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What is the angle θ between the tow rope and the center line

  1. Nov 9, 2016 #1
    1. The problem statement, all variables and given/known data
    Water skiers often ride to one side of the center line of a boat, as shown in the figure (Figure 1) . In this case, the ski boat is traveling at 15 m/s and the tension in the rope is 90 N.


    If the boat does 3700 N of work on the skier in 54.8 m, what is the angle θ between the tow rope and the center line of the boat?
    Walker4e.ch07.Pr017.jpg

    2. Relevant equations
    work=force x Δdistance

    3. The attempt at a solution
    I feel all over the place with this one. I don't know where to start. All i know is that I will be getting the angle of cosine since movement is in the horizontal direction.
     
  2. jcsd
  3. Nov 9, 2016 #2
    So you have a force of 90 N, and you have a distance of 54.8 meters. What if you multiply those two together? You get 4932 J. That number is larger than the 3700 N (Newton? units are wrong on the 3700) of work stated in the problem. So apparently, all of that 90 N force is not being used to perform work. So the angle θ has to somehow come into play. How much of that 90 N force is being used to produce work?
     
  4. Nov 10, 2016 #3
    just to add on what TomHart said... free body diagrams are very helpful...
     
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