91Ó°ÊÓ

Verify that the SI unit of impulse is the same as the SI unit of momentum.

A 0.15-kg baseball traveling in a horizontal direction with a speed of $20 \mathrm{m} / \mathrm{s}$ hits a bat and is popped straight up with a speed of \(15 \mathrm{m} / \mathrm{s} .\) (a) What is the change in momentum (magnitude and direction) of the baseball? (b) If the bat was in contact with the ball for 50 ms, what was the average force of the bat on the ball?

A pole-vaulter of mass \(60.0 \mathrm{kg}\) vaults to a height of $6.0 \mathrm{m}$ before dropping to thick padding placed below to cushion her fall. (a) Find the speed with which she lands. (b) If the padding brings her to a stop in a time of \(0.50 \mathrm{s},\) what is the average force on her body due to the padding during that time interval?

A rifle has a mass of \(4.5 \mathrm{kg}\) and it fires a bullet of mass $10.0 \mathrm{g}\( at a muzzle speed of \)820 \mathrm{m} / \mathrm{s} .$ What is the recoil speed of the rifle as the bullet leaves the gun barrel?

A 0.030 -kg bullet is fired vertically at \(200 \mathrm{m} / \mathrm{s}\) into a 0.15 -kg baseball that is initially at rest. The bullet lodges in the baseball and, after the collision, the baseball/ bullet rise to a height of $37 \mathrm{m} .$ (a) What was the speed of the baseball/bullet right after the collision? (b) What was the average force of air resistance while the baseball/bullet was rising?

If a particle of mass \(5.0 \mathrm{kg}\) is moving east at $10 \mathrm{m} / \mathrm{s}\( and a particle of mass \)15 \mathrm{kg}\( is moving west at \)10 \mathrm{m} / \mathrm{s},$ what is the velocity of the CM of the pair?

In the railroad freight yard, an empty freight car of mass \(m\) rolls along a straight level track at \(1.0 \mathrm{m} / \mathrm{s}\) and collides with an initially stationary, fully loaded boxcar of mass 4.0m. The two cars couple together on collision. (a) What is the speed of the two cars after the collision? (b) Suppose instead that the two cars are at rest after the collision. With what speed was the loaded boxcar moving before the collision if the empty one was moving at \(1.0 \mathrm{m} / \mathrm{s} ?\)

Two objects with masses \(m_{1}\) and \(m_{2}\) approach each other with equal and opposite momenta so that the total momentum is zero. Show that, if the collision is elastic, the final speed of each object must be the same as its initial speed. (The final velocity of each object is not the same as its initial velocity, however.)

A hockey puck moving at \(0.45 \mathrm{m} / \mathrm{s}\) collides elastically with another puck that was at rest. The pucks have equal mass. The first puck is deflected \(37^{\circ}\) to the right and moves off at $0.36 \mathrm{m} / \mathrm{s} .$ Find the speed and direction of the second puck after the collision.