A patrol car is parked d = 60 feet from a long warehouse, as shown in the figure below.

Question

A patrol car is parked d = 60 feet from a long warehouse, as shown in the figure below. The revolving light on top of the car turns at a rate of 1/2 revolution per second. The rate at which the light beam moves along the wall is r = 60𝜋 sec² 𝜃

 ft/sec.

(a) Find the rate r when θ is π/4.

 

 (b) Find the rate r when θ is 𝜋/3

 

 (c) Find the limit of r as θ→(π/2) ^– .

Answer 1

a)60pi*sec^2(pi/4) = 120pi ft/sec

b)60pi*sec^2(pi/3) = 240pi ft/sec

c) 60pi * lim_x-->pi/2(sec^2(x))

60pi(lim_x-->pi/2(sec(x)))^2

60pi(-inf)^2 = inf