Question

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 2.2 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?

What I did was
x/12=x+y/2
2x=12x+12y
10x=10y , took derivative
-10/12 dx/dy(2.2(
=-2.64 , I did not know what to do with the part when it says , when the man is 4 meters a way

Answer 1

Since you did not define what your x and y are, I have no way of checking what you did

In my sketch, I let the distance from the man to the light be x m, and the length of his shadow as y m
then by ratios ,
2/x = y/12
xy = 24
x dy/dt + y dx/dt = 0

when x=4, y=6 and dx/dt = 2.2
4dy/dt + 6(2.2) = 0
dy/dt = -13.2/4 = -3.3 m/s

the negative implies that his shadow is shrinking as expected when he walks towards the wall