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.
(C) You should deflect the ball

Answer 1

Answer:

(B) You should catch the hall

Explanation:

B) You should catch the ball.

case 1 : when ball is catched.

Mass of person catching = M

mass of ball = m

velocity of the ball just before catching = v

velocity of ball just after catching = 0

$\Delta P_{ball}$ = change in momentum of the ball = m (0 - v) = - mv

since,

$\Delta P_{person} =-\Delta P_{ball}$

$\Delta P_{person} =mv$

case 2 : when the ball is deflected back

velocity of the ball just before catching = v

velocity of ball just after catching = - v

$\Delta P_{ball}$ = change in momentum of the ball = m (- v - v) = - 2mv

since,  

$\Delta P_{person} =- \Delta P_{ball}$

$\Delta P_{person} = 2mv$

clearly we can see that the change in momentum is minimum in case when the ball is catched and hence keeps the speed of skateboard minimum