Please help with physics problem!!!?

Question

A 72 kg soccer player jumps vertically upwards and heads the 0.45 kg ball as it is descending vertically with a speed of 24 m/s. If the player was moving upward with a speed of 4.0 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

If the ball is in contact with the player's head for 20 ms, what is the average acceleration of the ball? (Note that the force of gravity may be ignored during the brief collision time.)
____ m/s2

Thank you so much! I only have a couple more hours to work on this and this was a problem that a group of students from my class could not find out.

Answer 1

Fortunately, momentum is conserved.

Initially, the ball had negative momentum (it was moving down) and the player and positive momentum (she was moving up).

m, v -> ball
M, V -> player

Pi = Pf

m v + M V = (m + M) vf

0.45 * -24 + 72 * 4 = (0.45 + 72) * vf
vf = 3.83 m/s



Convert 20 ms to 0.02 s

a = v / t = 3.83 / .02 = 191.5 m/s²

Answer 2

For part a, you can use conservation of momentum formulas, part b can be solved using the impulse formula. It's not really that difficult of a problem.