Question

A rotating light is located 20 feet from a wall. The light completes one rotation every 3 seconds. Find the rate at which the light projected onto the wall is moving along the wall when the light's angle is 10 degrees from perpendicular to the wall.

Answer 1

43.17 ft/s

Explanation:

Let the height of the wall is y.

distance of wall from light is 20 feet.

`tan\theta =(y)/(20)`

y = 20 tanθ .... (1)

time period, T = 3 second

`(d\theta)/(dt)=(2\pi)/(3)`

Differentiate equation (1) with respect to t.

`(dy)/(dt)=20sec^(2)\theta* (d\theta)/(dt)`

`(dy)/(dt)=20sec^(2)10* (2\pi)/(3)`

dy/dt = 20 x 2.16

dy/dt = 43.17 ft/s