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  3. Physics
  4. body is projected vertically upwards from the surface of the earth with a velocity equal to half the escape velocity. If R is the radius of the earth, maximum height attained by the body from the surface of the earth is

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Q. body is projected vertically upwards from the surface of the earth with a velocity equal to half the escape velocity. If $R$ is the radius of the earth, maximum height attained by the body from the surface of the earth is

BITSATBITSAT 2009

Solution:

Applying conservation of mechanical energy,
$\frac{1}{2} m\left(\frac{v_{e}}{2}\right)^{2}=\frac{m g h}{1+\frac{h}{R}} $
or $ \frac{v_{e}^{2}}{8}=\frac{g h}{1+\frac{h}{R}} $
ог $ \frac{2 g R}{8}=\frac{g h}{1+h / R} \ldots$ (i)
$\left(\because v_{e}=\sqrt{2 g R}\right)$
On solving Eq. (i), we get $h=\frac{R}{3}$.