Question

A 69.5 kg football player is gliding across very smooth ice at 2.25 m/s . he throws a 0.450 kg football straight forward. part a what is the player's speed afterward if the ball is thrown at 18.0 m/s relative to the ground?

Answer 1

We can solve the problem by using the law of conservation of momentum.

Initially, the player is moving together with the ball, so the total momentum is

`(M+m) v_i`
where M is the player's mass, m the ball's mass, and
`v_i` the speed at which the player+ball system is moving.

After the player throws the football, the momentum is

`Mv_p + m v_b`
where
`v_p` is the final velocity of the player and
`v_b` is the velocity of the ball (relative to the ground).

Requiring conservation of momentum:

`(M+m)v_i = Mv_p + mv_b`
we can calculate the only unknown quantity of the equation,
`v_p`:

`v_p = ((M+m)v_i - mv_b)/(M) = ((69.5 kg+0.45 kg)(2.25 m/s)-(0.45 kg)(18 m/s))/(69.5 kg)=2.14 m/s`

so, the player's final speed is 2.14 m/s.