Question

A projectile is fired vertically from the earth's surface with an initial speed of $10$ km/s.Neglecting air drag, how far above the surface of earth will it go ?

Answer 1

From energy conservation, since the velocity will be 0 at highest point,

$\frac{1}{2}m{\left(10000\right)}^2-\frac{GMm}{R}=-\frac{GMm}{d}$

$\frac{{10}^8}{2}-\left(9.8\right)\left(6400000\right)=-\left(9.8\right)\frac{{\left(6400000\right)}^2}{d}$

$d\approx 2.5\times {10}^{7}m$

Answer is $2.5\times {10}^{7}m$.