# Maximum height of a rocket

## Homework Statement

A rocket is launched at a planet of 600km radius, 5.29e22 kg mass, and 9.8068 m/s^2 surface gravity such that it reaches a maximum height 'h' with work 'x'. What is the value of 'x'? Ignore air resistance, and gravity is dependent on height.

## Homework Equations

Unsure of where to start.

## The Attempt at a Solution

None.

Last edited:

Kinetic energy.
Potential energy.
Work.

Kinetic energy.
Potential energy.
Work.

Could you clarify?

Do you know how all these are interrelated? Could you apply that relation to your problem?

gneill
Mentor

## Homework Statement

A rocket is launched at a planet of 600km radius, 5.29e22 kg mass, and 9.8068 m/s^2 surface gravity such that it reaches a maximum height 'h' if it undergoes a constant acceleration of 'x' m/s^2. Ignore air resistance, and gravity is dependent on height.

## Homework Equations

Unsure of where to start.

## The Attempt at a Solution

None.

Ask yourself, "at what height will it stop accelerating?" The question statement seems to indicate "never". If it always accelerates, what's the maximum height?

Ask yourself, "at what height will it stop accelerating?" The question statement seems to indicate "never". If it always accelerates, what's the maximum height?

Sorry, there was a mistake in the question. What I meant to say was how much work must be done in order achieve height 'h'.

gneill
Mentor
Sorry, there was a mistake in the question. What I meant to say was how much work must be done in order achieve height 'h'.

That's quite a departure from the original statement of the problem :uhh:

What do you know about the relationship between work and potential energy?

How does gravitational potential energy relate to the position of the rocket?

That's quite a departure from the original statement of the problem :uhh:

What do you know about the relationship between work and potential energy?

How does gravitational potential energy relate to the position of the rocket?

The gravitational potential energy is dependent on the square of the height, correct?

gneill
Mentor
The gravitational potential energy is dependent on the square of the height, correct?

Nope. There are two important relationships for gravitational potential energy that you should be familiar with. The first is for the potential when the field is assumed to be uniform and constant, such as in the region close to the surface of the Earth (in reality it is thus just a very good approximation). The second is the actual Newton's Law version which does not make an approximation.

1) ##PE = mgh~~~~~~~~## For close to the Earth's surface

2) ##PE = \frac{G M}{r}~~~~~~~~## In general for point masses (or ones that behave so)

The second form must used when the change in radial distance is significant (i.e. gravity depends upon height).

2) ##PE = \frac{G M}{r}~~~~~~~~##

This must be ##PE = -\frac{G M m}{r}##

gneill
Mentor
This must be ##PE = -\frac{G M m}{r}##

Indeed 