Water skiers often ride to one side of the center line of a boat, as shown in the figure. In this case, the ski boat is traveling at 15 m/s and the tension in the rope is 90 N. If the boat does 3500 J of work on the skier in 42.4 m, what is the angle θ between the tow rope and the center line of the boat?
No figure provided
To find the angle θ between the tow rope and the center line of the boat, we can use the formula for work:
Work = Force × Distance × cos(θ)
In this case, the work done by the boat is given as 3500 J, the distance is 42.4 m, and the tension in the rope is 90 N.
Rearranging the formula, we get:
cos(θ) = Work / (Force × Distance)
cos(θ) = 3500 J / (90 N × 42.4 m)
cos(θ) ≈ 0.925
To find the angle θ, we can use the inverse cosine function (cos^(-1)):
θ = cos^(-1)(0.925)
Using a calculator, we find that θ ≈ 22.1 degrees.
Therefore, the angle θ between the tow rope and the center line of the boat is approximately 22.1 degrees.