1) The centers of two bowling balls are positioned 1 meter apart in intergalactic space (ie so that gravitational effects from other sources are negligible). On Earth, one ball weighs 12 lbs (5.443 kg) and the other ball weighs 10 lbs (4.536 kg). Each ball is 8.5 inches (0.216 m) in diameter.
a) How long will it take for the balls to collide?
b) How far will each ball have traveled at the point of impact?
2) In a different part of intergalactic space, 10 bowling pins are positioned in a typical triangular arrangement with the centers of the 3 corner pins located at the apices of an equilateral triangle measuring 36 inches (0.914 m) on a side. A bowling ball is then positioned with the center of the bowling ball 60 feet (18.288 m) from the center of the closest pin. On Earth, the bowling ball weighs 16 lbs (7.257 kg) and each pin weighs 3.5 lbs (1.588 kg). (In this problem, assume the position of each pin to be fixed [ie so that neither the gravitational force of its neighbors nor of the approaching ball causes a change in its position]. Also, the diameters of the bowling ball and pins can be disregarded).
a) How long will it take for the bowling ball to strike the closest pin?
b) What will be the velocity of the ball at the time of impact?
Note: Just like in physics class, please show your calculations (ie not just the answer).