The helicopter in the drawing is moving horizontally to the right at a constant velocity. the weight of the helicopter is w=58000 n. the lift force l generated by the rotating blade makes an angle of 21.0° with respect to the vertical. (a) what is the magnitude of the lift force? (b) determine the magnitude of the air resistance r that opposes the motion.

This is the lifting force. 62126 N

Explanation:

To solve this problem, a free body diagram is useful, where the weight is in the vertical direction and the lifting force is inclined 21º; In this diagram we place an xy reference system, where the Y axis is in the weight direction. Therefore the force that we must decompose the lifting force, let's use trigonometry.

 Be careful since the angle is measured with respect to the vertical.

      sin θ = CO / H

      sin θ = Fx / F

     cos θ = CA / H

     cos θ = Fy / F

     Fy = F cost

let's apply Newton's second law to this system, let's start with the Y axis

      Fy -W = 0

We assume the helicopter in balance

     Fy = W

     F cos t = W

     F = W / cos θ

Calculates

    F = 58000 / cos 21

    F = 62126 N

This is the lifting force.