A particle is thrown vertically upwards with velocity 11.2 ~km ~s ⁻¹ from the surface of earth. Calculate its velocity at height 3 R . Where R is the radius of earth.

Step-by-step solution

Let a particle of mass m is thrown vertically upward with velocity v . Let its velocity be v^ at a height 3 R from the surface of the earth. According to the conservation of energy, 1 2 m v^2- G M m R = 1 2 m v^ 2 - G M m (R+3 R) v^2- 2 G M R =v^ 2 - 2 G M 4 R v^2-v^ 2 = -2 G M 4 R + 2 G M R = 6 4 G M R v^ 2 =v^2- 6 4 G M R v^ 2 = (11.2)^2- 3 2 g R ( g= G M R^2 )= (11.2)^2- 3 2 9.8 6400 1000 = (11.2)^2-(94.08) =5.6 ~km ~s ⁻¹