Question

The escape speed of a projectile on the earth’s surface is 11.2 km s–1. A body ofmass 200kg is projected out with a speed of 44.8km/s from the surface of earth. What is the speed of the body far away from the earth? Ignore the presence of the sun and other planets.

Answer 1

Explanation:

Escape velocity of a projectile from the Earth, v

esc

=11.2 km/s

Projection velocity of the projectile, v

p

=3v

esc

Mass of the projectile =m

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

f

Total energy of the projectile on the Earth =

2

1

mv

p

2

−

2

1

mv

esc

2

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

Total energy of the projectile far away from the Earth =

2

1

mv

f

2

From the law of conservation of energy, we have

21mvp2 − 21 mv esc2

= 21 mvf 2v f

= v p2 −v esc

=8 vesc = 8 ×11.2

=31.68 km/s