The illustration above (next column) shows a vane with a turning angle that moves with a

The illustration above (next column) shows a vane with a turning angle θ that moves with a steady speed v_c. The vane receives a jet that leaves a fixed nozzle with speed v.

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 v_c/v = 1/3.
b. Assuming that the are a large number of such vanes attached to a rotating wheel with peripheral speed, v_c, show that the power transmitted is maximum when v_c/v = 1/2.

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