Draw a right angled triangle ABC, where <B = 90 degrees
BC is the base, and BC = 12 m and C represents spot light on the ground and B is foot of the wall
Draw a perpendicular DE from a point D on hypotenuse, AC to a point E on BC
DE represents walking man and DE = 2 m
Now AB represents height of shadow, let AB = y
let EC = x
from similar triangles, ABC and DEC
AB/DE = BC/EC
y/2 = 12/x
y = 24/x
differentiating with respect to t
dy/dt = - (24/x^2) dx/dt
substitute x = (12 - 4) = 8 and dx/dt = 1.9 m/s
dy/dt = - (24 / 64)(1.9)
= -0.7125
length of shadow is decreasing at the rate of 0.7125 m /s
