A rogue band of colonists on the moon declares war and prepares to use a catapult to launch large boulders at the earth. Assume that the boulders are launched from the point on the moon nearest the earth. For this problem you can ignore the rotation of the two bodies and the orbiting of the moon.

a. What is the minimum speed with which a boulder must be launched to reach the earth?
Hint: The minimum speed is not the escape speed. You need to analyze a three-body system.
b. Ignoring air resistance, what is the impact speed on earth of a boulder launched at this minimum speed?