A bright light on the ground illuminates a wall 12 meters away. A man walks from the light straight toward the building at a speed of 1.2 m/s. The man is 2 meters tall. When the man is 4 meters from the building, how fast is the length of his shadow on the building decreasing?

Answer 1

As always, draw a diagram. Using similar triangles, the man's shadow height h when he is at a distance x from the light, is given by

2/x = h/12
or,
hx = 24
So, when the man is 4m from the wall (8m from the light) 8h=24, h=3

x dh/dt + h dx/dt = 0
Now plug in your values:

8 dh/dt + 3(1.2) = 0
dh/dt = -3.6/8 = -0.45 m/s