Dynamics_Part50

Dynamics_Part50 - Problem Set 7 Problem 2 Problem A man and...

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Problem Set 7: Problem 2. Problem: A man and a woman are standing at opposite ends of a small boat, ready to take turns diving into the water. The mass of the boat is M , while that of the man and woman is 3 5 M and 2 5 M , respectively. The boat is initially at rest. When each dives in opposite directions parallel to the boat’s centerline, his or her speed relative to the boat is V . Determine the velocity of the boat after both have dived under the following conditions. (a) The woman dives first, followed by the man. (b) The man dives first, followed by the woman. Solution: To solve, we observe that there are no external forces acting. This tells us that momentum is conserved when each person dives. We take care to write all velocities as absolute velocities. Also, we define the x axis to lie on the horizontal. (a) At the moment when the woman dives, the boat is at rest. Since her speed relative to the boat is V , then her absolute velocity after she dives is V i . Letting v 1 denote the velocity of the boat and the man (who hasn’t dived yet), momentum conservation tells us that
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