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Question

A lighthouse on an island is 3 km away from the nearest point p on a prefectly straight beacch.The light is revolving four times per minute.How fast is the beam of light moving along the beach when it is passing a point 1 km from p?

Answer 1

How long is the hypotenuse of the triangle formed by the beam of light, the beach, and a 3km line from the lighthouse to the nearest point on the beach?

L = sqrt(3^2 + 1^2)
= sqrt(10) km

This hypotenuse makes one complete revolution in 15 seconds. How long is the circumfrence that it traces out?

C = 2 * pi * sqrt(10) km

The speed of the tip end of the hypotenuse, in km / second, is

S = 2 * pi * sqrt(10) / 15