Maximizing Rocket Height: Calculating Gravitational Energy | Homework Statement

AI Thread Summary
To maximize the height of a rocket shot with a velocity less than escape velocity, the angle of launch relative to the horizon is crucial. The total energy equation indicates that the direction of launch does not affect the maximum height achieved, as it is determined solely by the initial velocity. However, the optimal angle for maximum height in projectile motion is typically 90 degrees, meaning the rocket should be fired straight up. The discussion emphasizes that since the rocket is not escaping Earth's gravity, it will follow a parabolic trajectory. Ultimately, launching at a 90-degree angle will yield the highest altitude for the given conditions.
Karol
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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
 
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Karol said:
A rocket is shot with velocity than the escape velocity

Greater than? Lesser than?
 
I fixed, smaller than
 
With the velocity less than escape velocity, the rocket executes projectile motion. So when is the height maximum?
 
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