A small plane tows a glider at constant speed and altitude. If the plane does 2.00×105J of work to tow the glider 135 m and the tension in the tow rope is 2560 N , what is the angle between the tow rope and the horizontal?
To find the angle between the tow rope and the horizontal, we can use trigonometry. The work done by the plane is given by the equation:
Work = Force × Distance × cos(θ),
where θ is the angle between the tow rope and the horizontal.
Given that the work done is 2.00 × 10^5 J, the distance is 135 m, and the tension in the tow rope is 2560 N, we can rearrange the equation to solve for cos(θ):
cos(θ) = Work / (Force × Distance).
Plugging in the values, we get:
cos(θ) = (2.00 × 10^5 J) / (2560 N × 135 m).
Now we can calculate the value of cos(θ):
cos(θ) = 0.5694.
To find the angle θ, we need to take the inverse cosine (cos⁻¹) of 0.5694:
θ = cos⁻¹(0.5694).
Using a calculator, we find that θ ≈ 55.6 degrees.
Therefore, the angle between the tow rope and the horizontal is approximately 55.6 degrees.