Question

A rotating light is located 13 feet from a wall. The light completes one rotation every 5 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

42.115 ft/s

Explanation:

The distance from the point closest to the light is given by

d = (13 ft)tan(α)

where,

α=angle from perpendicular.

Since the light travels through an angle of 2π radians in 5 seconds, the angle can be represented by

α = πt . . . . radians

and the rate of change of α is dα/dt = π (radians/second)

The rate of change of distance is:

dd/dt = (13 ft)sec(α)²(dα/dt) = (13π)(sec(10°)²) ft/s ≈ 42.115 ft/s