Calc III Projectile Homework: Muzzle Speed at 30 Degrees w/500m Max Height

[undrcvrbro]

Homework Statement

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?

Homework Equations

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!

 

[rootX]

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

You are missing energy conservation.

 

[undrcvrbro]

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

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

 

[undrcvrbro]

Does anyone want to get me started in the right direction?

 

[Fwahnak]

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

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

What useful value does the vertical velocity take at max height?