A rocket of mass $M$ is launched vertically from the surface of the earth with an initial speed $V$. Assuming the radius of the earth to be $R$ and negligible air resistance, the maximum height attained by the rocket above the surface of the earth is
A rocket of mass $M$ is launched vertically from the surface of the earth with an initial speed $V$. Assuming the radius of the earth to be $R$ and negligible air resistance, the maximum height attained by the rocket above the surface of the earth is
$R/\left( {\frac{{gR}}{{2{V^2}}} - 1} \right)$
$R\,\left( {\frac{{gR}}{{2{V^2}}} - 1} \right)$
$R/\left( {\frac{{2gR}}{{{V^2}}} - 1} \right)$
$R\left( {\frac{{2gR}}{{{V^2}}} - 1} \right)$
A rocket of mass $M$ is launched vertically from the surface of the earth with an initial speed $V$. Assuming the radius of the earth to be $R$ and negligible air resistance, the maximum height attained by the rocket above the surface of the earth is
$\Delta K.E. = \Delta U$
$ \Rightarrow \,\,\frac{1}{2}M{V^2} = G{M_e}M\,\left( {\frac{1}{R} - \frac{1}{{R + h}}} \right)$…(i)
Also $g = \frac{{G{M_e}}}{{{R^2}}}$…(ii)
On solving (i) and (ii) $h = \frac{R}{{\left( {\frac{{2gR}}{{{V^2}}} - 1} \right)}}$
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