The escape velocity of a projectile on the surface of earth is `11.2 kms^(-1)` . If a body is projected out with thrice this speed, find the speed of the body far away from the earth. Ignore the presence of other planets and sun.

Explanation

Here, `v_e = 11.2 kms^(-1) ` , velocity of projection of the body `v = 3v_e`. Let m be the mass of the projectile and `V_0` . be the velocity of the projectile when far away from the earth (i.e. out of gravitational field of earth). Then from the law of conservation of energy.
` 1/2 mv_0^2 = 1/2 mv^2 -1/2 mv_e^2`
`v_0 = sqrt(v^2 -v_e^2) = sqrt((3v_e)^2 - v_e^2)`
` = sqrt8 xx 11.2 = 31.68 kms^(-1)`