The math help thread

I'm not entirely sure the way I did it was correct, so that's your warning.


We need the equation that describes the location of tip P on the wall. So let's figure it out!

We'll call x the distance of the light from the wall. At any moment, the rays of light running lower than the angle of arctan(height/run) are blocked by the man, and makes the shadow. Therefore, P on the wall is described by:

Code:

f(t) = x - 3t
dx/dt = v(t) = -3

P(t) = (x - 3t)*(3/(x - 3t - 12)) + 3
     = (3*(x - 3t))/(x - 3t - 12) + 3
P'(t) = 3 * [-3*(x - 3t - 12) - -3*(x - 3t)] / (x - 3t - 12)^2
      = 108 / (x - 3t - 12)^2

x = 24 ft
P'(0) = 108/144 = .75 ft/s