How fast is the light beam moving (in ft/sec) along the wall when the beam makes angles of 𝜃 = 30°, 𝜃 = 60°, and 𝜃 = 85° with the line perpendicular from the light to the wall?

Question

A patrol car is parked 60 feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of 22revolutions per minute. How fast is the light beam moving (in ft/sec) along the wall when the beam makes angles of 𝜃 = 30°, 𝜃 = 60°, and 𝜃 = 85° with the line perpendicular from the light to the wall?

𝜃 = 30°

___ft/sec

𝜃 = 60°

____ft/sec

𝜃 = 85° (Round your answer to two decimal places.)

____ft/sec

Answer 1

x = 60tan(22·2πt/60) = 60tan(11πt/15) ft

x' = 44πsec²(11πt/15) ft/s

θ = 11πt/15 = 30°, x' = 44π ·sec²30° = 184.31 ft/s

θ = 11πt/15 = 60°, x' = 44π·sec²60° = 552.92 ft/s

θ = 11πt/15 = 85°, x' = 44πsec²85° = 18197.45 ft/s