Finding rate of change of shadow problem.

[ugeous]

Question: A 1.85 m tall man is walking toward a 12 m tall street light at night at a rate of 2.2 m/s. How fast is the length of his shadow changing when he is 12 m from the street light?

so, using similar triangles, i got that (x+y)/12 = x/1.85. I can rearrange this into x= or y=, but then I don't see how i can find the derivative of it (ex. x = (1.85x+1.85y)/12 -> finding derivative will eliminate x and y). Any help will be greatly appreciated.

Thanks!

 

[Dick]

The derivative of that is (dx/dt+dy/dt)/12=dx/dt/1.85. The problem statement tells you what one of those derivatives is. Which one and what's it's value?

 

[ugeous]

Oh I think I got it. So just to make sure: I solve for dx/dt plugging in -2.2 for dy/dt correct?

 

[Dick]

Oh I think I got it. So just to make sure: I solve for dx/dt plugging in -2.2 for dy/dt correct?

Exactly.

 

[ugeous]

Thanks a lot Dick!