Projectile angle and maximum height

[ThomasMagnus]

At what projection angle will the range of a projectile equal its maximum height?


I am having a lot of trouble with this one. Is there any way to solve this question without using double angle identities?

I know that this should be the first step:

Max height when Vy=o
Vfy²=Voy² + 2(a)(dy)

0=(Vo² + 2(a)(d)

Range= Vo² sin2(theta)/g


I'm stuck here. Can anyone help me?

Thanks!

 

[gneill]

What's wrong with double angle identities? They can always be undone. What does sin(2θ) become?

You're on the right track. Solve for the maximum height of the trajectory and set it equal to the range. Be sure to keep track of what's the total velocity and what are components.