A light is suspended above the ground and is being lowered towards the ground at a rate of 9 in/sec. A 6 foot tall person is on the ground and 8 feet away from the light. At what rate is the persons shadow increasing then the light is 15 feet above the ground?

Question

A light is suspended above the ground and is being lowered towards the ground at a rate of 9 in/sec.  A 6 foot tall person is on the ground and 8 feet away from the light.  At what rate is the persons shadow increasing then the light is 15 feet above the ground?

goformit100 · Answer

@UnkleRhaukus

unklerhaukus · Answer

picture

anonymous · Answer

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anonymous · Answer

you're asked about dx/dt...  
everything exactly like the previous problem, only difference is the relation between x and y ..

anonymous · Answer

similar triangles btw...  from your algebra days...

ashleynguyenx3 · Answer

So I use the same concept from last time? But what do I do with the 6?

anonymous · Answer

Find dx/dy from y/(8+x) =6/x AND we have dy/dt= -9
AND use dx/dt = dx/dy * dy/dt

anonymous · Answer

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anonymous · Answer

what he said...  or just use the chain rule explicitly, like we did in the previous problem...
easiest way (imo) would be...
solve for y:

y= (48+6x)/x

differentiate with respect to t (I'll leave that to you)

solve for dx/dt in terms of x,y and dy/dt...
plug in the values...

ashleynguyenx3 · Answer

Oh, I get how you got y/(8+x)=6/x now.

anonymous · Answer

there's a little trick in that they give you the value of 'y' rather than the value of 'x' at the specific time they're asking about....  you just have to use that value and the triangles in the sketch to find the value of 'x' at that time...

ashleynguyenx3 · Answer

So then would I get, dy/dt=x(6(dx/dt)-(48+6x)(dx/dt) / x^2

anonymous · Answer

looks good...

ashleynguyenx3 · Answer

I don't get where we would find all the values.

anonymous · Answer

dy/dt they give,  'y' you don't care about (except indirectly, as using it allows you to find 'x')
and dx/dt is what you're looking for...

anonymous · Answer

so:
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anonymous · Answer

make sense?

ashleynguyenx3 · Answer

Oh, yeah it does. Sorry, I didn't look back at the equation. Yeah it makes sense.

anonymous · Answer

great:)

anonymous · Answer

remember that dy/dt is negative...

anonymous · Answer

-9 ft/sec

ashleynguyenx3 · Answer

Okay, do I first solve for x? Then plug x into the derived equation?

anonymous · Answer

yep

ashleynguyenx3 · Answer

So after I get the answer, how would I know if it's decreasing or increasing? If the answer is negative or positive?

ashleynguyenx3 · Answer

Or if it's greater or less than -9?

anonymous · Answer

yep... the way I set it up is so it lays right on a cartesian coord. system...  ie right is +x, 'up' is +y, 'down' is -y  etc.

anonymous · Answer

so as the shadow gets longer x increases in length...

ashleynguyenx3 · Answer

Okay, I got it. Thanks again! :) I don't really understand related rates.

anonymous · Answer

heh.   you do now.

anonymous · Answer

I hope.

anonymous · Answer

:)

ashleynguyenx3 · Answer

Honestly, not really. But I'm sure if problem similar comes up, I'll know.