half of the semicircle with charge -Q is in the negative x-direction. These two fields cancel each other out at the origin, resulting in a net electric field of zero.
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if you hold a spoon in front of your face so that you see your image in the bowl of the spoon, your image is upright when you hold the spoon close to your face, but inverted when you hold the spoon far away. explain why this change occurs.
The change in the orientation of the image in the spoon happens due to the change in the angle of incidence and the reflection of light.
When we hold the spoon close to our face, the light rays from our face strikes the spoon at a smaller angle of incidence and gets reflected back to our eyes at a smaller angle,
So, the image you see in the spoon is upright.
When we hold spoon far away from our face, the light rays from our face strikes the spoon at a larger angle of incidence and gets reflected back to your eyes at a larger angle,
So, the image you see in the spoon is inverted.
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used to measure the center of a set of values. good for summarizing values that are generally very similar to one another. tool name from?
To determine the middle of a group of variables, use the mean. It works well for averaging data that are often quite comparable to one another.
The average is more frequently used to refer to mean. By summing up each value and dividing by the total number of values, it is computed. It is a useful method for condensing the core values, which are frequently extremely similar to one another.
Since it takes the average of all values in the data set, the mean is the most often used measure of central tendency. The median performs better than the mean for data from skewed distributions since it is unaffected by high values.
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--The complete question is, _________ is used to measure the center of a set of values. It is good for summarizing values that are generally pretty similar to each other.--
a stunt driver wants to make his car jump over 10 cars parked side by side below a horizontal ramp. the vertical height of the ramp is 2.0 m, and the horizontal distance he must clear is 24 m. with what minimum speed must he drive off the ramp?
The stunt driver must drive off the ramp with a minimum speed of 53.93 m/s to successfully clear the 10 parked cars.
The trick driver needs to get an upward level free from 2.0 m and a flat distance of 24 m. To find the base speed required, we can involve the kinematic condition for vertical movement affected by gravity:
vf^2 = vi^2 + 2 * g * Δy
where vf is the last speed (extent of speed), vi is the underlying speed (size of speed), g is the speed increase because of gravity (9.8 m/s^2), and Δy is the adjustment of vertical level. We need the underlying speed (vi) so we can rework the condition:
vi = √(vf^2 - 2 * g * Δy)
For this situation, Δy = 2.0 m, g = 9.8 m/s^2, and vf = 0 (last speed is 0 in light of the fact that the vehicle lands on the ground).
vi = √(0 - 2 * 9.8 * 2.0) = √(- 39.2) = 6.27 m/s
This is the base vertical speed the vehicle should need to clear the 10 left vehicles. To find the base speed, we should likewise consider the even speed expected to cover the distance of 24 m.
v = √(vi^2 + vh^2)
where vh is the even speed. Since the even distance is 24 m and the hour of flight can be determined utilizing the upward movement condition, we can utilize the condition:
vh = d/t
where d is the flat distance (24 m) and t is the hour of flight.
t = √((2 * Δy)/g) = √((2 * 2.0)/9.8) = 0.447 s
vh = 24 m/0.447 s = 53.67 m/s
At long last, the base speed can be found as:
v = √(vi^2 + vh^2) = √(6.27^2 + 53.67^2) = 53.93 m/s (adjusted to 2 critical digits)
In this way, the trick driver should drive off the slope with a base speed of 53.93 m/s to clear the 10 left vehicles effectively.
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a magnetic disturbance on the sun's surface is called question 71 options: the electromagnetic spectrum. the solar wind. a magnetospheric cyclone. a sunspot. g
"A magnetic disturbance on the sun's surface is called sunspot." The correct option is D.
The Sun's gases are constantly moving, which stretch and twist the magnetic fields. This motion creates a lot of activity on the Sun's surface, known as solar activity.
Sunspots are areas of lower surface temperature linked with concentrated magnetic field flux and vigorous magnetic activity on the Sun's photosphere that are darker than the surrounding photosphere regions on the visible solar disc. They typically come in opposite magnetic polarity pairs.
A geomagnetic storm is a significant disruption of the magnetosphere that happens when energy from the solar wind is exchanged very effectively into the space environment around Earth.
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suppose the 50 turn coil in the figure below lies in the plane of the page and originally has an area of 0.260 m2. it is stretched to have no area in 0.100 s. what is the magnitude (in v) of the average value of the induced emf if the uniform magnetic field points into the page and has a strength of 1.35 t?
The average induced emf is when the magnetic field B increases from 0. 10T to 0. 35T in 2 milliseconds.
Where is the magnetic field?The S pole of the Earth's magnetic field, which is close to its geographic north pole (see Magnetic North Pole), and the N pole, which is close to its geographic south pole, roughly form a magnetic dipole.
What is magnetic field and its unit?A magnetic field is produced in the area surrounding a magnetic dipole or a moving charge. The SI unit of field intensity for magnetic fields is the Tesla (T). The region where a magnet's magnetic force may be felt is known as the magnetic field.
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from a height of 2 m , you hit a tennis ball perfectly horizontally at 20 m/s . at the same time, you drop a tennis ball from the same height. which one hits the ground first?
The ball that was dropped from a height of 2 meters will hit the ground first. This is because the ball that was dropped was not given any horizontal velocity, so it will fall straight down with an acceleration of 9.8 m/s2.
What is the velocity?Velocity is a vector quantity that describes the rate and direction of an object's motion. It is defined as the rate of change of an object's position, with respect to time. Velocity is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of bodies. Velocity is usually expressed in meters per second (m/s), but it can also be expressed in other units such as kilometers per hour (km/h).
The ball that was hit with a horizontal velocity of 20 m/s will travel horizontally for a certain amount of time before it begins to fall and accelerate downwards. As a result, the ball that was dropped will hit the ground first.
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the advantage of a resistor is a higher power rating. a. wire-wound b. metal glaze c. carbon film d. metal film
The wire wound resistor has the highest power rating. Option a is the correct answer.
Resistors are the most fundamental and commonly used of all the electronic components, to the point where they are almost taken for granted but they play a vital role within a circuit.
A wirewound resistor is an electrical passive device that limits or restricts current flow in a circuit. Wirewound resistors are constructed using a conductive wire. The conductive wire is then wound around a non-conductive core.
Wire-wound Resistor have metallic bodies for heatsink mounting, very high wattage ratings.
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a good diffraction grating has 2210 lines/cm. what is the distance between two lines in the grating? answer in units of cm.
The distance between two lines in the grating is 0.00045 cm.
What is diffraction grating?A diffraction grating is an optical element with a periodic structure used in optics that diffracts light into many beams that move in various directions. A type of structural coloring is the coloration that is emerging.
A good diffraction grating has 2210 lines/cm, that means,
The diffraction grating has 2210 lines in 1 cm.
Hence, the distance between two lines in the grating is = (1 ÷ 2210) cm
= 0.00045 cm.
Hence, the distance between two lines in the grating is 0.00045 cm.
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in the n-t coordinate system, the origin is located on the particle group of answer choices true false
True, in the n-t coordinate system, the origin is located on the particle .
What is the NT coordinate system ?
Coordinates in the normal (n) and tangential (t) planes are frequently employed when the motion's path is known. The origin of the n-t coordinate system is on the particle (the origin moves with the particle). The t-axis is positive and tangent to the particle's path (curve) during the time it is being studied.
The genesis point in the normal-tangential coordinate system is the particle itself. The n-direction is always 90 degrees counterclockwise from the t-direction, which is the direction in which motion is now taking place. Unit vectors in the t and n directions are represented by the u-t and u-n vectors, respectively.
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Help please!!! List five general things we get from natural resources?
Answer:
Paper, clothing, fuel, cans, and jewelry
Explanation:
Calculate: An object’s weight is determined by its mass (m) and the acceleration due to gravity (g) affecting that object: w = mg. On Earth, g = 9. 8 m/s2.
What are the masses (in kilograms) of the three objects on the Gizmo? (Note: 1 N = 1 kg × m/s2)
The masses (in kilograms) of the three objects on the Gizmo is 14N object=1.42 kg, 80N object = 8.16kg, 98N object = 10kg
In physics, is gravity always 9.8?Gravity always accelerates objects at a rate of 9,8 m/s2 as it draws them toward the ground. Unless air resistance favors one item over another, all objects of study to the same rate due to gravity, despite differences in mass. Any two masses, bodies, or particles can be attracted to one another by the force of gravity.
Generally
For a Gizmo Bearing Mass of defined as integers
Say
14N, 80N, 98N
Therefore
For 14N
ω = m×g
14 = m×9.8
m1 = 1.42 kg
For 80N
ω = m×g
80 = m×9.8
m2 = 8.16kg
For 98N
ω = m×g
98 = m × 9.8
m3 = 10Kg
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a baseball is thrown straight up at a speed of 30.0 m/s. how much time will elapse for the ball to return to the ground?
The time it takes for the ball to return to the ground is approximately 3.06 seconds.
What is the resistance?Resistance is the opposition to the flow of an electric current, or the opposition to any change. It is measured in ohms and is denoted by the symbol Ω.
When a baseball is thrown straight up, it follows a parabolic path under the influence of gravity. At the highest point of its trajectory, the baseball momentarily comes to rest before falling back down to the ground. To find the time it takes for the ball to return to the ground, we can use the kinematic equations of motion.
The first step is to determine the initial velocity and the final velocity of the ball at the highest point of its trajectory. At the highest point, the ball momentarily comes to rest, so its final velocity is zero. The initial velocity of the ball is 30.0 m/s (assuming that air resistance is negligible).
The kinematic equation that relates the initial velocity, final velocity, acceleration, and time is:
[tex]\mathrm{v_f = v_i + a \times t}[/tex]
where [tex]\mathrm{v_f}[/tex] is the final velocity, [tex]\mathrm{v_i}[/tex]is the initial velocity, a is the acceleration (due to gravity), and t is the time.
At the highest point of its trajectory, the ball reaches a height of
[tex]\mathrm{h =(v_i)^2 / (2 \times g) }[/tex]
where g is the acceleration due to gravity (9.81 m/s²).
This is the maximum height that the ball reaches, and it takes the ball the same amount of time to reach this height as it does to fall back down to the ground.
Using the initial velocity and acceleration due to gravity, we can calculate the maximum height reached by the ball:
[tex]\mathrm{h =(v_i)^2 / (2 \times g) }[/tex]
= (30.0 m/s)^2 / (2 * 9.81 m/s^2)
= 45.9 m
The time it takes for the ball to reach this height is given by the kinematic equation:
[tex]\mathrm{h = v_i \times t + (1/2) \times a \times t^2}[/tex]
Rearranging and solving for time, we get:
[tex]\mathrm{t = (v_f - v_i) / a = - v_i / a}[/tex]
where the negative sign indicates that we are looking for the time it takes for the ball to return to the ground, which is the time it takes to fall from the maximum height.
Substituting the values, we get:
t = - (30.0 m/s) / (-9.81 m/s²) = 3.06 s
Therefore, the time it takes for the ball to return to the ground is approximately 3.06 seconds.
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an object is traveling arouind a circle with a radius of 13 feet. if in 40 seconds a central angle of 1/7 radian is swept out, what are the linear and angular speeds of the object
One worth of distance is covered by the object. The radius times 2 pi is the circumference. 1 metre is the radius.
Describe a radius?The distance from a circle's centre to just about any place on its periphery is known as the radius. The radius of a circle is the distance measured from the centre to any point within the circle, according to another definition.
The area of a circle is the measurement of the area contained within the circle. Radius: The radius of the a circle is indeed the farthest from to a spot on the edge. The letter "r" or "R" stands in for it.
How do circles work?A closed this double figure is a circle.
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Students measure how much work it takes to lift an object two meters. They use an inclined plane that is 3 meters long, an inclined plane that is 4 meters long, and a compound pulley. Which statement is correct?
The inclined planes and the compound pulley can be used to measure the work required to lift the object two meters, but the results will vary depending on the length of the inclined plane.
What is the compound ?A compound is a substance composed of two or more elements that are chemically bonded together. Compounds can exist in either a solid, liquid, or gaseous state, and they are held together by either covalent, ionic, or metallic bonds. Examples of compounds include water (H2O), table salt (NaCl), and carbon dioxide (CO2). Compounds are important in everyday life, as they are the basis of all matter around us. Compounds are essential components of the environment and are necessary for life to exist. Compounds are used in a variety of fields, ranging from medicine and healthcare to engineering and industrial processes.
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you set a tuning fork into vibration at a frequency of 683 hz and then drop it off the roof of the physics building where the acceleration due to gravity is 9.80 m/s2. determine how far the tuning fork has fallen when waves of frequency 657 hz reach the release point? (take the speed of sound in air to be 343 m/s.)
1180.7 meters far the tuning fork has fallen when waves of frequency 657 Hz reach the release point while taking the speed of sound in air to be 343 m/s.
We can determine the distance fallen by the tuning fork by considering the time it takes for the waves of frequency 657 Hz to reach the release point. We know that the speed of sound in air is 343 m/s, so the distance traveled by the sound waves is equal to the speed of sound multiplied by the time elapsed.
Let "d" be the distance fallen by the tuning fork and "t" be the time elapsed. The frequency of the tuning fork changes due to its motion under the influence of gravity, and this change in frequency is related to the distance fallen:
= f
= [tex]683 Hz \sqrt{*[1 - (d * g) / (343 m/s)^2]}[/tex]
here, "g" is the acceleration due to gravity.
Setting this expression equal to 657 Hz and solving for "d":
= 657 Hz
= [tex]683 Hz * \sqrt{[1 - (d * g) / (343 m/s)^2]}[/tex]
Solving for "d":
= d
= [tex](343 m/s)^2 * [1 - (657 Hz / 683 Hz)^2] / g[/tex]
adding the values:-
= d
= [tex](343 m/s)^2 * [1 - (657 Hz / 683 Hz)^2] / 9.80 m/s^2[/tex]
= [tex](343 m/s)^2 * [1 - (657 Hz / 683 Hz)^2] / 9.80 m/s^2[/tex]
= [tex](119056 m^2/s^2) * [1 - (657 Hz / 683 Hz)^2] / 9.80 m/s^2[/tex]
= [tex](12149.6 m^2/s^2) * [1 - (657 Hz / 683 Hz)^2] / 9.80 m/s^2[/tex]
= [tex](12149.6 m^2/s^2) * (1 - (657 Hz / 683 Hz)^2) / 9.80 m/s^2[/tex]
= [tex]12149.6 * [1 - (657 Hz / 683 Hz)^2] / 9.80 m[/tex]
= [tex]12149.6 * [1 - (657 Hz ÷ 683 Hz)^2] / 9.80 m[/tex]
= [tex]12149.6 * (1 - 0.0384) / 9.80 m[/tex]
= [tex]12149.6 * 0.9616 / 9.80 m[/tex]
= 1180.7 m
Therefore, the tuning fork has fallen a distance of 1180.7 m when waves of frequency 657 Hz reach the release point.
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a) if a circuit operates at a frequency of 20 mhz, how large can it be without the designer being concerned with ac effects? b) if a circuit with pulses of approximately 250 ns can tolerate delays of 25 ns, how large can the circuit be in cm? (1 point)
The size of a circuit that operates at a frequency of 20 MHz is dependent on the design of the circuit and the components used in it.
If the designer is concerned with AC effects, then the size of the circuit components should be a fraction of the wavelength of the signal. The wavelength of a 20 MHz signal is 15 meters, so the circuit components should be much smaller than that. The size of the circuit would depend on the speed of the components used in the circuit. Generally, the speed of the components determines how quickly signals can travel. For example, if the components used in the circuit are capable of sending signals at speeds of 1 cm/ns, then the circuit can be at most 25 cm in size.
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correct application of fermats theorem to fluid dynamics
Fermat's theorem, also known as the principle of least time, states that the path taken by light or any other wave between two points is the path that minimizes the time taken. In fluid dynamics, this theorem can be applied to the flow of fluids in pipes or channels.
The basic idea is that the fluid will take the path that minimizes the time it takes for it to travel from one point to another. In other words, the fluid will follow the path of least resistance, where resistance is determined by the fluid's velocity and the diameter of the pipe or channel.
For example, in a fluid flow system with multiple branches or turns, the fluid will tend to follow the path with the smallest diameter or the least amount of resistance, as this will be the quickest path for the fluid to take.
This can be important in designing fluid systems, as it can affect the flow rate, pressure, and energy consumption of the system.
In summary, the correct application of Fermat's theorem to fluid dynamics involves considering the time it takes for a fluid to travel from one point to another and selecting the path that minimizes that time. This can help in optimizing fluid flow systems and improving their efficiency.
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A hot-air balloon is ascending at the rate of 12 m/s and is 65 m above the ground when a package is dropped over the side. (a) How long does the package take to reach the ground? (b) With what speed does it hit the ground?
a) The package takes 2.45 seconds to reach the ground.
b) It hits the ground with a velocity of -24.1 m/s.
To answer this problem, we'll use the equation of motion for a freely falling object:
[tex]d = v_{0}t + 0.5at^{2}[/tex], where d is the distance fallen, [tex]v_{0}[/tex] is the initial velocity (0 m/s in this case), a is the acceleration due to gravity (-9.8 m/s²), and t is the time elapsed.
We can use this equation to find t:
d = 0.5(-9.8)t²
65 = -4.9t²
t = √(65 / -4.9) = 2.45 s
Using this time, we can find the final velocity:
[tex]v = v_{0} + at[/tex]
v = -9.8 * 2.45
v = -24.1 m/s
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what could the future of space exploration look like?
The future of space exploration is exciting and holds a lot of potential. Here are some developments that we might see in the coming years:
Increased privatization of space exploration: Private companies like Elon Musk's SpaceX and Jeff Bezos' Blue Origin are already making significant investments in space technology and are playing an increasingly important role in space exploration.
Return to the Moon: NASA is planning a return to the Moon by 2024 as part of its Artemis program, with the goal of establishing a sustainable presence on the Moon and using it as a stepping stone for future missions to Mars.
Human missions to Mars: In the next few decades, it's possible that we may see human missions to Mars. These missions would aim to establish a permanent human presence on the Red Planet and unlock its secrets.
Advancements in space technology: In the future, we may see advancements in propulsion technology, such as nuclear-powered engines, that could make space travel faster and more efficient. We may also see the development of more advanced robotics and artificial intelligence systems to help with tasks such as exploring and mapping other planets.
Increased international cooperation: Space exploration is becoming an increasingly international endeavor, with countries from all over the world working together on missions and sharing data and technology.
Overall, the future of space exploration is bright, and it's an exciting time to be alive as we continue to push the boundaries of our knowledge and explore the wonders of the universe.
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if you changed the source wavelength to a longer wavelength, e.g. 600nm, how would the distance between the zero order maximum and the third order maximum change?
If you change the source of wavelength to a longer wavelength (e.g. 600 nm), the distance between the zero order maximum and the third order maximum will decrease, since the numerator (λ) has increased.
The distance between the zero order maximum and the third order maximum in a diffraction pattern depends on the wavelength of the light and the size of the diffraction grating.
If you change the source wavelength from a shorter wavelength to a longer wavelength, the distance between the zero order maximum and the third order maximum will decrease. This is because the distance between the maxima in a diffraction pattern is inversely proportional to the wavelength of the light.
In mathematical terms, if 'd' is the distance between the maxima, 'λ' is the wavelength, and 'n' is the order of the maximum, then the relationship between these quantities is given by:
d = λ / (n × sinθ)
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