A body is projected vertically upwards from the surface of the Earth with an initial velocity v = gR , where R is the radius of the Earth and g is the acceleration due to gravity at the surface. The maximum height reached by the body from the surface of the Earth is:

Step-by-step solution

By the principle of conservation of mechanical energy, the loss in kinetic energy of the body equals its gain in gravitational potential energy. The initial kinetic energy of the body is: K = 1 2 mv^2 = 1 2 m( gR )^2 = 1 2 mgR The change in gravitational potential energy when the body reaches a maximum height h is: U = mgh 1 + h R Equating the loss in kinetic energy to the gain in potential energy: 1 2 mgR = mgh 1 + h R Cancelling mg from both sides: 1 2 R = hR R + h Cross-multiplying yields: R + h = 2h h = R Using