A body is projected vertically upwards from the surface of earth with a velocity sufficient enough to carry it to infinity. The time taken by it to reach height h is S .

Step-by-step solution

Applying energy conservation from ( 1   to   2 , 1 2   m · 2 GM R e - G M m R e = 1 2   m v 2 - G M m R + r ⇒ 1 2 m v 2 = G M m R + r ⇒ v = 2 G M R + r = d r d t ⇒   2 G M ∫ 0 t d t = ∫ R e R e + h ( R + r ) d r 2 G M · t = 2 3 ( R + r ) 3 2 R e R e + h t = 2 3 R e 3 2 GM 1 + h R e 3 2 - 1 G M R e 2 = g t = 1 3 2 R e   g 1 + h R e 3 2 - 1