How Fast Is the Shadow's Height Changing as the Dog Approaches the Wall?

[venger]

Homework Statement

A spotlight on the ground shines on a wall 14m away. If a dog, 0.5m tall, runs from the spotlight towars the building at a speed of 1 m/s, how fast is the height of the animal's shadow on the building decreasing when the dog is 5 meters from the building?

Wrt = with respect to

Homework Equations

Pythagoreon theorem, implicit differentiation, you name it.

The Attempt at a Solution

Knowing that Dc/dt is canine wrt time is 1 m/s and i am trying to find dh/dt 'h' for height wrt time

and I am stuck...
.
..
...
14^2 + wall^2 = Hyp^2

 

[drpizza]

This is called a "related rates" problem, not "implicit differentiation."

dc/dt? if you're using the pythagorean theorem, that implies (at least to me) that the dog is running on the hypotenuse??

At a glance, I'm having a tough time getting the pythagorean theorem to really work for me on this problem. Have you thought about the angle made by the flashlight between the ground and the beam to the top of the dog? Or, have you thought about similar triangles?

 

[HallsofIvy]

You should have put "similar triangles", not "Pythagorean theorem", in "Relevant Equations". Can you draw a picture and see why?

 

[venger]

Here i go furthering my development in related rates
let l be length of shadow and let x be ground covered with light
2/L = X/12
24=LX
L=24X^-1
dL/dt(1)=-24X^-2
dL/dt=-24(12-8)^-2
dL/dt=9/32