First slide

Gravitaional potential energy

Question

A projectile is fired vertically from the surface of earth with a speed $\sqrt{gR}$ . Where R is the radius of earth. How far above the earth’s surface would the projectile go?

Moderate

A

R
B

$\frac{R}{2}$
C

2R
D

$\frac{3 R}{2}$

Solution

Conserving energy, $\frac{1}{2} {mu}^{2} - \frac{GMm}{R} = - \frac{GMm}{R + h}$
$\Rightarrow \frac{1}{2} {(\sqrt{\frac{GM}{R^{2}} . R})}^{2} = \frac{GM}{R} - \frac{GM}{R + h} = \frac{GM . h}{(R + h) R^{}}$
Solving, h = R

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