Question

A ball is thrown downward; and its speed is v just before it strikes the ground. After the collision with the earth, it heads upward with a speed v. Which one of the following statements concerning this situation is truea) Only the magnitude of momentum of the earth is changed by collision (the correct answer, an explanation of why this is true would be very helpful)
b) the momentum of the earth is not changed by the collision
c) only the momentum of the ball is changed by the collision
d) the momentum of the ball is not changed by the collision
e) the collision causes both the momentum and the kinetic energy of the ball to change

Answer 1

For this case it is necessary to consider the assessments made between collisions of 'immovable' objects. In this case the earth is the immovable object or at least, it is approached by its mass. Considering the case of an inflatable ball of mass m that travels at a speed v towards the ground, it hits the floor and bounces with speed -v (Negative). The earth does not move, however, the momentum of the ball has changed by 2mv since the speed went from positive to negative. Applying the conservation of the momentum we know that the change of the momentum on the fly would be given under the function

$p = m\Delta V$

Considering the direction of the velocities this expression can be rewritten as

$p = m (v-(-v))$

$p = 2mv$

Therefore the correct answer would be

C. Only the momentum of the ball is changed by the collision