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## Homework Statement

A rocket accelerates to speed v

_{0}near the earth's surface,and then coasts upwards. Show that if

v

_{0}= 2sqrt(gR)

where R is the Earth's radius, then very far from the earth the rockets speed will be

v = sqrt(2gR)

## Homework Equations

The only equations I have thought of that may help are:

Escape Velocity:

v = sqrt(2GM/R)

Gravitational potential energy:

U= -GMm/r

## The Attempt at a Solution

I have attempted using energy conservation and solving for v, however the answer appears far from that required.

This lead me to think that perhaps linear approximation may be required but I am unsure how I would apply (1+x)

^{n}= 1+nx for x<<1 in this problem.