Question

The projectile motion is fired with velocity of magnitude vo at the angle feta. Find feta for which the maximum elevation of the projectile is twice its range

Answer 1

feta is a cheese, not much else. Theta is a Greek letter that is often used for an angle. But feta? it won't hold up more than about 30 degrees, and even then if falls down.

Vertical height=2*horiztal distance.

So vertical height first:

at the top, vertical velocity is zero.
vtop=vo*sinTheta-g t
or time to top is vo*sinTheta/g

then verticalmax height is
hmax=vo*sinTheta*vo*sinTheta/g

horizontal distance:
vo*cosTheta* vo sinTheta/g

then
vertical max=2*horizontal
(vo*sinTheta)^2 /g = 2*(vo^2 cosTheta*sinTheta)/g

or sintheta=2costheta

tan Theta=2
theta=arcTan2 or = 63.4349488 degrees

check all this.