Question

What is the equations to prove the answer is A?

Answer 1

Explanation:

Let's say your mass is M, the ball's mass is m, and the ball's speed is v.  Let's say your final speed is V.

Momentum is conserved.  If you catch the ball, your speed is:

mv = (m + M)V

V = mv / (m + M)

If you deflect the ball, your speed is:

mv = MV + m(-v)

V = 2mv / M

To compare these, we need the common denominator.

If you catch the ball:

V = mMv / (M (m + M))

If you throw the ball:

V = 2m(m + M)v / (M (m + M))

Comparing the numerators, we can see M < 2(m + M), so catching the ball results in a lower speed.