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. | Learn NCERT solution | Education portal Class 11 Physics | Study online Unit-8 Gravitation



Q.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.

 

 

Answer:-



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 = ( vp2vesc2 )1/2
= [ (3vesc)2vesc2 ]1/2
= √8 vesc
= √8 × 11.2  =  31.68 km/s.