# Average Velocity During a Collision

1. Homework Statement

A tennis ball has a mass of 0.057 kg. A professional tennis player hits the ball hard enough to give it a speed of 50 m/s (about 112 miles per hour.) The ball moves toward the left, hits a wall and bounces straight back to the right with almost the same speed (50 m/s). As indicated in the diagram below, high-speed photography shows that the ball is crushed about 2 cm at the instant when its speed is momentarily zero, before rebounding. Assume that the large force the ball exerts on the wall is approximately constant during contact.

What is the average speed of the ball during the period from first contact with the wall to the moment the ball's speed is momentarily zero?

2. Homework Equations
DeltaP=Fnet*DeltaT
rFinal=rInitial+Vavg*DeltaT

3. The Attempt at a Solution

I'm not sure how to find this. I could find the avg velocity if I had the time it took to bring the ball to a stop, but that's the next question. Any help is greatly appreciated.

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berkeman
Mentor
They say the slow-down force is constant. What does that tell you about the deceleration? What equation would you then use to express the velocity as a function of time? And what operation would you do to that v(t) function to figure out the average v?

What does that tell you about the deceleration?
That deceleration is constant over the time it takes to come to a stop

What equation would you then use to express the velocity as a function of time?
Vavg = deltaX/deltaT Is that what you mean? If so, I dont know deltaT...

Ok, I got the speed:25m/s It was Vi-Vf/2...too easy. I also have the time: .0008 sec. Now I need to find the force. There is an example in my book dealing with a person running into a wall. The equation they use is
F(x) = |mass*Vavg/deltaT|
I tried that but it didn't give me the right answer.

berkeman
Mentor
Well, F=ma, and you have the deceleration already, and the mass, right? Does that method give you the right answer?