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The escape velocity of a projectile on the earth's surface is 11.2kms1. A body is projected out with thrice this speed. What will be the speed of the body far away from the earth, that is, at infinity? Ignore the presence of sun and other planets

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Solution

Escape velocity from Earth is vesc=11.2kms1
Projection Velocity = vp=3vesc
Mass of projectile m, is projected with velocity vf
Total energy of projectile on Earth = 12mvp212mvesc2
Gravitational potential energy far away from Earth is zero, so the total energy of projectile far away from the Earth will be = 12vf2
From the law of conservation of energy,
12mvp212mvesc2=12mvf2vf=vp2vesc2=3vesc2vesc2=8vescvf=8×11.2=31.68kms1

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