Related Rates (similar triangles)

[phat2107]

Homework Statement

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 30 ft from the base of the pole?

Homework Equations

http://imageiso.com/out.php/i26481_Relatedrates.JPG

18/x = 6(x-y)

The Attempt at a Solution

y=30 ft

simplified 12x=18y

tip of shadow will be at 45 ft


d/dt 12x = d/dt 18y

dx/dt 12 = dy/dt 18

if i plug the 8ft/s as my dx/dt i get a dy/dt of 16/3ft/s

but that can't be the right answer since i didnt use the 30ft given in my original question

where am i going astray?

 

[LCKurtz]

You aren't going astray. Think about the fact that maybe the speed of the tip of the shadow only depends on how fast she is moving, and not where she happens to be.

 

[phat2107]

if what you said is true, than for some reason my answer of 16/3 isn't correct (its online so i get my answers right away if i am correct)

i still don't get what's wrong...

a little more insight will be greatly appreciated

 

[LCKurtz]

if what you said is true, than for some reason my answer of 16/3 isn't correct (its online so i get my answers right away if i am correct)

i still don't get what's wrong...

a little more insight will be greatly appreciated

Your analysis is fine. You just plugged your 8 feet/sec in for the wrong variable. It is dy/dt that is 8 and dx/dt you are seeking.