1. Usually, we do not walk or even stand on a lightweight boat or raft because of the danger of falling into the water. If you have ever stepped off a small boat onto a dock, however, you have probably noticed that the boat moves away from the dock as you step toward the dock or out of the boat. A heavy dog running on a long lightweight raft presents a similar situation. At first, the raft and the dog are at rest with respect to the water (see figure A below) so that

v_i= 0.

The dog then runs on top of the raft at

v_d=v_d

with respect to the water (see figure B below). The dog hasone sixththe mass of the raft. Find an expression for the velocity of the raft after the dog began running. (Use the following as necessary:v_d.)

2.