A 0.10kg dart is fired horizontally at the center of a 0.80kg vertically hanging block, sticking to it. The system reaches a maximum height, h, of 0.20m above the collision point. Find:
a) The velocity of the dart - block system just after the collision
b) The velocity of the dart before collision
c) The energy lost during the collision
d) If the dart gains its speed due to a spring system that is initially compressed 0.05m from its equilibrium position, determine the spring constant.
e) If the dart didn't stick to the block, but instead fell vertically after collision, would the initial velocity of the dart have to be greater, less than, or equal to the velocity that was found in part (b)? Justify.