# Calculate the Density of the planet

## Homework Statement

An astronaut lands on a new planet of radius R=3000km, and wants to measure its density. In order to do that, he drops a stone of unknown mass from the top of the space shuttle, which has a height of 92.5m and measures the time it takes it to reach the ground. t= 5s.
What is the density of the planet?

## Homework Equations

K=.5mv2
DeltaV= -GMm/Rf - (-GMm/Ri) where Rf and Ri are the radius of the planet and the radius of the planet + rocket height respectively.
K=delta V

## The Attempt at a Solution

I attempted to solve for the acceleration via kinematics.
I used .5at2=dY and found
a=2.72 m/s2.
Next, I calculated the final velocity using
I then proceeded to use my Energy equations in order to isolate big M. Unfortunately, my answer is negative and doesn't make sense.. Ehh, actually, the magnitude of it is within reason, but it being negative is what is getting me
answer= -3.77*10^23.. I don't think units cancel properly with what I did :/. Can anyone give me a pointer? I can do the rest if I can just calculate this mass.

What I did, was after I calculated the a from my kinematics,
I set $$\frac{G(bigM)m}{r2}$$=aplanetm
The little m's cancel leaving me with the ability to calculate M.

The problem now, is which r do I choose? I can choose R of the planet plus rocket height, or R of the planet. It shouldn't make a difference though because the planet's radius is
3*10^6m and the rocket is only 95m tall, correct?

Redbelly98
Staff Emeritus