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 on Question #47517-Physics-Quantum Mechanics

A sailboat moves north for a distance of $d = 10.00 \, \text{km}$ when blown by a wind from the exact southeast with a force of $F = 2.00 \cdot 10^{4} \, \text{N}$ . The sailboat travels the distance in $t = 1.0 \, \text{h}$ . 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.

Solution

The work was done by the wind is

$$W = \vec {F} \cdot \vec {d} = F d \cos 4 5 {}^ {\circ},$$

where $45{}^{\circ}$ is angle between the directions of a force and a distance.

$$W = 2. 0 0 \cdot 1 0 ^ {4} N \cdot 1 0. 0 0 \cdot 1 0 ^ {3} m \cdot \cos 4 5 {}^ {\circ} = 1. 4 1 \cdot 1 0 ^ {8} J.$$

The wind's power is

$$P = \frac {W}{t} = \frac {1 . 4 1 \cdot 1 0 ^ {8} J}{1 . 0 \cdot 3 6 0 0 s} = 3 9. 2 k w a t t.$$

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