# Find the largest initial velocity

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1. Jan 25, 2016

### CGI

1. The problem statement, all variables and given/known data

2. Relevant equations
I know that this could be solved through kinematics.

3. The attempt at a solution

I thought that I could use the range equation to solve for Vo, but since there is an initial height, I don't think that could work. I thought that maybe I could use the height of a projectile equation

30 = 3 + (Vo^2sin^2(78)/(2g)) but the numbers don't work out for me.

I would really appreciate the help right now!

2. Jan 25, 2016

### cnh1995

You should not consider the initial height of 3ft. For the ball to not hit the ceiling, it's maximum height should be equal to the vertical distance between ceiling and the point of projection. Also, make sure you convert 'g' into ft/s2.

3. Jan 25, 2016

### Staff: Mentor

I notice that the problem doesn't mention whether the serve has to be a good one or not (i.e., it doesn't specify that it needs to make it over the net, or land inside the opposing team's court area). I think that losing those criteria would make things much easier

4. Jan 25, 2016

### CGI

Oh okay. You're right that would definitely help. Okay then, for example, if it needed to get to Point B, could I say

30 = Vo^2sin^2theta/2g ?

5. Jan 25, 2016

### PeroK

You were right the first time! Ignore the first part of post #2 and put the 3 back in.

I wouldn't worry about the net and the court just yet. Find the maximum $v_0$ and then check the trajectory. If it turns out to be a foul serve, then too bad, you'll have to start again. But, you might hope that doesn't happen.

6. Jan 25, 2016

### CGI

Okay, I get that V initial = 42.63, but that doesn't seem like a reasonable answer..I think

7. Jan 25, 2016

### PeroK

Why not? That'll be ft/s I take it?

8. Jan 25, 2016

### CGI

After looking up some average volley ball serves, I guess it's actually not too far fetched. And yes, that's in ft/s

9. Jan 25, 2016

### PeroK

If you want, you could work out whether the serve makes it over the net. I may have been too optimistic in my earlier post!

10. Jan 25, 2016

### Ray Vickson

What is your numerical answer? Why do you think it is wrong?

As far as I can see your equation is correct, and as long as you are careful to use units consistently you ought to get the right answer.

Note added in edit: your post containing the numerical solution (in fact, all of posts # 4, 5, 6, 7, 8, 9) appeared on my screen only after I pressed the 'enter' key; that type of thing happens to me a lot on this Forum. My answer agrees with yours.

11. Jan 25, 2016

### CGI

Awesome! Thanks everyone! You really helped me understand this!