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Unformatted text preview: 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 M and 2 M , 5 5 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 v1 denote the velocity of the boat and the man (who hasn't dived yet), momentum conservation tells us that 0= 3 2 M (-V i) + M + M 5 5 v1 = v1 = 8 2 M v1 = M V i 5 5 1 Vi 4 When the man dives, his speed relative to the boat is V and he's moving in the positive x direction. Since the boat is moving at a speed of 1 V in the positive x direction, the man's absolute velocity at the moment 4 he dives is 5 V i. Denoting the velocity of the boat by v2 , momentum conservation tells us that 4 8 M 5 1 Vi 4 = 3 M 5 5 V i + M v2 4 = M v2 = 3 2 MV i - MV i 5 4 Therefore, we conclude that Therefore, after both the man and woman have dived, the boat moves with velocity given by v2 = - 7 Vi 20 (b) At the moment when the man dives, the boat is at rest. Since his speed relative to the boat is V , then his absolute velocity after he dives is V i. Letting ~1 denote the velocity of the boat and the woman, v momentum conservation tells us that 0= 2 3 M (V i) + M + M 5 5 ~1 v = 7 3 M ~1 = - M V i v 5 5 ...
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This note was uploaded on 05/12/2010 for the course AME 301 taught by Professor Shiflett during the Spring '06 term at USC.
- Spring '06