Question

The escape velocity of a body on the earths surface is $V_E$. A body is thrown up with a speed $\sqrt{5}{V}_E$ . Assuming that the sun and planets do not influence the motion of the body, velocity of the body at infinite distance is :

• A. $0$
• B. $V_E$
• C. $\sqrt{2}{V}_E$
• D. $2V_E$

Answer 1

Answer: (D)

$2V_E$

Potential energy on surface of earth,
$P.E=-GMm/R=1/2m{v}_e^2$
By Energy conservation,
$P.E+1/2m{v}^2=1/2M{v}_{inf}^2$
Thus, $v_{inf}=2v_e$