he adventurous robot M.A.N.D.I. is orbiting Saturn’s moon Dione. She wants to cause an impact with themoon to kick up some of th
e surface dust so that she can do a spectral analysis of it. She tosses a steel ball bearing inthe opposite direction of her orbital velocity with just the right impulse to make the ball come to a dead stop. That’sthe back story. The actual problem starts here: The ball, starting with zero velocity, falls straight down to the surfaceof the moon. If the moon has a radius of5.61×103m and a mass of1.10×1021kg, and if the ball bearing starts at analtitude of2.73×103m above the surface of the moon, how fast will it be going when it hits the surface? Note thatthe gravitational constantG= 6.67408×10−11N m2/kg2.
When there are two bodies, a and b, whose velocities measured by a third observer (in this case, the ground) are and respectively, the relative velocity of B with respect to A is given by:
Thus, the velocity of the girl relative to the lawnmower is:
