A rocket starts vertically upwards with speed \( v_{0} \). Show that its speed \( v \) at a heig...

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A rocket starts vertically upwards with speed \( v_{0} \). Show that its speed \( v \) at a height \( h \) is given by
\[
v_{0}^{2}-v^{2}=\left[(2 g h)\left(1+\frac{h}{r}\right)\right]
\]
Where \( R \) is the radius of the earth. Hence deduce the maximum height reached by a rocket fired with speed equal to \( 90 \% \) of escape velocity.
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