Question

Find an expression for the escape velocity of a body when projected from the surface of the earth. Show that the escape velocity from the earth's surface is about 11-2 km/sec.​

Answer 1

Answer:

31.68 km per second

explanation

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

Let velocity of the projectile far away from the Earth=vf

Total energy of the projectile on the Earth =21mvp2−21mvesc2

Gravitational potential energy of the projectile far away from the Earth is zero.

Total energy of the projectile far away from the Earth =21mvf2

From the law of conservation of energy, we have

21mvp2−21mvesc2=21mvf2

vf=vp2−vesc2

     =8vesc

     =8×11.2

     =31.68 km per second

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