Question

Charlie, who is 6 feet tall, walks away from a streetlight that is 16 feet high at a rate of 6 feet per second, as shown in the figure. Express the length s of Charlie's shadow as a function of time.

Answer 1

From similarity of triangles we have
s/4 = (s+d)/16 and so 4s = s + d and therefore s = d/3. Assuming he starts walking at t=0 from the street light (there is no figure to check this out) then d=5t and we then have s = (5/3) t

Answer 2

6.2 ft : 5 ft shadow
? ft : 17 ft shadow

height of light
= 6.2*17/5
= 21.08'

Answer 3

Yes there is similarity of triangles. But let's check out your s = (5/3)t and let us say that t is a 1 second. so Charlie has moved 6 feet.