Classical Mechanics

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Relative Motion: Dropping Things on a Rocket


An astronaut is riding in a rocket that is accelerating upwards away from the surface of the Earth at $a_R = 14.2\:m/s^2$. A few minutes after takeoff the astronaut accidentally drops a pen. The pen takes $0.340\:s$ to fall $1.30\:m$ to the floor.

What is the altitude of the rocket in kilometers when the astronaut drops the pen? Ignore any affects of air resistance on the pen and take the mass and radius of the Earth to be $5.97\times 10^{24}\:kg$ and $6.37\times 10^6\:m$, respectively.