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

`implies` Suppose initial speed of body = v
Final speed of body = v.
From conservation of mechanical energy
Kinetic energy + potential energy of this body
on earth = kinetic energy + potential energy at infinity distance. `:. 1/2 mv^2 -(GM_Em)/(R_E)=1/2mv^2+0`
`:. 1/2 mv^2 -1/2 mv_e^2 =1/2 mv^2`
`" " [ :. v_e = sqrt((2GM_E)/(R_E))]`
`:. v^2 = v^2 -v_e^2 `
Here `v = 3v_e` and hence
`v = sqrt8 v_e`
`= (sqrt8)(11.2 km//s)`
`= 31.67 ~~31.7 km//s`