A street light is at the top of a 14.5 ft. tall pole. A man 5.3 ft tall walks away from the pole with a speed of 5.5 feet/sec along a straight path. How fast is the tip of his shadow moving when he is 47 feet from the pole?

Answer 1

I trust you made a sketch.
On mine I let the distance between the man and the post be y ft, and the length of his shadow be x ft
By similar triangles:
5.3/x = 14.5/(x+y)
5.3x + 5.3y = 14.5x
9.2x = 5.3y
92x = 53y
92 dx/dt = 53 dy/dt
but we know dy/dt = 5.5
so dx/dt = 53(5.5)/92 = appr 3.2 ft/sec

Notice that the fact that he is 47 ft from the pole is irrelevant.

Answer 2

the shadow's length is changing at dx/dt.

the tip of the shadow is moving at

dy/dt + dx/dt

Answer 3

Go with Steve's answer.

Mine gives the rate at which the shadow is lengthening, I missed the part where they want the rate at which the shadow is moving.
so
dy/dt + dx/dt
= 5.5 + 3.2
etc