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Velocity

Areal Velocity and Time Averages

Question: Show that the areal velocity is constant for a particle moving under the influence of an attractive force given by F(r) = -kr. Calculate the time averages of the kinetic and potential energies and compare the results of the viral theorem.

Falling Objects on the Earth and Moon

Imagine that you are sitting on top of a 10-meter tower and drop two objects: a $20 gold piece (weight = 33g, diameter = 34mm) and a silver dollar (weight =26.7 g, diameter = 38mm). 1. Which, if either, falls faster? How do you support your answer? 2. If you repeated the same experiment on the Moon, what would you notice?

Recoil Velocity When Firing a Gun

The lead female character in a movie is standing at the edge of an offshore oil rig. As she fires a gun, she is driven back over the edge and into the sea. Suppose the mass of a bullet is 0.010 kg and its velocity is 720 m/s. Her mass (including the gun) is 51 kg. (a) what recoil velocity does she acquire in response to a si

Dynamics: Escape Velocity

See attached file for full problem description Escape velocity. We suppose that r = -gR^2/r^2. Suppose that a rocket is fired straight up, from the surface of the Earth with a velocity that is exactly half of the escape velocity. How high will the rocket go?

Free Fall: Time and Distance

Question: You are at the top of a 500 meter television tower and drop a hammer. For each of the first 7 seconds of free fall, calculate the distance that the hammer falls and its velocity at that particular moment. - How long will the hammer fall until it hits the ground? - What will be the final (terminal) velocity when it

Acceleration, velocity, distance

1. How would you describe the change in velocity each second for an accelerating object? 2. How would you describe the amount of distance fallen each second for an accelerating object? 3. a) Is there gravity on the Moon? b) What would happen if you doubled the mass of the object that is falling to the surface?

Rocket equation of motion and exhaust velocity.

See attached file for full problem description. 1) (a) Consider a rocket traveling in a straight line subject to an external force Fext acting along the same line. Show the equation of motion is mv = - mvex + Fext. (3.29) (b) Specialize to the case of a rocket taking off vertically (from rest) in a gravitational

Free fall: distance and velocity

You are the top of a 500 meter tower and drop a hammer. For each of the first 7 seconds of freefall, calcucate the distance that the hammer fall, and its velocity at that particular moment.

A Ball's Velocity When an Opposing Player Fields the Ball

A volleyball is spiked so that it has an initial velocity of 15 m/s directed downward at an angle of 55 degrees below the horizontal. What is the horizontal component of the ball's velocity when the opposing player fields the ball?

Inclined Plane

The velocity of a 1.9 kg block sliding down a frictionless inclined plane is found to be 1.15 m/s. 1.40 s later, it has a velocity of 5.35 m/s. What is the angle of the plane with respect to the horizontal (in degrees)?

Projectile Motion and Classical Mechanics

(See attached file for full problem description with diagrams) --- A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of 16.0 m/s. The cliff is h = 22.0 m above a flat horizontal beach, as shown in Figure P3.24. Figure P3.24 How long after being released does the stone stri

Projectile motion and geometry problems involving cosine law and sin law.

1. A ball thrown vertically upward is caught by the thrower after 4.00 s. (a) Find the initial velocity of the ball. m/s (b) Find the maximum height it reaches. m 2. A mountain climber stands at the top of a 40.0 m cliff that overhangs a calm pool of water. She throws two stones vertically downward 1.00 s apart and

Find the tension in the cable.

A stuntman is being pulled along a rough road at a constant velocity, by a cable attached to a moving truck. The cable is parallel to the ground. The mass of the stuntman is 109 kg, and the coefficient of kinetic friction between the road and him is 0.87 . Find the tension in the cable.

Time, Distance and Velocity Problems

Problem #1. A car traveling at constant speed of 30m/s passes a trooper hidden behind a bush. Once second after the speeding car passes the bush, the trooper sets off in chase with a constant acceleration of 3.0 m/s2. How long does it take the trooper to overtake the speeding car? How far does the trooper travel during this tim

Set of 5 problems on kinematics

1) A car covers one-quarter of the distance to the next town at 40km/h, another quarter at 50 km/h and the rest at 90km/h. Find the car's average speed for the entire distance. 2) In order to qualify for the finals in a racing event, a race car must achieve an average speed of 250km/h on a track with a total length of 1600

One end of a spring is attached to a solid wall...

One end of a spring is attached to a solid wall while the other end just reaches to the edge of a horizontal, frictionless tabletop, which is a distance H above the floor. A block of mass M is placed against the end of the spring and pushed toward the wall until the spring has been compressed a distance X. The block is released

Motion in Two Dimensions

A bird is flying horizontally at 6.0 m/s with a fish in its mouth. It accidentally drops the fish. How much time passes before the fish's speed doubles? and how much additional time would be required for the fish's speed to double again?

Physics problems: Velocity, Speed, Acceleration

1) Wiley Coyote has missed the elusive roadrunner once again. This time, he leaves the edge of the cliff at 50 m/s horizontal velocity. If the canyon is 100 meters deep, how far from the edge of the cliff does the coyote land? a) 100 meters b) 200 meters c) 225 meters d) 250 meters e) 300 meters 2) An artillery she

For women's volleyball the top of the net is 2.24 m above the floor

For women's volleyball the top of the net is 2.24 m above the floor and the court measures 9.0 m by 9.0 m on each side of the net. Using a jump serve, a player strikes the ball at a point that is 3.0 m above the floor and a horizontal distance of 8.0 m from the net. If the initial velocity of the ball is horizontal, a) what mi

Applications of the Doppler Effect

1. A cyclist and a railway train are approaching each other. The cyclist is moving at 10m/s and the train at 20m/s. the engine driver sounds a warning siren at a frequency of 480 Hz. Calculate the frequency heard by the cyclist (a) before and (b) after the train has passed by. (speed of sound in air = 340m/s). 2. For the equa

3 Circular Motion Problems

1. A circular disk of radius 30 cm is rotating with an angular acceleration of 1 radian/ s2. What is the tangential acceleration of a point on the rim of the disk? What is its centripetal acceleration if the angular speed is 3 rev / s? 2. A 980 Kg car traveling at 20 m/s rounds a curve of radius 40 m. What is the friction f

Uniform Circular Motion

A 25.0kg sled rests on a frictionless surface. It is attached by a 5.00m rope to a post in the ice. Once given a push, the sled revolves uniformly in a circle around the post. If the sled makes five complete revolutions every minute, what is the force (F) that is exerted on it by the rope?

Projectile Motion

A cannon, located 60.0m from the base of a vertical 25.0m tall cliff, shoots a 15kg shell at 43.0 digress above the horizontal toward the cliff. 1). What must the minimum muzzle velocity be for the shell to clear the top of the cliff? 2) The ground at the top of the cliff is level, with a constant elevation of 25.0m

Problems on kinematics and dynamics

6.) An airplane flies due south with respect to the ground at an air speed of 900 km/h for 2.0 hr before turning and moving southwest with respect to the ground for 3.0 hr. During the entire trip, a wind blows in the easterly direction at 120 km/h. (a) What is the plane's average speed with respect to the ground? (b) What is the

Linear Velocity of the Tire

If the tires on a bicycle have an angular velocity of 1 rad/s and a radius of 0.5 m, what is the linear velocity of the tire? How far will the bicycle travel in 10 seconds? a. linear velocity = 5 cm/s, distance = 50 meters b. linear velocity = pi m/s, distance = 10 pi meters c. linear velocity = 1 m/s, distance = 10 meters

Calculations Related to Impulse/Momentum

An 85-kg jogger is heading due east at a speed of 2.0 m/s. A 55-kg jogger is heading 32° north of east at a speed of 3.0 m/s. Find the magnitude and direction of the sum of the momenta of the two joggers.