calculus related rates help.?

Question

Not sure how to work this problem.

a spotlight on the ground shines on a well 12 meters away. If a man 2meters tall walks from the spotlight toward the building at a speed of 1.6m/s, how fast is the length of his shadow on the building decreasing when he is 4 m away from the building?

THANKS

Answer 1

Assume the spotlight is a point source on the ground. Let
x = man's distance from the building
h = the height of his shadow.
dx/dt = his walking speed = - 1.6 m/s
h/12 = 6/(12 - x)
h = (1/2)(1/(12 - x))
dh/dt = (dh/dx)(dx/dt)
dh/dt = (1/2)(1/(12 - x)^2)(dx/dt)
dh/dt = (1/2)(- 1.6)/(12 - 4)^2
dh/dt = - 0.8/64
dh/dt = - 0.0125 m/s