A projectile is projected with velocity k v e in vertically upward direction from the ground into space ( v e is the escape velocity and k

Question

A projectile is projected with velocity k v e in vertically upward direction from the ground into space ( v e is the escape velocity and k < 1 ) . If air resistance is considered to be negligible then, the maximum height, from the centre of the earth, to which it can go will be ( R is the radius of the earth)

TestHub · Accepted Answer

Kinetic energy = potential energy 1 2 m k v e 2 = m g h 1 + h R 1 2 m k 2 2 g R = m g h 1 + h R h = R k 2 1 - k 2 Height of projectile from the earth surface = h Height from the centre = r = R + h = R + R k 2 1 - k 2 On solving, r = R 1 - k 2

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