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 ballthe 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, show the orignial equation with steps that you used to get to the final one. will rate right away!

B) You should catch the ball.

Explanation:

Initially when you are standing on the skate board then no force is acting on you in the lateral direction that tends to move you.

But as you try to catch or deflect a heavy ball in the opposite direction you experience a force in the lateral direction which will move or tend to you on the skate board because you are changing the momentum of the ball.

this is in accordance with the Newton's second law of motion which states that the rate of change in momentum is directly proportional to the force applied.

Mathematically:

where:

m = mass of the object moving with velocity v

t = time taken to change the momentum of the body

represents the change in quantity

When you change the momentum of the body by catching the ball you have to change the momentum of the ball from m.v to 0 which takes time t.

In this case the change in momentum is .

But  when you revert the momentum of the ball with equal velocity then the  change in momentum is from m.v to m.(-v) i.e. in time "t" which requires much greater effort (almost double, since time might vary slightly) than the catching the ball. So, greater the force more is the speed attained on the skateboard.