A boat with a horizontal tow rope pulls a water skier. She skies off to the side,

so the rope makes an angle of 15.0° with her direction of motion, but in the
same direction as the boat is traveling. The tension in the rope is 160 N. How
much work is done on the skier by the rope during a displacement of 400 m?

Fx = 160 * cos(15) = 155N

W.D. = 155 * 400 = 62kN

To find the work done on the skier by the rope, we can use the formula:

Work = Force * Distance * Cos(theta)

where:
- Work is the work done on the skier (in Joules)
- Force is the tension in the rope (in Newtons)
- Distance is the displacement of the skier (in meters)
- Cos(theta) is the cosine of the angle between the force vector and the displacement vector

Given:
Force (tension in the rope) = 160 N
Distance = 400 m
Theta = 15.0° (angle between the rope and the skier's direction of motion)

First, we need to convert the angle from degrees to radians:
Theta (radians) = Theta (degrees) * pi / 180
Theta (radians) = 15.0° * pi / 180
Theta (radians) = 0.2618 radians

Now, we can calculate the work done on the skier:
Work = 160 N * 400 m * Cos(0.2618 radians)

Using a scientific calculator or an online calculator, we find:
Work ≈ 62,862 J

Therefore, the work done on the skier by the rope during a displacement of 400 m is approximately 62,862 Joules.

To find the work done on the skier by the rope, we can use the formula:

Work = Force * Distance * cos(theta)

Where:
- Work is the work done on the skier
- Force is the tension in the rope
- Distance is the displacement of the skier
- theta is the angle between the force and the displacement

In this case, the tension in the rope is 160N, the displacement is 400m, and the angle between the force and the displacement is 15.0°.

So, we can plug these values into the formula to find the work done:

Work = 160N * 400m * cos(15.0°)

To evaluate this expression, we need to find the cosine of 15.0°. Using a calculator, we find that cos(15.0°) is approximately 0.9659.

Substituting the value into the equation:

Work = 160N * 400m * 0.9659

Now we can calculate the work:

Work = 61,734J

Therefore, the work done on the skier by the rope during a displacement of 400 m is approximately 61,734 Joules.