Chapter 12.1, Problem 12.71P

The parasailing system shown uses a winch to let rope out at a constant rate so that the 70-kg rider moves away from the boat, which is traveling with a constant velocity. At the instant shown, the rope has a length of 30 m, it is increasing in length at a constant 1 m/s, the angle is increasing at a rate of 0.05 rad/s, and $\ddot{\theta }$ is −0.01 rad/s². Knowing that when the rope makes a 30° angle with respect to the water, the tension in the rope is 10 kN, determine the magnitude and direction of the force of the parasail on the parasailor.

Fig. P12.71