Chapter 2.3, Problem 31P

Suppose that a rocket is launched straight up from the surface of the earth with initial velocity $v_0=\sqrt{2gR}$, where $R$ is the radius of the earth. Neglect air resistance.

Find an expression for the velocity $v$ in terms of the distance $x$ from the surface of the earth.

Find the time required for the rocket to go $240,000$ mi(the approximate distance from the earth to the moon). Assume that $R=4,000$ mi.