Question about universal gravitation

[Hannahj1]

Homework Statement

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 traveling upwards at 4.5km/s at this time.
a) what is the total energy of the booster at this time?
b) Will it return to earth?

Homework Equations

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

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.

 

[gneill]

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.

 

[Chestermiller]

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

 

[Hannahj1]

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.

thank you so much!