Concept explainers
A 180-lb man and a 120-lb woman stand at opposite ends of a 300-lb boat, ready to dive, each with a 16-ft/s velocity relative to the boat. Determine the velocity of the boat after they have both dived, if (a) the woman dives first, (b) the man dives first.
Fig. P13.150
(a)
Find the velocity of the boat
Answer to Problem 13.150P
The velocity of the boat
Explanation of Solution
Given information:
The weight of the man
The weight of the woman
The weight of the boat
The relative velocity of the boat
The acceleration due to gravity (g) is
Calculation:
Calculate the mass of the man
Substitute
Calculate the mass of the woman
Substitute
Calculate the velocity of the boat when woman dives first
Show the free body momentum diagram of the boat system after the woman dives as in Figure (1).
Calculate the velocity of the diving of the woman
Here,
Substitute
Calculate the initial momentum
Substitute
The final velocity of the woman after diving is zero, so the final momentum of the woman
Calculate the momentum of boat and man after the woman dives using the relation:
Here,
Substitute
The expression for principle of conservation of momentum as follows;
Substitute
Calculate the velocity of the boat after the man dives
Show the free body momentum diagram of the boat after man dives as in Figure (2).
Calculate the velocity of the diving of the man
Substitute
Calculate the initial momentum
Substitute
Calculate the momentum of the boat after the woman has dived using the relation:
Calculate the final momentum of the boat after the man has dived
Substitute
The expression for the principle of conservation of momentum to the man and boat as follows;
Substitute
Substitute
Therefore, the velocity of the boat
(b)
Find the velocity of the boat
Answer to Problem 13.150P
The velocity of the boat
Explanation of Solution
Given information:
The weight of the man
The weight of the woman
The weight of the boat
The relative velocity of the boat
The acceleration due to gravity (g) is
Calculation:
Show the free body momentum diagram of the boat system after the man dives as in Figure (3).
Calculate the velocity of the diving of the man
Here,
Substitute
Calculate the initial momentum
Substitute
The final velocity of the man after diving is zero, so the final momentum
Calculate the momentum of boat and woman after the man dives using the relation:
Substitute
The expression for principle of conservation of momentum to the man as follows;
Substitute
Show the free body momentum diagram of the boat after man dives as in Figure (4).
Calculate the velocity of the diving of the woman
Here,
Substitute
Calculate the initial momentum
Substitute
Calculate the final momentum of the boat after the woman has dived
Substitute
Calculate the velocity of the boat after the woman dives
Substitute
Substitute
Therefore, the velocity of the boat
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Chapter 13 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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