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.

Explanation

Escape velocity of the projectile on the Earth.s surface `= v_(e) = 11.2 km s^(-1)`.
Velocity of projection of body = v = 3 v e.
Let v. be the velocity of the body far away from the earth. By the law of conservation of energy.
`(1)/(2)m(v.)^(2) = (1)/(2)m v^(2) - (1)/(2) m v_(e)^(2)`
`v. = sqrt(v^(2) - v_(e)^(2)) = sqrt((3v_(e))^(2) - v_(e)^(2))`
`= sqrt(8) v_(e) = sqrt(8) xx 11.2`
`= 31.68 km s^(-1)`