In the design of an amusement-park ride, the cars are attached to arms of length R which are hinged to a central rotating collar which drives the assembly about the vertical axis with a constant angular rate ω = θ˙. The cars rise and fall with the track according to the relation z = (h/2)(1 − cos 2θ). Find the R-, θ-, and Φ-components of the velocity v of each car as it passes the position θ = π/4 rad.

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y R |h -- -- |h Problem 2/180