A rotating light is located 25 feet from a wall. The light projected on the wall is moving at a rate of 1.5 feet per second when the light's angle is 15 degrees from perpendicular to the wall. If the light is turning at a constant rate, how many seconds does it take to go around once?
How do you get in seconds?
draw a diagram. It is clear that
tanθ = x/25
so
sec^2θ dθ/dt = 1/25 dx/dt
1.0353 dθ/dt = 0.04 * 1.5
dθ/dt = .057 rad/s
dθ/dt is constant, and since there are 2π radians in one revolution, the period is 2π/.057 = 110 seconds
Better check my math; 2 minutes/rev seems like a long time