Question

a baseball player wants to hit a ball so that he can hit more home runs. he wants to maximize the change in momentum of the ball while it is in contact with the bat. what should the player do? hit the ball with as little force as possible for as long as possible. hit the ball with as big a force as possible but for the smallest possible amount of time. hit the ball with the biggest possible force for the longest possible time. none of the above.

Explanation:

To maximize the change in momentum (\(\Delta p\)), we use the impulse - momentum theorem, which states that the impulse \(J\) (the change in momentum) is given by \(J = F\times\Delta t\), where \(F\) is the force applied and \(\Delta t\) is the time over which the force is applied. To maximize \(\Delta p\) (since \(J=\Delta p\)), we need to maximize the product of force \(F\) and time \(\Delta t\).

• Option A: Hitting with as little force as possible will decrease the product \(F\times\Delta t\), so this is incorrect.
• Option B: Hitting for the smallest possible time will decrease the product \(F\times\Delta t\) even if the force is big, so this is incorrect.
• Option C: Hitting with the biggest possible force and for the longest possible time will maximize the product \(F\times\Delta t\), which maximizes the change in momentum.
• Option D: Since option C is correct, this is incorrect.

Answer:

C. Hit the ball with the biggest possible force for the longest possible time.