Question

A boy hits a baseball with a bat and imparts an impulse I to the ball. The boy hits the ball again with the same force, except that the ball and the bat are in contact for twice the amount of time as in the first hit. The new impulse equals:

• A. half the original impulse
• B. the original impulse
• C. twice the original impulse
• D. four times the original impulse

Answer 1

Answer: (C)

twice the original impulse

Answer 2

Impulse ($I$) is defined as the change in momentum ($\Delta p$) or the integral of force ($F$) over time ($\Delta t$): $I = \Delta p = \int F dt$. If the force is constant, $I = F \Delta t$. Let the original impulse be $I_1 = F \Delta t_1$. In the second hit, the force $F$ is the same, but the contact time is doubled, so $\Delta t_2 = 2\Delta t_1$. The new impulse is $I_2 = F \Delta t_2 = F (2\Delta t_1) = 2 (F \Delta t_1) = 2I_1$. Therefore, the new impulse is twice the original impulse.