Chain rule

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nazmi

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Joined
Nov 24, 2009
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Hi there.. this question kinda confusing me..
i ask my lecturer already.. but, he said my answer isn't correct..
i've done it already..
need someone to consult me where did i do wrong..

Two straight roads intersect at right angles. Car A, moving on one of the roads,
approaches the intersection at 60km/h and Car B, moving on the other road,
approaches the intersection at 80km/h. At what rate is the distance between the
cars changing when A is 0.5km from the intersection and B is 0.7km from the
intersection?

i tried to solve it..
da/dt = -60km/h
db/dt = -80km/h

X = (a^2 + b^2)^1/2

dX/dt = ?

X(dX/dt) = a(da/dt) + b(db/dt)
0.86km(dX/dt) = (.5km)(-60km/h) + (.7km)(-80km/h)

i got dX/dt = -100km/h

am i done it right?
 
You have the right idea.

\(\displaystyle \sqrt{(.5)^{2}+(.7)^{2}}=.86\)
 
i still got 0.86.. and i assume u round up the number..
am i right?
.5^2 = 0.25
.7^2 = 0.48
(0.25 + 0.48)^1/2 = 0.860232526
 
\(\displaystyle \text{car A rate}=\frac{dx}{dt}=-60\)

\(\displaystyle \text{car B rate}=\frac{dy}{dt}=-80\)

But \(\displaystyle D^{2}=x^{2}+y^{2}\)

\(\displaystyle \frac{1}{D}\left(x\frac{dx}{dt}+y\frac{dy}{dt}\right)=\frac{1}{.86}\left(.5(-60)+.7(-80)\right)=-100\)

I agree.

This is almost identical to the famous related rates 'ladder problems'

This seems rather straight forward. I would like to see how your instructor does it.
 
hurmm.. i'm still wondering why did my lecturer told me that there's something
wrong with my solution.. :(
 
\(\displaystyle -100 \ is \ incorrect, \ -100 \ km/hr \ is \ correct.\)

\(\displaystyle When \ doing \ a \ problem \ concerning \ units, \ since \ all \ the \ units \ cancel, \ except \ the \ final \ one, \ if \ you\)

\(\displaystyle \ do \ not \ use \ the \ appropriate \ units, \ your \ answer \ is \ wrong.\)

\(\displaystyle After \ thought: \ I \ am \ as \ guilty \ as \ the \ next \ person \ in \ forgetting \ this \ "axiom", \ but \ do \ as \ I \ tell\)

\(\displaystyle \ you, \ not \ as \ I \ do.\)
 
Good point. I, as one can see, am guilty of the same thing after all these years. Like forgetting the C (constant) when integrating.
 
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