Newton's Law of Gravitation

Q: The Moon can be modelled as a sphere of radius of 1740km and mass 7.34X10^22 kg. A rocket of mass m is fired vertically from the surface of the Moon with speed 1.5km/s. It may be assumed that all forces on the rocket other than the gravitational attraction of the Moon can be ignored.

a) Find the speed of the rocket when it's at a height of 10km above the surface of the moon.

b) Find the maximum distance from the Moon's surface reached by the rocket.

For part a) I tried to use the formula F= (GMm)/(r^2) by intergrating it with the limites 1740 and 1750, and equated it to the integral of mv, but the answer was wrong, so could someone explain the method I should have used please?