Lighthouse on the Coast

[Puzzle Prime]

A lighthouse is x miles away from the coast. Its beam makes 1 revolution per minute. How fast is the beam moving along the beach, when the point on the beach it lightens up is y miles away from the point on the beach closest to the lighthouse?

[Vivek]

The distance from the base of the lighthouse to the light beam is not going to change as it revolves and it is sqrt(x^2+y^2). So The speed is 2*pi*sqrt(x^2+y^2) per minute.