A water skier, moving at a speed of 8.61 m/s, is being pulled by a tow rope that makes an angle of 34.9 ° with respect to the velocity of the boat. The tow rope is parallel to the water. The skier is moving in the same direction as the boat. If the tension in the tow rope is 137 N, determine the work that it does in 14.9 s.

work=tension*velocity*time*cosine angle

where angle =34.9deg

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This almost exact problem was answered.

To determine the work done by the tension in the tow rope, we can use the formula for work:

Work = Force * Distance * cos(theta)

Where:
- Work is the work done by the force, measured in joules (J).
- Force is the magnitude of the force applied, measured in newtons (N).
- Distance is the distance over which the force is applied, measured in meters (m).
- Theta (θ) is the angle between the direction of the force and the direction of motion.

In this case, the force is the tension in the tow rope (137 N), the distance is the distance traveled by the water skier in 14.9 s, and the angle (theta) is the angle between the direction of the force and the direction of motion.

First, let's calculate the distance traveled by the water skier:
Distance = Velocity * Time

Given that the velocity is 8.61 m/s and the time is 14.9 s:

Distance = 8.61 m/s * 14.9 s = 128.189 m

Next, let's calculate the angle between the direction of the force and the direction of motion:
theta = 34.9°

Now, we can substitute the values into the work formula:

Work = 137 N * 128.189 m * cos(34.9°)

Using a calculator, we can calculate the cosine of 34.9°, which is approximately 0.819:

Work = 137 N * 128.189 m * 0.819

Finally, we can calculate the work:

Work = 14216.8 J

Therefore, the work done by the tension in the tow rope is approximately 14216.8 joules.