# Homework Help: Ball Velocity Problem

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1. Feb 17, 2015

### mathguy2

1. The problem statement, all variables and given/known data
A player swinging a tennis racket comprises a very heavy flat object (the racket-arm body combination) which makes a head-on collision with a very light object (the 2 ounce ball). The ball leaves the racket according to the formula:

Vball = ε × Vracket

The United States Tennis Association imposes a rule on ball manufacturers:

σ = 1.5

If the racket is moving at 60 mph, how fast does the ball come off the racket? How fast would a player have to swing the racket in order for the serve to come off the racket at 120 mph? A superball will come off a heavy racket with

ε = 1.9

How fast does it come off a racket moving at 70 mph?

2. Relevant equations
All are stated.

3. The attempt at a solution

I'm having trouble conceptualizing this problem. In addition, the added information, σ = 1.5 confuses me because that symbol, σ, appears nowhere in the equation. Also, how many solutions are required? 3? The way I see it, I need to see how fast the ball comes off the racket if the racket is moving at 60mph (solution 1). I have to see how fast a player would have to swing the racket in order for the serve to come off the racket at 120 mph (solution 2). And I have to figure out how fast the ball comes off a racket moving at 70 mph (solution 3).

The added information about the "superball" is really confusing me as well. Is the weight of the ball 1.9 or is the weight of the ball 2.0? I'm very confused about the constants I should be using.

So for instance, for the first part of the question: "If the racket is moving at 60 mph, how fast does the ball come off the racket?"

Vball = ε × Vracket

Vball = ε × 60

but what is E? is it 1.5, or 2 oz?

Last edited: Feb 17, 2015
2. Feb 17, 2015

### haruspex

The only way I can make sense of the question is to suppose that ε and σ mean the same.

3. Feb 17, 2015

### mathguy2

But if they're the same why are there different values ? That's the problem exactly as it's written, and I agree, it makes no sense.

Perhaps this information: "The United States Tennis Association imposes a rule on ball manufacturers:

σ = 1.5"

is a red herring? Cruel, but possible?

4. Feb 17, 2015

### haruspex

The first is for a tennis ball, the second for a superball.

5. Feb 17, 2015

### mathguy2

So then for: "If the racket is moving at 60 mph, how fast does the ball come off the racket?"

Vball = ε × Vracket

Vball = ε × 60

Vball = 1.5 x 60

Vball = 90mph if the racket moves at 60mph?

6. Feb 17, 2015

### haruspex

I have no better suggestion. You said the other questions were easy. If the above is correct, does it seem about the right level of difficulty?

7. Feb 17, 2015

### mathguy2

It seems too remedial, but when working through all three plug and chug solutions, the numbers seem to be accurate representations of what would likely occur. I think you're all correct, though. The wording of the problem is just ambiguous to a certain extent, and I think it lends itself to confusion and perhaps overthinking. The wording, "2 oz ball" early in the problem was confusing because I kept thinking I had to use that constant, but I think its just poor writing to a certain extent. The "2 oz" ball just refers to the entire problem, I guess, where the ball is always less than 2 oz's in every formula.

Solution 1: Vball = 90mph if the racket moves at 60mph.

Solution 2: Vracket = 80mph if the serve travels at 120 mph

Solution 3 (superball): Vball = 133 mph w/ superball and racket speed of 70mph

8. Feb 17, 2015

### mathguy2

I appreciate the replies very much, though, because I would've sat here and squinted at this problem for a few hours (I wish that were hyperbole, but it isn't).