A water-skier of mass 70 kg is pulled from rest by a tow rope that exerts a constant…
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A water-skier of mass 70 kg is pulled from rest by a tow rope that exerts a constant horizontal force of 500 N. The skier moves in a straight line on a calm lake where a 250 N resistive drag force due to water acts opposite the direction of motion. Assume the tow force and the drag force remain constant over the interval considered. After the skier has traveled 60 m, the tow rope is released.
(a) Calculate the work done on the skier by (i) the tow rope and (ii) the water drag during the 60 m interval.
(b) Determine the skier’s speed at the moment the rope is released.
(c) Compute the average power supplied by the tow rope to the skier during the 60 m interval.
(d) Calculate the mechanical efficiency of the towing process, defined as the ratio of the skier’s gain in kinetic energy to the total work done by the tow rope.