Problem 1. (15 points) A spring gun has a spring of unknown force constant k. When the spring of the gun is initially compressed a distance of d = 0.200 meters from its natural length, and the gun is aimed vertically upward, a ball of mass 2.50 kg, stating from rest, is shot to a height of 0.500 meters above the end of the unstretched (and uncompressed) spring. See the figure below. Assume the spring has negligible mass, and ignore of resistance. Note: Position 1: the spring is compressed d = 0.200 meters and the ball is at rest Position 2: the spring has its natural length, i.e., not compressed nor stretched Position 3: the ball is at its maximum height (a) Calculate the value of the spring force constant k. (7 points) AV 0. 50 m 1= 0,2m NNNNNNNN NNNNNNNN 2 3 (b) What is the speed of the ball at position 2? (8 points)