Maximizing Rocket Height: Calculating Gravitational Energy | Homework Statement

[Karol]

Homework Statement

A rocket is shot with velocity smaller than the escape velocity. at what angle to the horizon should it be fired in order to reach maximum height.

Homework Equations

Total energy: $E=\frac{1}{2}mv^2-\frac{GMm}{r}$

The Attempt at a Solution

The equation isn't vectorial, it doesn't say anything about direction, so, i guess in any direction you shoot it it will reach the same height, but the answer is 90⁰

 

[PhysicoRaj]

A rocket is shot with velocity than the escape velocity

Greater than? Lesser than?

 

[Karol]

I fixed, smaller than

 

[PhysicoRaj]

With the velocity less than escape velocity, the rocket executes projectile motion. So when is the height maximum?