A69.5 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?

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

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

After the player throws the football, the momentum is

where  is the final velocity of the player and  is the velocity of the ball (relative to the ground).

Requiring conservation of momentum:

we can calculate the only unknown quantity of the equation, :


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