A small plane tows a glider at constant speed and altitude.

If the plane does 2.00X10^5 J of work to tow the glider 165 m and the tension in the tow rope is 2660 N, what is the angle between the tow rope and the horizontal?

work=Tension*distance*cosTheta

solve for theta

To find the angle between the tow rope and the horizontal, we can use the work-energy principle.

The work done by the plane is given by:

Work done = Force x Distance x cos(θ)

Where:
- Force is the tension in the tow rope (2660 N)
- Distance is the distance covered by the glider (165 m)
- θ is the angle between the tow rope and the horizontal (the required angle)

Rearranging the equation, we can solve for cos(θ):

cos(θ) = Work done / (Force x Distance)
cos(θ) = (2.00x10^5 J) / (2660 N x 165 m)

Now, let's plug in the given values and calculate:

cos(θ) = (2.00x10^5 J) / (2660 N x 165 m)
cos(θ) ≈ 0.45367

Finally, we can calculate the angle θ by taking the inverse cosine (arccos) of both sides of the equation:

θ ≈ arccos(0.45367)
θ ≈ 63.45 degrees (rounded to two decimal places)

Therefore, the angle between the tow rope and the horizontal is approximately 63.45 degrees.

To find the angle between the tow rope and the horizontal, we can use the concept of work done.

The work done (W) is given by the equation: W = F * d * cosθ

Where:
- W is the work done (in joules)
- F is the force applied (in newtons)
- d is the displacement (in meters)
- θ is the angle between the force and the displacement (in degrees)

In this case, we know the work done (2.00x10^5 J), the force applied (2660 N), and the displacement (165 m). We need to determine the angle (θ).

Rearranging the formula, we can solve for cosθ: cosθ = W / (F * d)

Substituting the given values, we have: cosθ = (2.00x10^5 J) / (2660 N * 165 m)

Evaluating this expression, we find cosθ ≈ 0.45, using a calculator.

Now, to determine the angle θ, we can take the inverse cosine (arccos) of cosθ:

θ = arccos(0.45)

Calculating this using a calculator, we find θ ≈ 63.4 degrees.

Therefore, the angle between the tow rope and the horizontal is approximately 63.4 degrees.

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