# Tennis ball's final velocity without it's initial

1. Jun 1, 2014

### danyork

1. The problem statement, all variables and given/known data
Here is the question I'm trying to answer:

A tennis player hits a 1.45 kg tennis ball with a racket of mass 2.5 kg. If he hits the ball with a velocity of 7.5 m/s and then stops, what impulse did he imply on the ball? What is the ball’s velocity?

2. Relevant equations
Δpball = -Δpracket = mvi - mvf
ma initialva initial + mb initialvb initial = ma finalva final + mb finalvb final

3. The attempt at a solution
I was able to determine the impulse on the ball as 2.5 * 7.5, which is 18.75 kg m/s (ignoring sig figs for now). What I'm stuck on is how to determine the balls final velocity without the problem stating the initial velocity. Should I assume the initial is 0 m/s (this seems wrong). I'm thinking there has to be another formula to use, but I can't figure it out. Without knowing the ball's initial velocity or the time of impact I'm out of ideas.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jun 1, 2014

### danyork

Forgot to mention two things:
1. It's a little unclear, but the racket's final velocity is 0m/s.
2. I did search other forums and found some similar ones to this one, but none looking for the ball's final velocity without mentioning it's initial.
Thanks in advance for any help.

3. Jun 1, 2014

### dauto

It's implied that the initial velocity is zero.

4. Jun 1, 2014

### danyork

Okay, thank you dauto.

5. Jun 1, 2014

### haruspex

That's one monster of a tennis ball, about 26 times the standard mass.
Even so, if the mass of the racket exceeds the mass of the ball yet the racket is brought to rest by the impact then something very strange is going on. The KE has increased!

6. Jun 2, 2014

### tms

Don't assume that the ball's initial velocity is zero, but solve for it, using energy and momentum conservation. You can then use that value to find the ball's final velocity.

7. Jun 2, 2014

### haruspex

Yes, that makes more sense, but you have to assume the collision is perfectly elastic.

8. Jun 2, 2014

### tms

That's a pretty common assumption in introductory physics problems, especially those with three-pound tennis balls.