Answer:
42.115 ft/s
Step-by-step 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
