Question

Maximum height reached by a rocket fired with a speed equal to 50% of the escape velocity from earth's surface is:

• A. R/2
• B. 16R/9
• C. R/3
• D. R/8

Answer 1

The correct option is C R/3

The body reaches maximum height when the kinetic energy of the body becomes zero.

$-\frac{GMm}{R}+\frac{1}{2}m{v}^2=-\frac{GMm}{R+H}$

$v=\frac{\sqrt{\frac{2GM}{R}}}{2}=\sqrt{\frac{GM}{2R}}$

Hence,

$-\frac{GMm}{R}+\frac{1}{2}m\frac{GM}{2R}=-\frac{GMm}{R+H}$

$-\frac{3GMm}{4R}=-\frac{GMm}{R+H}$

$H=\frac{R}{3}$