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
[tex](M+m) v_i[/tex]
where M is the player's mass, m the ball's mass, and [tex]v_i[/tex] the speed at which the player+ball system is moving.
After the player throws the football, the momentum is
[tex]Mv_p + m v_b[/tex]
where [tex]v_p[/tex] is the final velocity of the player and [tex]v_b[/tex] is the velocity of the ball (relative to the ground).
Requiring conservation of momentum:
[tex](M+m)v_i = Mv_p + mv_b[/tex]
we can calculate the only unknown quantity of the equation, [tex]v_p[/tex]:
[tex]v_p = \frac{(M+m)v_i - mv_b}{M} = \frac{(69.5 kg+0.45 kg)(2.25 m/s)-(0.45 kg)(18 m/s)}{69.5 kg}=2.14 m/s [/tex]
so, the player's final speed is 2.14 m/s.
