What Is the Angle of Initial Velocity for a Projectile at Half Maximum Height?

[Lmaonade]

Homework Statement

At half its maximum height, the speed of a projectile is three-fourth its initial speed. What is the angle of the initial velocity vector with respect to the horizontal

Homework Equations

any projectile equation

The Attempt at a Solution

?

 

[mgb_phys]

Split the total speed into a vertical and horizontal component.
u_horiz = V cos(angle) u_vertical = V sin(angle)
The horizontal component doesn't change and the vertical component obeys v^2 = u^2 - 2 g h

 

[Lmaonade]

okay so i tried splitting the horizontal and vertical components, but in the end and it doesn't accomplish anything because you get 2 unknown variables, also how would you account for the givens, such as, at half the max height you have 3/4 the initial velocity?

also i have tried using the equation V^2=V(o)^2 + 2 a x
from that i set V to (3/4 V(o))
g to (9.81) and
x to (x/2)
in the end that doesn't work out either??