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The crate is being lifted up the inclined plane using the
motor M and the rope and pulley arrangement shown.
Determine the speed at which the cable must be taken up
by the motor in order to move the crate up the plane with a
constant speed of 4 ft/s .

Step-by-step

Position-Coordinate Equation: Datum is established at fixed pulley B . The position of point P and crate A with respect to datum are s_{P} and s_{A}, respectively.

2 s_{A}+\left(s_{A}-s_{P}\right)=l
3 s_{A}s_{P}=0

Time Derivative: Taking the time derivative of the above equation yields

3 v_{A}v_{P}=0

since v_{A}=4 ft/s
(+)

3(4)-v_{P}=0

v_{P}=12 ft/s

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