Question

A boat with a horizontal tow rope pulls a water skier. She skis off to the side, so the rope makes an angle of 15° with the forward direction of motion. If the tension in the rope is 180 N, how much work does the rope do on the skier during a forward displacement of 300 m?

A) 1.40 × 10^4 J.
B) 5.40 × 10^4 J.
C) 5.22 × 10^4 J.
D) -5.22 × 10^4 J.

Answer 1

The work done by the rope on the skier can be calculated using the formula: Work = Force x Distance x cos(angle). Plugging in the given values, the work done is approximately 51984 J.

Step-by-step explanation:

The work done by the rope on the skier can be calculated using the formula:

Work = Force x Distance x cos(angle)

In this case, the force is the tension in the rope (180 N), the distance is the forward displacement of the skier (300 m), and the angle is the angle between the rope and the forward direction of motion (15°).

Plugging in the values, we get:

Work = 180 N x 300 m x cos(15°)

Using a calculator, we find that cos(15°) is approximately 0.9659. So, the work done by the rope on the skier is:

Work ≈ 180 N x 300 m x 0.9659 ≈ 51984 J.

Therefore, the correct answer is C) 5.22 × 10^4 J.