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

Answer:

Work done = 1.414 × 10⁸ J

Power of the wind = 3.9 × 10⁴ W

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

$P = \frac{1.414 \times 10^8 J}{3600 s} = 3.9 \times 10^4 W$

Answer 2

Answer: The work done by the boat is $2\times 10^8 Joules$.

The power of the wind is $5.55\times 10^4 watts$.

Explanation:

Force of the wind in the boat = $2.00\times 10^4 N$

Displacement of the boat = 10 km = 10,000 m

Work done = Force × Displacement =

$2\times 10^4 N\times 10,000 m=2\times 10^8 Joules$

Duration of time for which boat sailed = 1 hour

Power of the wind = $\frac{Energy}{Time}$

=$\frac{2\times 10^8 Joules}{1\times 60\times 60 seconds}=5.55\times 10^4 watts$

The work done by the boat is $2\times 10^8 Joules$.

The power of the wind is $5.55\times 10^4 watts$.