Question

A street light is at the top of a 18 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 8 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 50 ft from the base of the pole?

Answer 1

the key is to relate similar triangles

Answer 2

\[\frac{18}{d+s}=\frac{6}{s}\]
\[18s = 6d+6s\]
derive
\[18s'=6d'+6s'\]
d'=8\[18s'-6s'=6(8)\]
\[s'=\frac{48}{18-6}\]

but thats just the shadows rate of change from the person; d'+s' is the speed that the shadow is moving across the ground

Answer 3

oh ok...i got this far...but then afterwards i kind of got stuck

Answer 4

whats the afterwards?

Answer 5

I did take the d/dx of that and came up with 48/12 which is the same as u got, but then i got stuck

Answer 6

s' = 4; now, the top of the shadow is moving away from the person at a rate of 4

the person is moving at a rate of 8

8+4 = 12 is the speed of the shadow as it moves across the ground