First slide

Gravitaional potential energy

Question

A satellite is projected with a velocity $\sqrt{1.5}$ times the orbital velocity just above the surface of earth. Initial velocity of the satellite is perpendicular to the surface of earth. The maximum distance of the satellite from surface of earth will be

Moderate

A

2 R_e
B

8 R_e
C

4 R_e
D

3 R_e

Solution

By energy conservation
$- \frac{G M m}{R} + \frac{1}{2} m \frac{1.5 G M}{R} = - \frac{G M m}{R + h}$
$\frac{1}{4 R} = \frac{1}{R + h} \Rightarrow h = 3 R$

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