Use related rates to solve this question:
A vertical cliff makes a perfectly straight shore line. A lighthouse is placed 200 metres off shore. The lighthouse's lamp shines a rotating beam of light. The lamp rotates and makes 3 revolutions each minute. During part of each revolution the lamp illuminates a moving spot on the cliff. (Use meters, seconds, and meters/second)

a) How fast is the spot of light moving at the point on the cliff closest to the lighthouse? (Draw a diagram)

b) How fast is the spot of light moving at the point on the cliff that is 200 metres from the point closest to the light house? (Show on the diagram)

c) Where on the cliff is the spot of light moving at its slowest speed? (Show on the diagram)

d) Where on the cliff is the spot of light moving 4 times its slowest speed? (Show on the diagram)