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Homework Statement:

A helicopter is flying horizontally with constant velocity ##v## and carries a survivor who hanging on a rope with length ##l##. Suddenly the pilot receives a message he has to pull the the survivor into the the helicopter as soon as possible. A paramedic on board starts to pull a hanging rope with such force that the length of rope is shortening with velocity ##v_k##.
What is the angle ##\theta## between the rope and vertical line?
Relevant Equations:
 Relevant equations are below.
We have 2 forces affecting the rope: 1. Gravitational force of the body ##=mg## and 2. Force of air = Force of drag= ##F_{AIR}##.
The length of the rope is shortening with the velocity ##v_k##.
So to figure out the angle ##\theta## I wrote:
##R##= force of rope
##R_x = F_{AIR}##
##R_y = mg##
Now I know the acceleration is the first derivative of velocity, but don't know how to incorporate this with the angle ##\theta##, length of the rope and ##v_k##.
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