Related Rates Problem - Calc 1

[unreal trout]

A street light is at the top of a 24 ft pole. A 4 ft tall girl walks along a straight path away from the pole with a speed of 8 ft/sec.
At what rate is the tip of her shadow moving away from the light (ie. away from the top of the pole) when the girl is 24 ft away from the pole?

Can anyone help me solve this problem? I keep getting the answer wrong.

[royal jacinth]

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[haughty tapir]

How have you tried to solve the qn

Have you like drawn a diagram yet

Or have you yet to even start

I'll just draw a crude diagram

[unreal trout]

yah i tried using similar traingles

idk why is it wrong

[haughty tapir]

x=d/5

[unreal trout]

for the tip of the shadow, shouldnt it be the rate of change of shadow + speed i.e. (8/5) + 8?

[haughty tapir]

No

It's rate of change of shadow multiplied by speed

(1/5)*8

By chain rule

[unreal trout]

how?

sorry but i didnt get it

i have never used chain rule in a related rates problem before

[haughty tapir]

x/(x+d) =4/24

x/(x+d) =1/6

x=1/5d

dx/dD=1/5

dx/dt=dD/dt*dx/dD=8*1/5=8/5

[unreal trout]

i got 8/5 for just the rate of change of the shadow

[haughty tapir]

Mhm

Gimme a sec

[unreal trout]

okay

did you find it?

i keep getting 48/5 for the rate of change of the tip of shadow

[haughty tapir]

Mb I misread the qn jn

It's away from the top of the pole

Not the horizontal dist

Find rate of change of h

@unreal trout

Sorry I was on a coaster jn

[unreal trout]

no worries

thank you for clearing the concept to me

i didnt notice the subtle chang in the question pattern

usually its always the horizontal rate of change

[haughty tapir]

You're correct in saying 48/5 was the horizontal rate of change

Mb abt that

But yea in this case they want the h

[unreal trout]

i finally got the answer

thank you for your help @haughty tapir

[haughty tapir]

Np

[unreal trout]

+close

[rustic dune]

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[rustic dune]

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@unreal trout

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