Question

A racquetball strikes a wall with a speed of 30 m/s and rebounds in the opposite direction with a speed of 26 m/s. The collision takes 20 ms. What is the average acceleration of the ball during the collision with the wall?

Answer 1

The average acceleration of the ball during the collision with the wall is
`a=2,800m/s^(2)`

Step-by-step explanation:

Known Data

We will asume initial speed has a negative direction,
`v_(i)=-30m/s`, final speed has a positive direction,
`v_(f)=26m/s`,
`\Delta t=20ms=0.020s` and mass
`m_(b)`.

Initial momentum

`p_(i)=mv_(i)=(-30m/s)(m_(b))=-30m_(b)\ m/s`

final momentum

`p_(f)=mv_(f)=(26m/s)(m_(b))=26m_(b)\ m/s`

Impulse

`I=\Delta p=p_(f)-p_(i)=26m_(b)\ m/s-(-30m_(b)\ m/s)=56m_(b)\ m/s`

Average Force

`F=(\Delta p)/(\Delta t) =(56m_(b)\ m/s)/(0.020s) =2800m_(b) \ m/s^(2)`

Average acceleration

`F=ma`, so
`a=(F)/(m_(b))`.

Therefore,
`a=(2800m_(b) \ m/s^(2))/(m_(b)) =2800m/s^(2)`