Question

A sailboat moves north for a distance of 10.00 km when blown by a wind from the exact southeast with a force of 2.00 × 104 N. The sailboat travels the distance in 1.0 h. How much work was done by the wind? What was the wind’s power? Your response should include all of your work and a free-body diagram.

Answer 1

Work done = 1.414 × 10⁸ J

Power of the wind = 3.9 × 10⁴ W

Step-by-step explanation:

Work done by the wind is scalar product of force and displacement of the sailboat.

W = F.s = F s cos θ

Here, sailboat is moving Northwards when Wind from South-East strikes it. Thus, the angle between force and displacement is θ =45°

F = 2.00×10⁴ N

s = 10.00 km = 10⁴ m

W = 2.00×10⁴ N × 10⁴ m × cos 45° = 1.414 × 10⁸ J

Power of the boat = work done per unit time

time = 1 h = 3600 s

`P = (1.414 * 10^8 J)/(3600 s) = 3.9 * 10^4 W`