Question

A body is thrown vertically upwards with a velocity $4km{s}^{-1}$ from earth's surface. Up to what height will it go? Radius of the earth is $6400km$ and $g=10{ms}^{-2}$.

Answer 1

By law of conservation of energy,

The decrease in kinetic energy = increase in Gravitational potential energy

$\begin{array}{c}\frac{1}{2}m{v}^2=\frac{mgh}{1+\frac{h}{R}}\\ h=\frac{v^2}{2g-\frac{v^2}{R}}\\ h\frac{{\left(4\times {10}^3\right)}^2}{2\times 9.8-\frac{{\left(4\times {10}^3\right)}^2}{6.4\times {10}^6}}=9.35\times {10}^{5}m=935km\end{array}$