Question:
The initial velocity $v_{i}$ required to project a body vertically upward from the surface of the earth to reach a height of $10 \mathrm{R}$, where $\mathrm{R}$ is the radius of the earth, may be described in terms of
escape velocity $v_{\mathrm{e}}$ such that $v_{i}=\sqrt{\frac{x}{y}} \times v_{\mathrm{e}}$. The value of $x$ will be________.
Solution:
$\frac{-\mathrm{GMm}}{11 \mathrm{R}}=\frac{-\mathrm{GMm}}{\mathrm{R}}+\frac{1}{2} \mathrm{mv}^{2}$
$v=\sqrt{\frac{20 G M}{11 R}}$
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