Question

The escape speed of a projectile on the earth’ surface is 11.2 km –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 1

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

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)mv2f

From the law of conservation of energy, we have