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

Answer:

43.17 ft/s

Step-by-step explanation:

Let the height of the wall is y.

distance of wall from light is 20 feet.

$tan\theta =\frac{y}{20}$    

y = 20 tanθ    .... (1)

time period, T = 3 second

$\frac{d\theta}{dt}=\frac{2\pi}{3}$

Differentiate equation (1) with respect to t.

$\frac{dy}{dt}=20sec^{2}\theta\times \frac{d\theta}{dt}$

$\frac{dy}{dt}=20sec^{2}10\times \frac{2\pi}{3}$

dy/dt = 20 x 2.16

dy/dt = 43.17 ft/s