Question

The escape velocity of a projectile on the earths surface is $ 11.2\,\,km{{s}^{-1}} $ . A body is projected out with thrice this speed. The speed of the body far away from the earth will be:

• A. $ 22.4\,km{{s}^{-1}} $
• B. $ 31.7\,km{{s}^{-1}} $
• C. $ 33.6\,km{{s}^{-1}} $
• D. none of these

Answer 1

Answer: (B)

Key Idea : Applying conservation of energy. By law of conservation of energy $(U+K)_{\text {surface }}=(U+K)_{\infty}$
$\Rightarrow \quad-\frac{G M m}{R}+\frac{1}{2} m\left(3 v_{e}\right)^{2}=0+\frac{1}{2} m v^{2}$
$\Rightarrow -\frac{G M}{R}+\frac{9 v_{e}^{2}}{2}=\frac{1}{2} v^{2}$
Since, $\nu_{e}^{2}=\frac{2 G M}{R}$
$\therefore -\frac{v_{e}^{2}}{2},+\frac{9 v_{e}^{2}}{2}=\frac{1}{2} v^{2}$
$\Rightarrow v^{2} =8 \,v_{e}^{2} $
$\therefore v =2 \sqrt{2} \,v_{e}$
$=2 \sqrt{2} \times 11.2$
$=31.7 \,kms ^{-1}$