A boat is being pulled along a canal with a cable asshown in the image. The boat

Question

A boat is being pulled along a canal with a cable asshown in the image. The boat moves in the direction of the arrow. The cable is at an angle e 25° relative to the direction the boat is moving. The boat has a mass of 5244 kg. The tension in the rope is 896 N and constant. The boat starts at rest and ends up moving at 5.4 m/s after going a distance D 297 m. What is the work done by the tension in the rope in moving the boat? Give your answer in Joules to at least three significant digits. You will not be graded on the number of digits, this is just be be sure that your answer is not considered incorrect due to rounding. Do not include units in your answer.

Explanation / Answer

W = work done = force x distance moved in its direction (along line of action)

=> W = 896*cos25°(297) = 241179.37 J ~= 241.2 kJ

also time taken = s/[v] =297/2.7= 110 s

acceleration = [v - u ]/ t = [5.4-0]/110 = 0.049 m/s²

Newton's II law: F = ma = F

=> F in the boat movement direction = 5244(0.049) = 257.4 N

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