Question

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 deflect the ball back towards 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 minimize your speed on the skateboard? Choose one of the following three answers.
A) Your final speed on the skateboard will be the same regardless whether you catch the ball or deflect the ball.

B) You should catch the hall.

B) You should deflect the ball

The answer is you should catch the ball to minimize speed. What I need is a math-based and THOROUGH explanation. Any formulas you use to prove, please show the ORIGNIAL equation with steps that you used to get to the final one. Please! will rate right away!

Answer 1

To solve this problem we will apply the concept related to the moment, which describes the change in speed in proportion to the body mass. The momentum can be described under the general equation

$p = mv$

Where,

m = mass

v = Velocity

The change in momentum is the difference between the final moment and the initial moment

$\Delta p = p_f - p_i$

Where,

$p_f =$ Final momentum

$p_i =$ Initial momentum

After catching the ball, the ball comes to rest position and speed of the ball is zero.

$p_f = 0$

The change in momentum on catching the ball is

$\Delta p = 0 - mv$

$\Delta p = -mv$

The momentum during the catching of the ball is

$p_i = mv$

Now during deflection of the ball, we know that there is an initial momentum and a negative final momentum because it moves with the same speed but in the opposite direction, that is

$p_f = -mv$

The momentum is negative since during deflection the ball moves with same speed in opposite direction

$\Delta p = -mv-mv$

$\Delta p = 2-mv$

Therefore, the correct ansswer is B: catch the ball in order to minimize your speed on the skateboard