A body is projected vertically upwards from the surface of planet of radius R with a velocity equal

Question

A body is projected vertically upwards from the surface of planet of radius R with a velocity equal to $1 / 3^{	ext {rd }}$ the escape velocity for that planet. The maximum height attained by the body is\

Professor PC Thomas Classes · Answer

From energy conservation principle total energy at the time of projection is equal to the total energy at the highest point. $$ \begin{aligned} & -\frac{\mathrm{GMm}}{\mathrm{R}}+\frac{1}{2} \mathrm{mv}_{\mathrm{p}}^{2}=-\frac{\mathrm{GMm}}{\mathrm{R}+\mathrm{h}}+0 \ & \mathrm{v}_{\mathrm{p}}=\frac{1}{3} \mathrm{v}_{\mathrm{e}}=\frac{1}{3} \sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}} \end{aligned} $$