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 .

Question

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 &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; S .

Aicharya · Accepted Answer

Applying energy conservation from ( 1 &#160; to &#160; 2 , 1 2 &#160; m &#183; 2 GM R e - G M m R e = 1 2 &#160; m v 2 - G M m R + r &#8658; 1 2 m v 2 = G M m R + r &#8658; v = 2 G M R + r = d r d t &#8658; &#160; 2 G M &#8747; 0 t d t = &#8747; R e R e + h ( R + r ) d r 2 G M &#183; 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 &#160; g 1 + h R e 3 2 - 1

A body is projected vertically upwards from the surface of earth with a velocity sufficient enough to carry…

Solution