Answer:
29.2 ft/s
Explanation:
The distance of the light's projection on the wall
y = 13 tan θ
where θ is the light's angle from perpendicular to the wall.
The light completes one rotation every 3 seconds, that is, 2π in 3 seconds,
Angular speed = w = (2π/3)
w = (θ/t)
θ = wt = (2πt/3)
(dθ/dt) = (2π/3)
y = 13 tan θ
(dy/dt) = 13 sec² θ (dθ/dt)
(dy/dt) = 13 sec² θ (2π/3)
(dy/dt) = (26π/3) sec² θ
when θ = 15°
(dy/dt) = (26π/3) sec² (15°)
(dy/dt) = 29.2 ft/s
