Gravitation NCERT Solutions Class 11 Physics - Solved Exercise Question 8.18

Question 8.18:
The escape speed of a projectile on the earth’s surface is 11.2 km s–1. A body is projected out with thrice this speed. What is the speed of the body far away from the earth? Ignore the presence of the sun and other planets.
Solution:
Escape velocity of a projectile from the Earth, vesc = 11.2 km/s
Projection velocity of the projectile, vp = 3vesc
Mass of the projectile = m
Velocity of the projectile far away from the Earth = vf
Total energy of the projectile on the Earth = (1/2)mvp2 - (1/2)mvesc2
Gravitational potential energy of the projectile far away from the Earth is zero.
Total energy of the projectile far away from the Earth = (1/2)mvf2
From the law of conservation of energy, we have
(1/2)mvp2 - (1/2)mvesc2  =  (1/2)mvf2
vf = ( vp2 - vesc2 )1/2
= [ (3vesc)2 - vesc2 ]1/2
= √8 vesc
= √8 X 11.2  =  31.68 km/s

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