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# Velocity

### Kinematics: How fast was the car going?

1) A policeman investigating an accident measures the skid marks left by a car. He determines that the distance between the point that the driver slammed on the brakes and the point where the car came to a stop was 34.0 m. From a reference manual he determines that the coefficient of kinetic friction between the tires and the ro

### Final velocity of baggage carrier

In problem 14.3(a), if the velocity of the 30 lb and 40 lb suit cases are 12 ft/s and 5 ft/s, respectively, when the first suit case of 30 lb was tossed into the carrier, the final velocity of the baggage carrier after the second baggage tossed into the carrier is: a. 4.25 ft/s b. 4.67 ft/s c. 3.87 ft/s d. 5.67 ft/s

### Calculating The Acceleration And Velocity Of A Block

A block lies on a plane tilted at an angle theta = 22.0* to the horizontal, with the coefficient of kinetic friction mu_k = 0.17. a) Determine the acceleration of the block as it slides down the plane. b) If the block starts from rest 9.3 m up the plane from its base, what will be the block's speed when it reaches the bottom o

### Spring and Simple Harmonic Motion

See attached file for full problem description. 1. Gina's favorite exercise equipment at the gym consists of various springs. In one exercise, she pulls a handle grip attached to the free end of a spring to 0.80 m from its unstrained position. The other end of the spring is held in place by the equipment frame. What is the magn

### Newton's 2nd Law - Kinetics

Dynamics 12.8 A car has been traveling up along a 2 percent grade at a constant speed of 55 miles/hr. If the driver does not change the setting of the throttle or shift gears as the car reaches the top of the hill, what will be the acceleration of the car as it starts moving down the 3 percent grade? Dynamics 13.7 A 24-

### Orbital Mechanics

A lunar landing craft needs to hover just above the surface of the moon, which has a gravitational acceleration of (1/6) g. The exhaust velocity is 2000m/s but fuel amounting to only 20% of the total mass can be used. How long can the landing craft hover?

### Energy Questions

1) Find the curl, delta x F, for the following forces: (a) F = kr; (b) F = (Ax, By2, Cz3); (c) F = (Ay2, Bx, Cz), where A, B, C and k are constants. 2) Verify that the gravitational force - GMmr/r2 on a point mass m at r, due to a fixed point mass M at the origin, is conservative and calculate the corresponding potent

### Rotationial kinematics

A basketball player is balancing a spinning basketball on the tip of his finger. The angular velocity of the ball slows down from 18.5 to 14.1 rad/s. During the slow-down, the angular displacement is 85.1 rad. What is the time it takes for the ball to slow down?

### Rotational Kinematics of a Gymnast

A gymnast is performing a floor routine. In a tumbling run she spins through the air, increasing her angular velocity from 3.00 to 5.00 rev/s while rotating through one-half of a revolution. How much time does this maneuver take?

1. Dennis Chapman did not eat for a few days and went to a restaurant which says buffet all you can eat just \$4.95. Dennis was so happy that he started eating and eating till the owner of the restaurant asked Dennis "May I help you sir?". Dennis said yes, just go away and let me eat. After eating Dennis weight from 185 lb becam

### 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?

### According to Newton's Third Law, a force in one direction produces an equal force in the opposite direction.

According to Newton's Third Law, a force in one direction produces an equal force in the opposite direction. If the force that acts on a cannonball and the recoiling cannon are equal in magnitude, why does the cannon not recoil with the same velocity at the cannonball?

### Velocity of Elastic Balls

Two identical balls are traveling toward each other with velocities of -4.0 and 7.0 m/s and they experience an elastic head-on collision. What are the velocities (magnitude and direction) of each ball after the collision?

### Elastic collision

A 1055kg van, stopped at a traffic light, is hit directly in the rear by a 715 kg car traveling with a velocity of 2.25 m/s. Assume that the transmission of the van is in neutral, the brakes are not being applied, and the collision is elastic. What is the final velocity of (a) the car and )b) the van?

### 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

### Recoil velocity on a raft

A 55 kg swimmer is standing on a stationary 210 kg floating raft. The swimmer then runs off the raft horizontally with a velocity of 4.6 m/s relative to the shore. What is the recoil velocity that the raft would have if there were no friction and resistance due to the water?

### 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

### Free Fall from a Moon Tower

What would the results be if you fell while on a 450 meter tower on the Moon, where a = 1.65m/s^2 ? Given the distance fallen D = (0.5)(1.65)* t^2 (meters) ( V= 1.65 t) Downward Velocity (meters/sec) and the elapsed time is 0,1,2,3,...7 sec.

### 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.

### Collision Between an Atom and an Electron

If an electron of 58 eV had a head-on collision with a Ba atom at rest, what would be the kinetic energy of the recoiling Ba atom? Assume an elastic collision. (Take the atom to be the most abundant isotope of the element).

### Velocity of Niagara Falls

Suppose the water at the top of Niagara Falls has a horizontal speed of 2.7 m/s just before it cascades over the edge of the falls. At what vertical distance below the edge does the velocity vector of the water point downward at a 75 degree angle below the horizontal?

### Question about projectile motion of a rocket

A rocket is fired at a speed of 75 m/s from ground level, at an angle of 60 degrees above the horizontal. The rocket is fired toward an 11.0 m high wall, which is located 27 m away. By how much does the rocket clear the top of the wall?

### Height Between Climbers

A rock climber throws a small first aid kit to another climber who is higher up the mountain. The initial velocity of the kit is 11 m/s at an angle of 65 degrees above the horizontal. At the instant when the kite is caught, it is traveling horizontally, so its vertical speed is zero. What is the vertical height between the two c

### 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)?

### How to Find the Radius of a Chamber

At an amusement park there is a ride in which cylindrically shaped chambers spin around a central axis. People sit in seats facing the axis, their backs against the outer wall. At one instant the outer wall moves at a speed of 3.2 m/s, and an 83 kg person feels a 560 N force pressing against his back. What is the radius of a cha