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The escape velocity of the earth is “v”. If an object is thrown vertically upwards with a velocity “kv”, what is the speed of the object at infinity?

The escape velocity of the earth is “v”. If an object is thrown vertically upwards with a velocity “kv”, what is the speed of the object at infinity? Correct Answer v(k2-1)1/2

From the law of conservation of energy, we have; (m x (kv) 2)/2 – (G x M x m)/R = (m x p2)/2 m = Mass of object M = Mass of earth R = Radius of the earth p = Velocity of the object at infinity (kv)2/2 –(g x R) = p2/2 (kv)2/2 – v2/2 = p2/2; v = (2 x g x R) ½ (k2-1)v2 = p2 Therefore; p = v(k2-1) 1/2.

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