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## Homework Statement

A projectile is launched from the earth’s surface at initial speed v

_{i}at angle θ

_{0}with the

horizontal. When the projectile is at its maximum height h, it has half the speed it had

when it was at half its maximum height h/2

At what angle was the projectile launched?

## Homework Equations

## The Attempt at a Solution

I know that the velocity vector at the highest point is v

_{i}cosθ, and I know that the maximum height of the parabola is (v

_{i}sinθ)

^{2}/ 2g. At this point, I don't really know where to go. I'm not sure how to relate height and velocity together with what I know. I was doing this earlier and I tried to go further, but I just ended up with a lot of variable/trig function couples that don't make sense. I could take a picture of all the work I've done, but you wouldn't be able to follow it. I barely know what I tried.

You don't really have to answer it for me, just what should the next step be?