A = angle light is from straight at wall
x = distance along waall from that point
A = angle from that point
then
tan A = x/25
d(tan A)/dt
= sec^2 A dA/dt = (1/25)dx/dt
what we want to know is dA/dt, the turning rate
so
sec^2(15) dA/dt = (1/25)(1.5)
solve for dA/dt, the turning rate
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?
1 answer