A$75-$kg$$soccer player jumps vertically upward and heads the$0\mathrm{.}45$ kg$$ball as it is descending vertically with a speed of$24$m$/$s$.($Note that the force of gravity may be ignored during the brief collision time.$)$

$($a$)$

If the player was moving upward with a speed of$4\mathrm{.}0$ m$/$s$$just before impact, what will be the speed of the ball immediately after the collision if the ball rebounds vertically upwards and the collision is elastic?

$$m$/$s

$($b$)$

If the ball is in contact with the player's head for$24$ms$,$what is the average acceleration of the ball?

$$m$/$s$2$