Question

The escape speed of any projectile on Earth's surface is 11.2 km/s. A body is projected with thrice this speed. What is the speed of the body far away from the earth? Ignore the presence of the sun & other planets.

• A. 31 km/sec
• B. 33.6 km/sec
• C. 27.8 km/sec
• D. 22.8 km/sec

Answer 1

The correct option is A 31 km/sec

Let the velocity of the body far away from the earth be $v_{\infty }$. The sum of kinetic and potential energy will be constant for the body.

Applying

K.E + PE = Constant
$\frac{1}{2}m{v}^2-\frac{GMm}{R_E}=\frac{1}{2}m{v}_{\infty }^2-0$
$\frac{1}{2}m(3v_e{)}^2-\frac{GMm}{R_E}=\frac{1}{2}m{v}_{\infty }^2$
$\frac{9m}{2}.\frac{2GM}{R_E}-\frac{GMm}{R_E}=\frac{1}{2}m{v}_{\infty }^2$
$v_{\infty }=\sqrt{8\frac{2GM}{R_E}}=\sqrt{8}{V}_e$
$=31km/sec$