# Calc III: Projectile

1. Oct 1, 2009

### undrcvrbro

1. The problem statement, all variables and given/known data
A gun if fired with an angle of elevation of 30 degrees. What is the muzzle speed if the maximum height of the shell is 500 m?

2. Relevant equations

3. The attempt at a solution
I haven't gotten very far at all. I'm not sure how to even start this one. I know that because the angle is 30 degrees:

$$\frac{1}{2}(\sqrt{3}i + k)$$

The above is the only bit of info that I'm sure I should use in this problem. The rest of this is just to show you what I actually know....I'm not sure if the following will help me solve this problem or not...

$$\\a(t) =-gi$$

Sorry If I'm not giving you much to work with. Any thing to help get me started would be much appreciated!

2. Oct 2, 2009

### rootX

It is a simple physics problem. Why don't treat it as a physics problem then?

You are missing energy conservation.

3. Oct 2, 2009

### undrcvrbro

I can't. If I used a Physics equations for a calculus homework my prof would probably be worried about my state of mind.

4. Oct 2, 2009

### undrcvrbro

Does anyone wanna get me started in the right direction?

5. Oct 2, 2009

### Fwahnak

Forget about the actual values of hight, velocity ect to begin with.

Set about working out the of max hight of a trajectory in terms of \theta and the initial velocity. Max hight is dependent only on the verticle component of the initial velocity. clearly the verticle movement of the projectile is subject to negitive accelleration due to gravity a=-g. integrate this equation (remember your intial verticle velocity?) and you have and equation for the verticle component of velocity.

What useful value does the verticle velocity take at max hight?