Basic question of Newtons Laws

You are standing on a skateboard initially at rest. A friend throws a very heavy ball towards you. You can either catch the object or deflect the object back toward your friend (such that it moves away from you with the same speed as it was originally thrown). What should you do in order to maximize your speed on the skateboard?

a. catch the ball
b. your final speed on the skateboard will be the same regardless whether you catch the ball or deflect the ball
c. deflect the ball back

I would love an explanation for this. Thank you!

C. Deflect the ball.

You want to deflect the ball because this creates a larger impulse. You could think of deflecting the ball by splitting it up into catching, and throwing the ball. First, you would catch the ball, which would push you forward with some speed. (This speed would obviously be equal to option A, where you catch the ball.) Now, you would throw the ball back to him (these two processes would be equivilient to deflecting the ball. By throwing a mass away from you, this would now cause you to move even faster! Wooahhh! So yes, answer C will get you moving fastest.

c. deflect the ball back
By the law of momentum conservation:-
=>m1u1+m2u2 = m1v1+m2v2
=>mu + M.0 = m(-u) + Mv
=>v = 2mu/M