Question

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.

Answer 1

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