Chapter 12, Problem 12.127RP

The parasailing system shown uses a winch to pull the rider in toward the boat, which is traveling with a constant velocity. During the interval when θ is between 20° and 40° (where t = 0 at θ = 20°), the angle increases at the constant rate of 2°/s. During this time, the length of the rope is defined by the relationship $r=125-\frac{1}{3}{t}^{3/2}$, where r and t are expressed in meters and seconds, respectively. At the instant when the rope makes a 30° angle with the water, the tension in the rope is 18 kN. At this instant, what is the magnitude and direction of the force of the parasail on the 75-kg parasailer?

Fig. P12.127