The 445-kg ram of a pile driver is designed to fall 2.21 m from rest and strike the top of a 261-kg pile partially embedded in the ground. The deeper the penetration, the greater is the tendency for the ram to rebound as a result of the impact. Calculate the velocity v of the pile immediately after impact for the following three conditions: (a) initial resistance to penetration is small at the outset, and the ram is observed to move with the pile immediately after impact; (b) resistance to penetration has increased, and the ram is seen to have zero velocity immediately after impact; (c) resistance to penetration is high, and the ram is seen to rebound to a height of 88 mm above the point of impact. Why is it permissible to neglect the impulse of the weight of the ram during impact