The illustration below shows a vane with a turning angle θ which moves with a steady speed vc. The vane receives a jet that leaves a fixed nozzle with speed θ.
(a) Assume that the vane is mounted on rails as shown in the sketch. Show that the power transmitted to the cart is maximum when vc/v = 1/3
(b) Assuming that the are a large number of such vanes attached to a rotating wheel with peripheral speed, vc, show that the power transmitted is maximum when vc/v = 1/2.
