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

You have to deflect the ball

Explanation:

When you catch the ball the kinetic energy is transferred to your body from the ball, the final velocity of the ball will be equal to yours because all the energy of the ball has been distributed to you and the ball equaly.

But when you hit the ball back, part of the energy will remain mostly on the ball. The impact energy from the contact moment will be transfered into your motion.

it is very well related to a lot of things but with my limited knowledge i can confidently say that the answer is space.

can be answered using momentum.

momentum = p

p1= mass1 * velocity1

p1 = p2

therefore

p1 = 6kg * 4m/s

p1 = 24kgm/s

p2=m2 * v2

24 kgm/s = 7kg * v2

v2 = 24 kgm/s / 7kg

v2= 3.42 m/s