# Homework Help: Question about universal gravitation

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1. Jul 16, 2015

### Hannahj1

1. The problem statement, all variables and given/known data
A piece of an empty rocket booster fuel tank (mass 45 kg) is ejected from a rocket that is 2100 km above the Earth's surface. It is travelling upwards at 4.5km/s at this time.
a) what is the total energy of the booster at this time?

2. Relevant equations
Total mechanical energy = ½mv^2 - GMm / r

3. The attempt at a solution
for a, should i use kinetic and potential energy and plug in values? like find the total mechanical energy
and for b, you find the total mechanical energy if you didnt have to do that for a, then if the value is positive it won't return to earth but if its negative, it will.

2. Jul 16, 2015

### Staff: Mentor

Hi Hannahj1, Welcome to Physics Forums!

Yes, it looks like they're looking for the total mechanical energy in part (a).

Yes, the total mechanical energy is diagnostic of whether or not a given orbit is bound or unbound, as you've stated.
You also have the option of determining the escape velocity at the given distance and comparing it to the booster's speed.

3. Jul 16, 2015

### Staff: Mentor

Are you saying that, if your answer to a is positive, it won't return and if your answer to a is negative, it will?

Chet

4. Jul 16, 2015

### Hannahj1

thank you so much!!!