A street light is mounted at the top of a 6 meter tall pole. A man 2m tall walks away from the top with a speed of 1.5 m/s along a straight path. How fast is the tip of his shadow moving when he is 10m from the pole?

Answer 1

Let
x = distance of man from pole
s = length of shadow
Then
s/2 = (x+s)/6
3s = x+s
2s = x
2 ds/dt = dx/dt
ds/dt = 1.5/2 = 0.75 m/s
it does not matter how far away from the pole the man is.

Answer 2

The wording in this question is always tricky

Oobleck found the rate at which the shadow increasing,
the question was how fast is the tip of the shadow moving, that is,
d(x+y)/dt = .75 + 1.5 or 2.25 m/s

(just like if I am walking in the same direction as a train going at 80 km/h
and I am walking at 4 km/h, I am moving at 84 km/h)

Answer 3

dang! Way to watch, Reiny!
Although I'm sure that Erich caught that, too.