A somewhat tricky projectile problem

[musicfairy]

Homework Statement

A sping-loaded gun can firen a projectile to a height h if it is fired straight up. If the same gun is pointed at an angle of 45degrees from the vertical, what maximum height can now be reached by the projectile?

The Attempt at a Solution

The answer is h/2. I don't know how to get there. I tried by using one of the kinematics equations but it didn't work out. This is my attempt:

v_y = vsin(x)t + .5gt²

vy = v/sqrt(2)



This is what I tried to do. It's obviously wrong and I got stuck at that part. I'm not used to doing problems without numbers. If any of you have any tips on how to get better at them please share your tips.

 

[rock.freak667]

Well at the max height, the final vertical velocity is zero.

so if

$$v_y^2=u^y^2+2gs$$

what would be the height,s?