Impulse of a Ball - Greatest Change in Momentum

[I Like Pi]

Homework Statement

If a tennis player were to throw his ball against a wall, which impulse would be the greatest? The throw, the bounce, or the catch?

Homework Equations

I = F * t
P = m * v

The Attempt at a Solution

I believe the bounce is the greatest, as it has the greatest change in momentum, but I can't explain my thought...

 

[issacnewton]

yes you are right. bounce has the greatest change in momentum. let's say that velocity before the impact is $$\vec{v}$$ , then velocity after the bounce would be
$$-\vec{v}$$. so initial momentum is $$m\vec{v}$$ and final momentum is
$$-m\vec{v}$$. so the change in momentum would be $$-m\vec{v}-m\vec{v}$$ which is $$-2m\vec{v}$$. but when the ball is caught, final momentum is zero, so the change in momentum is $$0-m\vec{v}$$ which is $$-m\vec{v}$$
same argument can be made for the case when the the ball is thrown.

Edit: I am assuming above that the kinetic energy is not lost. Even if the kinetic energy is lost, the reasoning is not affected.

 

[I Like Pi]

yes you are right. bounce has the greatest change in momentum. let's say that velocity before the impact is $$\vec{v}$$ , then velocity after the bounce would be
$$-\vec{v}$$. so initial momentum is $$m\vec{v}$$ and final momentum is
$$-m\vec{v}$$. so the change in momentum would be $$-m\vec{v}-m\vec{v}$$ which is $$-2m\vec{v}$$. but when the ball is caught, final momentum is zero, so the change in momentum is $$0-m\vec{v}$$ which is $$-m\vec{v}$$
same argument can be made for the case when the the ball is thrown.

Edit: I am assuming above that the kinetic energy is not lost. Even if the kinetic energy is lost, the reasoning is not affected.

Hey! Thanks for the reply! It makes sense, and I assume when the ball is thrown it is the reverse? The initial momentum is zero?

Thank you!

 

[issacnewton]

yes, when the ball is thrown, the initial momentum is zero. and final momentum is
$$m\vec{v}$$ so the change in momentum is $$m\vec{v}$$ which is a smaller change in absolute terms than in the case of bouncing ball.