- #1

Benjamin Fogiel

- 2

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## Homework Statement

A rocket burns out at an altitude h above the Earth's surface. Its speed v

_{0}at burnout exceeds the escape speed v

_{esc}appropriate to the burnout altitude. Show that the speed v of the rocket very far from the Earth is given by v=(v

_{0}

^{2}-v

^{2}

_{esc})

^{1/2}

## Homework Equations

KEf-KEi=Ui-Uf

## The Attempt at a Solution

I plugged in the values of kinetic and potential energies:

(m

_{1}v

^{2})/2 - (m

_{1}v

_{0}

^{2})/2 = (-Gm

_{1}m

_{2})/r

_{1}+ (Gm

_{1}m

_{2})/r

_{2}

Simplified to get:

v

^{2}=(-2Gm

_{2})/r

_{1}+ (2Gm

_{2})/r

_{2}+ v

_{0}

^{2}

Im not sure where to go from here