Maximum height of a rocket

1. Sep 9, 2012

000

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

Unsure of where to start.

3. The attempt at a solution

None.

Last edited: Sep 9, 2012
2. Sep 9, 2012

voko

Kinetic energy.
Potential energy.
Work.

3. Sep 9, 2012

000

Could you clarify?

4. Sep 9, 2012

voko

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

5. Sep 9, 2012

Staff: Mentor

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?

6. Sep 9, 2012

000

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'.

7. Sep 9, 2012

Staff: Mentor

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?

8. Sep 9, 2012

000

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

9. Sep 10, 2012

Staff: Mentor

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).

10. Sep 10, 2012

voko

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

11. Sep 10, 2012

Indeed