I figured out this homework problem, after many tries, but I'm confused about the correct final answer. Here's the question:
The rebounding ball, mass of 0.06 kg, traveling horizontally at 7.6 m/s, is caught by a player who brings it to rest. During the process, her hand moves back 0.60 m. What is the impulse received by the player?
I = Δp
I = FΔt
F = ma
The Attempt at a Solution
So in the end I just used I = Δp. I did I = (mvf) - (mvi) = (0.06)(0) - (0.06)(-7.6) = 0.456 kg⋅m/s.
Before I was using the kinematics equations to solve for the acceleration of the ball when it slowed down from 7.6 m/s to 0 m/s in the 0.6 m the player's hand moved when catching it. Then I used the acceleration to get the time taken for this process. Then I plugged the acceleration value and the mass of the ball into F = ma to find the force on the ball by the player's hand. Finally, I plugged in this force into I = Favg.Δt to find the impulse. But doing so I got 0.493 N⋅s, which was wrong.
Why is the answer solved without taking into account the distance traveled by the player's hand?