The escape velocity from the surface of earth is v e . A body is projected with velocity 3 v e . With what constant velocity will it move in the inter planetary space?

Step-by-step solution

If v be the velocity in the inter planetary space and U i ,   U f initial and final PE Then, by the law of conservation of energy, U i + K i = U f + K f - G M e m R e + 1 2 m 3 v e 2 = 0 + 1 2 m v 2 - G M e R e + 9 2 v e 2 = 1 2 v 2 ⇒    - 2 G M e R e + 9 V e 2 = v 2 ⇒    - 2 g R e 2 R e + 9 v e 2 = v 2    ∵ G M e = g R e 2 - 2 g R e + 9 × 2 g R e = v 2           ∵ v e 2 = 2 g R e 16   g R e = v 2 ⇒    v =