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?

 

[HalfLostAndSearching]

I would like to clarify a few points about the problem before providing a response. First, it is important to define the variables and units used in the equations. In this case, the mass of the rocket and the planet, as well as the distance between them, should be specified. Additionally, the units for energy should also be stated (e.g. Joules).

Now, let's address the main question at hand. The angle at which the rocket should be fired in order to reach maximum height depends on the specific situation and cannot be determined solely from the given information. The equation provided only calculates the total energy of the system, but does not take into account other factors such as air resistance, atmospheric conditions, and the specific design and capabilities of the rocket. These factors can greatly affect the trajectory and maximum height of the rocket.

Furthermore, the statement that the answer is 900 is incorrect. The maximum height of the rocket would depend on the initial velocity and angle at which it is fired, as well as the factors mentioned above. It is possible that with a lower initial velocity, the rocket may reach a higher maximum height when fired at a different angle.

In conclusion, it is important to consider all the variables and factors at play in order to accurately determine the angle at which the rocket should be fired to reach maximum height. Simply relying on one equation and a given answer may not provide an accurate solution. As a scientist, it is important to thoroughly analyze and consider all aspects of a problem before providing a response.