Question

A patrol car is parked 50 feet from a long warehouse The light on the car turns at a rate of 30 revolutions per minute. How fast is the light beam moving along the wall when the beam makes the fol­ lowing angles with the line perpendicular from the light to the wall?

(a)=30° (b)= 60° (c)=70°

Answer 1

If x is the distance from the closest point on the wall,

x/50 = tanθ
1/50 dx/dt = sec^2(θ) dθ/dt