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Question

A rocket coasts in an elliptical orbit around Earth. To attain the greatest amount of KE for escape for a given amount of fuel, should it fire its engines to accelerate forward when it is at the apogee or at the perigee? (Hint: Let the formula $F d=\Delta \mathrm{KE}$ be your guide to thinking. Suppose the thrust $F$ is brief and of the same duration in either case. Then consider the distance $d$ the rocket would travel during this brief burst at the apogee and at the perigee.)

Solution

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Kinetic energy is a product of mass of an object and its velocity squared. This means that in equation ' $Fd=\Delta E_k$ ' distance satellite will travel during a short burst is proportional to the difference in velocity $\textbf{squared}$ .