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A rotating light is located 17 feet from a wall. The light completes one rotation every 4 seconds. Find the rate at which the light projected onto the wall is moving along the wall when the light's angle is 15 degrees from perpendicular to the wall.

User Sam Hobbs
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1 Answer

4 votes

the light is 17 feet from the wall

angular speed is found with

w = change in rotation / change in time

2pi / 4

pi / 2

y = 17 tan(θ)

derivative

y = 17 sec^2 (θ)

y = 17 * pi/2 * sec^2(θ)

y = 17 * pi/2 * sec^2(15)

y = 28.62 ft per second

User Etlsh
by
8.5k points
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