﻿ 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.  from Physics Gravitation Class 11 Manipur Board

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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.

Escape velocity of a projectile from the Earth, vesc = 11.2 km/s

Projection velocity of the projectile, vp = 3vesc

Mass of the projectile =

Velocity of the projectile far away from the Earth = v

Total energy of the projectile on the Earth = mvp2 - mvesc

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

Total energy of the projectile far away from the Earth = mvf

From the law of conservation of energy, we have

mvp2 - mvesc2  =   mvf
vf = ( vp2 - vesc)1/2

= [ (3vesc)2 - vesc2 ]1/2

= √8 vesc

= √8 × 11.2

=  31.68 km/s.
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The position co-ordinates of two particles of masses m1 and m2are (x1, y1, z1) and (x2, y2, z2) respectively. Find the coordinates of the centre of mass.

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