The speed of the ferry boat is 16.67 meters per second.
The Pythagorean theorem is what?At a velocity of 10.0 m/s, the boat crossed the calm sea. Un = 2.00 m/s, river water speed Let v represent the ferry's effective river crossing speed, allowing it to travel directly to the location on the opposite side. We can then express their velocities as shown below.
What made Pythagoras well-known?Greek philosopher Pythagoras made significant contributions to mathematics, astronomy, and music theory. Although the Babylonians were aware of the theorem 1000 years before Pythagoras, he may be the first to use it.
We can use the formula for momentum:
p = mv
where p is momentum, m is mass, and v is velocity or speed.
Rearranging this formula to solve for velocity, we get:
v = p/m
Substituting the given values, we get:
v = 25000 kg-m/s / 1500 kg
v = 16.67 m/s
Therefore, the speed of the ferry boat is 16.67 meters per second.
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the angular resolution of a telescope is never smaller than its diffraction limit. group of answer choices true false
The statement given is true. The angular resolution of a telescope is never less than its diffraction limit.
The larger telescope will always have the higher spectral resolution than the smaller telescope while observing at the same wavelength. The angular resolution of a telescope is at no time smaller than its diffraction limit.
Generally, many telescopes are devices that gather all the light within some aperture of diameter d and bring it to a focus. The limit to the angular resolution of a telescope is settled by diffraction. The angular resolving power or the resolution of a telescope is the smallest angle among the close objects which can be seen clearly to be separate.
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Lyza’s team is pulling against Paxton’s team in tug of war. Both teams are pulling on the rope, but the rope is not moving. What statement best describes the forces acting on the rope?
The statement that would best describe the forces acting on the rope is that forces are in equilibrium.
What is equilibrium force?
Equilibrium force refers to a state in which the net force acting on an object is zero, meaning the object is either at rest or moving at a constant velocity.
This means that the sum of all forces acting on an object is equal to zero and there is no net acceleration. The object is said to be in a state of mechanical equilibrium.
So if both teams are pulling on the rope, but the rope is not moving, it simply means that the rope is in equilibrium, that is all the forces are equal.
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what is the diffraction limit of a 130-meter radio telescope observing radio waves with a wavelength of 21 centimeters?
The diffraction limit of the 130-meter radio telescope observing radio waves with a wavelength of 21 centimeters is 0.0022 meters.
The diffraction limit of a radio telescope is defined as the minimum size of the telescope's aperture that is necessary to produce a diffraction-limited image of an incoming wave. It is given by the formula:
d = 1.22 * λ / D
where d is the diffraction limit, λ is the wavelength of the incoming wave, and D is the diameter of the telescope's aperture.
In this case, the wavelength of the incoming wave is 21 centimeters, or 0.21 meters, and the diameter of the telescope's aperture is 130 meters. Plugging these values into the formula, we get:
d = 1.22 * 0.21 / 130 = 0.0022 m
So, the diffraction limit of the 130-meter radio telescope observing radio waves with a wavelength of 21 centimeters is 0.0022 meters.
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The efficiency of a petrol car engine is 40%. The speed of the car is 9.0 m s−1 when the power developed by the
engine is 20 kW. Calculate how many kilometres the car can go with one litre of petrol when driven at this speed.
The efficiency of a petrol car engine is 40%. The speed of the car is 9.0 m s−1 when the power developed by the engine is 20 kW. the car can go with one liter of petrol when driven at this speed is 9.0 m/s.
The amount of energy in one liter of petrol is 45 MJ. The efficiency of the engine is 40%. Therefore, the amount of energy converted to useful work is 18 MJ. The power developed by the engine is 20 kW. Therefore, the time taken for the car to travel one kilometer is Time = (1 km)/(9.0 m/s) = 111.11 s .
The amount of energy used to travel one kilometer is Energy = (20 kW)(111.11 s) = 2222.2 kJ Therefore, the amount of energy available from one liter of petrol is Energy = (45 MJ)(1000 kJ/MJ) = 45000 kJ The car can travel Distance = (45000 kJ)/(2222.2 kJ/km) = 20.22 km with one liter of petrol when driven at a speed of 9.0 m/s.
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g 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?
There would be an increase in the maximum order.
How will the wavelength change?If you change the source wavelength to a longer wavelength, for example, from 500 nm to 600 nm, the distance between the zero order maximum and the third order maximum would increase.
The distance between the diffraction peaks in a diffraction grating is proportional to the wavelength of the light. As the wavelength increases, the distance between the diffraction peaks also increases. The diffraction peaks are also proportional to the order of the diffraction. Therefore, as the wavelength increases, the distance between the zero order maximum and the third order maximum also increases.
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A marble is rolling at a velocity 100cm/sec with a momentum of 10,000 g-cm/sec. What is it’s mass?
Answer:
100g
Explanation:
Use the formula,
momentum = mass* velocity
Now substitute the respective values,
10,000g - cm/s = m * 100 cm/s
m = 10⁴ g-cm/s / 100 cm/s
m = 100g
And we are done!
suppose that 2 j of work are needed to stretch a spring from its natural length of 30 cm to a length of 42 cm. how much work (in j) is needed to stretch it from 35 cm to 40 cm?
The work needed to stretch the spring from 35 cm to 40 cm is 0.35 Joule. The result is obtained by using the formula for potential energy of a spring.
How to count the potential energy of a spring?The potential energy can be expressed as
P.E = ½kx²
Where
k = spring constantx = spring displacementSuppose that 2 J of work are needed to stretch a spring from its natural length of 30 cm to a length of 42 cm. Find work (in Joule) is needed to stretch it from 35 cm to 40 cm!
We have P.E₁ = 2 J when
x₁ = (42 - 30) cm
x₁ = 12 cm
x₁ = 0.12 m
The spring constant is
P.E₁ = ½kx₁²
2 = ½k(0.12)²
4 = 0.0144k
k = 277.77
k ≈ 278 N/m²
When it stretches for
x₂ = (40 - 35) cm
x₂ = 5 cm
x₂ = 0.05 m
The work needed will be
P.E₂ = ½kx₂²
P.E₂ = ½(278)(0.05)²
P.E₂ = 139(0.0025)
P.E₂ = 0.35 Joule
Hence, to stretch it from 35 cm to 40 cm, the work needed is 0.35 Joule.
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B. An object with a mass of 500,000 Kg and an object with a mas of 700.00 k have a force df grantsionalateshor between them that measures 00045N. How far apart are the two objects?
The two objects are approximately 22,201.86 meters apart.
The formula we use to determine the gravitational force between objects is;
F = G * (m1 * m2) / r^2where;
F is the force of gravity, G is the gravitational constant (6.67430 × 10^-11 m^3 kg^-1 s^-2)m1 and m2 refer to the masses of the objects,r refers to the distance between the objects' centers.Rearrange this formula to solve for the distance between the objects, we get;
r = sqrt((G * m1 * m2) / F)Substituting the given values, we get:r = sqrt((6.67430 × 10^-11 m^3 kg^-1 s^-2 * 500000 kg * 700.00 kg) / 0.00045 N)r = 22201860 metersThe two objects are roughly 22,201.86 meters apart, according to the calculation.
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an object in shm oscillates with a period of 4.0 s and an amplitude of 10 cm. how long does the object take to move x
An object in SHM oscillates with a period of 4.0 s and an amplitude of 10 cm. The object takes to move is 0.409s.
The time it takes for an object in simple harmonic motion (SHM) to move a certain distance can be calculated using the formula:
x = A sin ωt
where,
t is the time to move a distance x, time period T = 4 s
A is the amplitude of the oscillation
ω is Angular frequency = 2π/T= 1.57 rad/s
Then,
x = A sin ωt
6 = 10 sin(1.57t)
sin(1.57t) = 0.6
1.57 t = 0.6435
t= 0.409s.
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reflects from the mirror, and reaches point b. how far below the top edge does the ray strike the mirror?
The distance below the top edge at which the ray strikes the mirror depends on the angle of incidence.
What is ray strikes?Ray tracing is a computer graphics rendering technique for generating an image by tracing the path of light as it interacts with an object or scene. Ray tracing is capable of producing a very high degree of visual realism, including effects like reflections, refractions, and shadows.
The distance below the top edge at which the ray strikes the mirror depends on the angle of incidence. The angle of incidence is the angle between the incident ray and the normal to the mirror surface. The distance below the top edge can be found using the law of reflection which states that the angle of incidence is equal to the angle of reflection. If we denote the angle of incidence as θ and the distance below the top edge as h, then we can calculate h using the tangent of θ.
h = tan(θ) * distance from point a to the top edge of the mirror
Therefore, the distance below the top edge at which the ray strikes the mirror depends on the angle of incidence.
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what is the volume of an aluminum ball at 10°c if its volume at 160°c is 300cm3?
The volume of the aluminum ball is 297 cm³.
What is the volume of the aluminum ball?
The volume of an object changes with temperature, according to the law of linear thermal expansion.
The volume of the aluminum ball is calculated as follows;
V = V₀ ( 1 + 3αΔθ )
where;
V₀ is the initial volume of the aluminumα is the coefficient of linear expansion of aluminumV = 300 cm³ ( 1 + 3 x 23 x 10⁻⁶ x (-150 ) )
V = 297 cm³
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Similarities and differences between thermionic emission and liquid evaporation
There are both similarities and differences between thermionic emission and liquid evaporation elaborated below.
Vapourization is the process by which the liquid state transforms into the vapour state, and thermonic emission is the thermally induced inflow of charge carriers.
The thermally convinced ingress of charge carriers from a face or over an implicit-energy barrier is known as thermionic emission. This happens because, as we are aware, the thermal energy applied to the carrier overrides the material's ability to perform its intended function.
The process through which a liquid transforms into a gas is known as vaporisation. The molecules' kinetic energy increases along with the temperature. The force of attraction between the molecules weakens as a result of this increase in kinetic energy, allowing them to escape into the environment as vapours.
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A weight hangs motionless from a spring, with a spring constant of 75 N/m. The spring stretched from its original length by 0.333 meters. How much weight hangs from the spring?
Group of answer choices
15 N
45 N
35 N
25 N
Answer:
25 N
Explanation:
You can just observe the units of the numbers given to know that
75 N/m * .333 m = 25 N
2. a solid conducting sphere (or any shaped conductor), charged either positively or negatively, has no electric field inside it. how is this so?
It has a consistent distribution of the charges in a solid conducting sphere (or any shaped conductor), charged either positively or negatively, has no electric field inside it.
When retained in an electric or magnetic field, the basic physical characteristic of matter, electric charge, produces a force. A moving electric charge creates a magnetic field, and an electric charge is related with an electric field. Magnetic and electric fields combine to form the electromagnetic field. The interaction of the charges results in the electromagnetic force, which is the fundamental force in physics. Tell us about electric charges, their varieties, and their characteristics throughout this session. A scalar quantity is an electric charge. In addition to having a magnitude and direction, a quantity must also abide by the laws of vector addition, such as the parallelogram law of vector addition and the triangle law of vector addition. The quantity is only referred to as a vector quantity after vector addition.
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At Absolute Zero Temperature (0 Kelvin), state how much thermal energy an object has. At Absolute Zero Temperature, state the pressure that a fluid exerts on its system container.
At absolute zero temperature, the pressure of a fluid will approach zero.
What is absolute zero?
Absolute zero is the lowest temperature that can be reached in the universe and is defined as 0 Kelvin (K) on the Kelvin scale. It is equivalent to -273.15°C on the Celsius scale and -459.67°F on the Fahrenheit scale.
At absolute zero temperature (0 Kelvin), an object has zero thermal energy. This is because the definition of absolute zero temperature is the point at which an object has the minimum possible amount of thermal energy. At this temperature, all matter is in its lowest energy state and all random thermal motion has stopped.
Regarding the pressure of a fluid at absolute zero temperature, it is important to note that absolute zero temperature does not necessarily mean that the fluid is at a pressure of zero. The pressure of a fluid is determined by its temperature and its volume, not by its absolute temperature alone. The pressure of a fluid in a container is related to the average kinetic energy of the molecules in the fluid and their number density.
So, At absolute zero temperature, the pressure of a fluid will approach zero, but it will not be exactly zero because even at this temperature, the fluid molecules still have a non-zero kinetic energy due to their quantum mechanical motion.
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A steel wrecking ball is moving with 30,000 J of kinetic energy. The ball collides witha spring and comes to a complete stop. If the spring has a k = 50,000 N/m how much is the spring compressed?
Answer:
1.02 m
Explanation:
We are here given that ,
Kinetic energy= 30,000 J spring constant= 50,000N/mWe need to find out the compression in the spring. As we know that,
[tex]\longrightarrow E = \dfrac{1}{2}kx^2 \\[/tex]
where [tex]x[/tex] is the compression in the spring. So that,
[tex]\longrightarrow 30,000 J = \dfrac{1}{2}\times 50,000 \times x^2 \\[/tex]
[tex]\longrightarrow x^2=\dfrac{60,000}{50,000} \\[/tex]
[tex]\longrightarrow x^2=\dfrac{6}{5}= 1.2m^2\\[/tex]
[tex]\longrightarrow x=\sqrt{1.2} m \\[/tex]
[tex]\longrightarrow \underline{\underline{ x \approx 1.02 \ m }} \\[/tex]
and we are done!
how does a simple cell work
Answer:
A simple cell can be made by connecting two different metals in contact with an electrolyte
Activity 3 A driver parked his car in the open on a hot day because he wanted to go for lunch in a small town A man in the tow. advised the driver to park the car under a tree shade but the driver refused. Task: Prepare a comprehensive message with reasons that would convince the driver to pack the car under the shade.
Answer:
Dear driver,
I hope this message finds you well. I am writing to you today because I noticed that you have parked your car in the open on this hot day. I understand that you are planning to go for lunch in the town, but I would like to respectfully offer you some advice.
I strongly recommend that you park your car under the shade of a tree. There are several reasons for this that I would like to share with you. Firstly, parking your car in direct sunlight can cause the interior to become extremely hot and uncomfortable, which can make it difficult to get back into your vehicle after lunch. This can also cause the steering wheel and other interior surfaces to become too hot to touch, which can be dangerous.
Furthermore, parking your car in direct sunlight can also have a negative impact on the health of your car. The intense heat can cause the dashboard, upholstery, and other materials to fade and deteriorate over time. It can also increase the risk of interior damage from sun exposure and make the car look older than it actually is.
Finally, parking under the shade of a tree will help to keep your car cooler, which can make it more comfortable for you to get back into and drive when you are ready to leave. This can also help to extend the life of your car and maintain its appearance.
I hope that these reasons have convinced you to park your car under the shade of a tree during your time in the town. If you have any further questions or concerns, please don't hesitate to reach out to me.
Thank you for your time and consideration.
Explanation:
water in a tank is at the pressure of 5.5 mpa and temperature of 260oc. the saturation pressure at the same temperature is 4.69 mpa. what is the phase of water?
The water in the tank has become superheated and is in the vapour phase.
Water has a saturation pressure of 4.69 MPa at 260°C. The water pressure in the tank is 5.5 MPa, which is larger than the saturation pressure. So, the water in the tank has become superheated.
Superheated water is water that is in the vapour phase but at a temperature greater than its typical boiling point. This can happen when water is heated at a continuous pressure higher than the saturation pressure for that temperature. Despite being beyond the typical boiling point, the water molecules in this state have a lot of energy and are not condensing into a liquid.
Understanding the phase of water in a given circumstance is critical in a variety of engineering and scientific applications. Understanding the phase of water in a steam turbine, for example, is critical for effective operation and minimising equipment damage in power plants. Understanding the phase of water in food preparation can effect the quality and preservation of the product.
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determine the constant force prequired to cause the 0.5-kg slider to have a speed at position 2. the slider starts from rest at position 1 and the unstretched length of the spring of modulus is 200 mm. neglect friction.
The constant force required to cause the 0.5-kg slider to have a speed at position 2 is proportional to the square root of the product of the modulus of the spring and the mass of the slider, and is directly proportional to the speed of the slider at position 2.
The kinetic energy of the slider at position 2 can be expressed as:
[tex]Ek = 0.5 * m * v^2[/tex]
where m is the mass of the slider and v is its speed at position 2.
[tex]0.5 * k * x^2 = 0.5 * m * v^2[/tex]
[tex]k * x^2 = m * v^2[/tex]
[tex]x = sqrt(m * v^2 / k)[/tex]
The force required to compress the spring by a distance x is equal to:
[tex]F = k * x[/tex]
Substituting the value of x, we get:
[tex]F = k * sqrt(m * v^2 / k)[/tex]
Simplifying this expression, we get:
[tex]F = sqrt(k * m) * v[/tex]
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answer this please (questions below)
How much KE does the pendulum have at the highest point?
What is the total ME at the highest point?
How much KE does the pendulum have at the lowest point?
What is the mass of the pendulum?
The kinetic energy at the lowest point is 52 J
What is the Kinetic energy?Kinetic energy is the energy an object possesses due to its motion. It is equal to the work done on an object to increase its speed.. It is related to the concept of work, as the amount of work done on an object is equal to the change in its kinetic energy. Kinetic energy is an important concept in many areas of physics.
From the law of the conservation of energy we know that tghe kinetic energy is;
62 J - 10 J
= 52 J
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20 points !! An ultraviolet wave from the Sun traveling at the speed of light has a wavelength of 3 × 10−8m. Calculate the frequency of this wave.
Answer:
[tex]1.0 \times 10 {}^{16} per \: second[/tex]
or simply
1.0×10¹⁶/sExplanation:
Greetings !!
Given values :-speed of light= 3×10⁸
wavelength= 3×10-⁸
required value :-frequency= ?
solution:-Firstly, recall the velocity-wavelenght equation
V=f λSubstitute known variables into the equation
(3×10⁸) = f(3×10-⁸)Solve for frequency
f= 1.0×10¹⁶/s.If you have any questions or unclear ideas tag on comment box
Hope it helps!!!
Rudy spies a trout 9,800 centimeters from his fishing boat, 7 minutes after casting his fishing line into the water. The trout begins to swim at 3,500 centimeters per minute toward the boat. At this velocity, how long will it take the trout to reach the boat?
The directional speed of an item in motion, as measured by a specific unit of time and observed from a certain point of reference, is what is referred to as velocity.
How to define velocity?
It will take the trout 2.8 minutes to reach the boat.
Use the following formula to solve for the time it takes the trout to reach the boat:
time = distance/velocity
distance = 9,800 centimeters (the starting distance between the trout and the boat)
velocity = 3,500 centimeters per minute (the velocity of the trout swimming toward the boat)
put in the values:
time = 9,800 / 3,500
time = 2.8 minutes
So, it will take the trout 2.8 minutes to reach the boat.
The directional speed of an item in motion, as measured by a specific unit of time and observed from a certain point of reference, is what is referred to as velocity. Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is traveling along a path. In other words, velocity is a vector, whereas speed is a scalar value. Since it is a vector quantity, the definition of velocity requires both magnitude (speed) and direction.
We can say that forces produce changes in velocity because they alter an object's speed or direction. Keep in mind that acceleration is a modification of velocity.
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A vector is represented by a(n)………?
Answer:
An Alphabet with an arrow on top
Explanation:
Vectors are denoted by alphabets in boldface or alphabets with arrows above them
compare this to the diffraction limit of the hubble space telescope for visible light. why, to be useful, radio telescopes must be much larger than optical telescopes?
Radio telescopes must be larger than optical telescopes because of the longer wavelengths of radio waves, which result in a lower diffraction limit.
The diffraction limit of a telescope is determined by its aperture size, or the diameter of its collecting area. For the Hubble Space Telescope, the diffraction limit for visible light is approximately 0.05 arcseconds. This means that the telescope can resolve structures or details that are separated by at least 0.05 arcseconds of an angle.
On the other hand, radio telescopes are much larger than optical telescopes because radio waves have longer wavelengths than visible light. The diffraction limit of a radio telescope is proportional to the wavelength of the radiation it observes. Because radio wavelengths are much longer than those of visible light, radio telescopes must be much larger in order to achieve the same level of resolution as optical telescopes.
In addition, radio telescopes can detect emissions from much larger structures in space, such as galaxies and clusters of galaxies. These emissions are typically very weak and difficult to detect, so radio telescopes must have a large collecting area in order to detect them.
To sum up, radio telescopes must be larger than optical telescopes because of the longer wavelengths of radio waves, which result in a lower diffraction limit, and the need to detect weak radio emissions from large structures in space.
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Which phase of matter is made up of particles that are packed closely together, with both a definite shape and a definite volume?
A. Gas
B. Liquid
C. Plasma
D. Solid
The correct option is D. Solid phase of matter is made up of particles that are packed closely together, with both a definite shape and a definite volume.
In physics, a Solid is a state of matter characterized by its ability to maintain a fixed shape and volume when subjected to external forces. The particles in a solid are tightly packed together and have a fixed position relative to each other, giving the solid its rigidity.
Solids have a definite shape because their particles cannot move past one another, and they have a definite volume because the particles are tightly packed together. The properties of solids, such as density, thermal conductivity, and electrical conductivity, depending on the arrangement of their particles and the forces between them.
Solids can exist in different crystal structures, depending on the arrangement of their atoms or molecules. Examples of solids include metals, minerals, and rocks, as well as everyday objects such as tables, chairs, and buildings. Solids are important in many areas of physics, including materials science, condensed matter physics, and solid-state electronics.
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determine the moment of each of the three forces about point b MF1(B)=? MF2(B)=? MF3(B)=?
MF1(B)= 149.52 N - m, MF2(B)= 600 N - m, MF3(B)= ON - m.
Explain about force?
Force is a vector quantity that is defined as the rate of change of momentum of an object with respect to time. It is measured in Newtons (N) and is the product of mass and acceleration, according to Newton's second law of motion. Force can be applied by pushing, pulling, or twisting an object and can be used to create motion, stop motion, or change the direction of motion. Force can also influence the shape of an object through compression, tension, and shear.
(MF₁) B = F₁ cos 30° (3) – F₁ sin 30° (4)
= 250 cos 30° (3) — 250 sin 30° (4)
= 649.52 - 500
= 149.52 N - m
(MF₂) B = F₂ cos 60° (4) – F₂ sin 60° (0)
= 300 cos 60° (4) — 300 sin 60° (0)
= 600 - 0
= 600 N - m
As the force F3 passes through point B, moment of the force F3 about point B is zero.
(MF3)B = ON - m
Therefore, MF1(B)= 149.52 N - m, MF2(B)= 600 N - m, MF3(B)= ON - m is the answer.
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A rhinoceros is at the origin of coordinates at time t1=0. For the time interval from t1 to t2= 10.0s, the rhino's average velocity has x-component -3.20 m/s and y-component 5.40 m/s.
*At time t2=10.0s what is the x-coordinate of the rhino?
*At time t1=10.0s what is the y-coordinate of the rhino?
*How far is the rhino from the origin?
At t2=10.0s, the x-coordinate of the rhino is -32 and at time t1=10, the y-coordinate of the rhino is 64.8m. The rhino is 72.27 m.
Given:
x-component of avg. velocity is 3.20 m/s.
x-component of avg. velocity 5.40 m/s.
initial position of rhino, (x1,y1)= (0,0)
initial time, t1=0s
final time, t2=12s
a) As we know that average velocity is total displacement per unit time.
Position of x-coordinate of the rhino:
Vx= x2/t2
-3.20= x2/10
x2= -32m
Position of y-coordinate of the rhino:
Vy= y2/t2
5.40= y2/12
y2= 64.8 m
Now the distance from the origin:
s=[tex]\sqrt{x2^{2} +y2^{2} }[/tex]
s=[tex]\sqrt{(-32)^{2} } + (64.8)^{2} \\[/tex]
s=[tex]\sqrt{1024}+ 4199.04[/tex]
s=72.27 m
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what is the angular momentum of a thin loop of radius 2m and mass 1 kg, rotating at a velocity of 4 rad/s?
The angular momentum of a thin loop of radius 2m and mass 1 kg, rotating at a velocity of 4 rad/s is 8 kg·rad/s
What is angular momentum?
The rotational equivalent of linear momentum is angular momentum, often known as moment of momentum or rotational momentum. It is a conserved quantity, meaning that the total angular momentum of a closed system stays constant, making it a significant physical quantity. Both the direction and the amplitude of the angular momentum are always conserved. The functional characteristics of motorbikes, frisbees, bullets, and gyroscopes are due to the conservation of angular momentum.Angular momentum conservation also explains why storms occur.Given : m=1 kg w=4 rad/s r=2 mm
So, angular momentum L=mwr
⟹ L=1×4×2
= 8 kg rad /s
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how far you can tilt the cup before the cup's center of mass passes over the origin, allowing the cup to fall over.
The maximum angle at which the cup can be tilted without falling over is when the gravitational torque is equal and opposite to the torque produced by the weight of the cup acting on the point of contact with the table.
The maximum angle at which a cup can be tilted before it falls over depends on the ratio of the radius of the base of the cup to its height. If the cup is a uniform circular cylinder, then its center of mass is located at a distance of half the height of the cup from the origin. When the cup is tilted, the gravitational force acting on the cup produces a torque that tends to rotate the cup around the point where it touches the table.
By setting these two torques equal to each other and solving for the maximum angle, we can determine how far the cup can be tilted before it falls over.
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