Question

Water skiers often ride to one side of the center line of a boat, as shown in Figure 7-16. In this case, the ski boat is traveling at 15 m/s and the tension in the rope is 65 N. If the boat does 3500 J of work on the skier in 58.7 m, what is the angle θ between the tow rope and the center line of the boat?

Answer 1

Work done is the force applied over a distance relative to the cosine of the angle to which it is applied. Assuming constant everything, and no resistive force provided from the water...
\[\Large \begin{array}{l}
W = F\Delta r\cos \theta \\
\cos \theta = \frac{W}{{F\Delta r}}\\
\theta = {\cos ^{ - 1}}\left( {\frac{{3500}}{{65 \cdot 58.7}}} \right) = 23.46^\circ
\end{array}\]