In the design of an amusement-park ride, the cars are attached to arms of length r = 25 m which are hinged to a central rotating collar which drives the assembly about the vertical axis with a constant angular rate ω = 0.34 rad/s. the cars rise and fall with the track according to the relation z = (h/2)(1-cos 2θ) where h = 6.8 m. find the r-, θ-, and ϕ-components of the velocity v of each car as it passes the position θ = 42°.