Jack and Jill are maneuvering a 2900 kg boat near a dock. Initially the boat\'s

Question

Jack and Jill are maneuvering a 2900 kg boat near a dock. Initially the boat's position is <3,0,4> m and its speed is 1.9 m/s. As the boat moves to position <5,0,5> m, Jack exerts a force <-340,0,240> N and Jill exerts a force <110,0,330> N.

A. How much work does Jack do?

B. How much work does Jill do?

C. What is the angle between the force that Jill exerts and the average velocity of the boat?

D. Assuming that we can neglect the work done by the water on the boat, what is the final speed of the boat?

Explanation / Answer

m = 2900kg
boat's initial position = (3,0,4)
speed = 1.9m/s

second position = (5,0,5), after time t

F jack = -340i + 240 k
F jill = 110i + 330 k

A. Work done by jack = F.s = [-340i + 240k].[(5-3)i + (5-4)k] = -680 + 240 = -440 J
B. Work done by jill = F.s = [110i + 330k].[2i + k] = 220+330 = 550 J
C. Average velocity's direction is given by the vector = 2i + k
Angle with x axis = arctan(1/2) = 26.56 deg
Angle of jill's force with x axis = arctan(330/110) = 71.56 deg
Angle diff = 45 deg
D. Net Work done = 550 - 440 = 110 J
Hence let final speed be v
0.5*2900*1.9^2 + 110 = 0.5*2900*v^2
v = 1.919 m/s

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