The escape velocity of a body on the earth surface is 11.2 km/s. If the same body is projected upward with velocity 22.4 km/s, the velocity of this body at infinite distance from the centre of the earth will be: [2023]

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Solution

Q.
The escape velocity of a body on the earth surface is 11.2 km/s. If the same body is projected upward with velocity 22.4 km/s, the velocity of this body at infinite distance from the centre of the earth will be: [2023]

1 $11.2 \sqrt{2}$ $km/s$

2 Zero

3 $11.2$ $km/s$

4 $11.2 \sqrt{3}$ $km/s$

Ans.
(4)

The velocity at infinite distance when speed of projection and escape velocity are given, $v_{\infty}^{2} = v^{2} - v_{e}^{2}$

where $v$ is projection velocity

$v_{e}$ is escape velocity. Given, $v = 2 v_{e}$

So, $v_{\infty} = \sqrt{{(2 v_{e})}^{2} - v_{e}^{2}}$ $;$

$v_{\infty} = \sqrt{3} v_{e} = 11.2 \sqrt{3}$ $km / s$

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