Question

Maximum height reached by a particle fired with a speed equal to 50% of escape velocity from the earth surface is given by $R/x$. Find the value of $x$. ($R$ = radius of earth)

Answer 1

3

Answer 2

Using conservation of energy, the initial kinetic energy equals the change in potential energy: $\frac{1}{2}m(\frac{v_e}{2})^2 = \frac{mgh}{1+h/R}$. Substituting $v_e^2=2gR$, we get $\frac{mgR}{4} = \frac{mgh}{1+h/R}$. Solving for $h$ yields $h=R/3$. Since the height is given as $R/x$, we have $x=3$.