First slide

Gravitaional potential energy

Question

The escape velocity of a projectile on the earth's 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 :

Moderate

A

22.4 km s^-1
B

31.7 km s^-1
C

33.6 km s^-1
D

none of these

Solution

$\begin{array}{l} - \frac{GMm}{R} + \frac{1}{2} m {(3 v_{e})}^{2} = 0 + \frac{1}{2} {mv}_{\infty}^{2} \\ \Rightarrow v_{\infty} = 33 .6 km / s \end{array}$

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