IMPLICIT DIFFERENTIATION (PLEASE CAN SOMEONE HELP)

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Danie;l

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1)

Two cars are travelling on perpendicular roads toward the same intersection. One of them, an Audi, is going west toward it at 52 km/hr. The other, a BMW, is going north toward it at 65 km/hr.
At what rate are the cars approaching each other when the Audi is 500 m east of the intersection and the BMW is 1.2 km south of the intersection?
 
Danie;l said:
1)

Two cars are travelling on perpendicular roads toward the same intersection. One of them, an Audi, is going west toward it at 52 km/hr. The other, a BMW, is going north toward it at 65 km/hr.
At what rate are the cars approaching each other when the Audi is 500 m east of the intersection and the BMW is 1.2 km south of the intersection?
Click to expand...
First draw sketch of the "situation". Then calculate the relative velocity of one car w.r.t. to the other.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem.
 
"at what rate" certainly could be interpreted as "WRT time".

It's a right triangle and a Pythagorean Theorem. If you cannot interpret the drawing, you should get up to speed on your Geometry.

1) When the Audi is 500 m east of the intersection and

2) the BMW is 1.2 km south of the intersection?

Are 1) and 2) the same MOMENT? Or is this two different questions?
 
At t = 0 seconds

Two cars are travelling on perpendicular roads toward the same intersection. One of them, an Audi, is going west toward it at 52 km/hr. The other, a BMW, is going north toward it at 65 km/hr.

How far apart are they? No idea. We can't solve without some sort of fixed point. Thus, after THE SAME time period has elapsed: <== I made an assumption and I stated it.

t = r hours

the Audi is 500 m east of the intersection (already through!) and the BMW is 1.2 km south of the intersection (still approaching)

We may be expecting the vehicles to meet at the intersection. This appears not to be the case. We know that this distance is 5002+12002m\sqrt{500^2 + 1200^2} m We'll need this later.

How far are they from the intersection at any time after that?

t = s hrs = # of hours travelled after the first r hours that got us close to the intersection.

Audi: 500 m + s * 52 kmh = S(s)
Similarly
Beemer: 1200 m - s*65 kmh = Q(s)
Assuming 500m past and 1200m short are the same moment. <== I made an assumption and I stated it.
We're also assuming the speeds are constant. <== I made an assumption and I stated it.

Now, what is the distance between the two vehicles? Let's call it "D(t)". Then we have:

For just over one minute more, we have the Audi fleeing the intersection SLOWER than the BMW is approaching the intersection, sort of a chase. It is this moment that concerns us. At this moment, they are getting closer - the distance is DECREASING. We had better get a negative number by the time we think we're done.

D2=S2+Q2D^{2} = S^{2} + Q^{2}
Applying the derivative:

DdDdt=SdSdt+QdQdtD\dfrac{dD}{dt} = S\dfrac{dS}{dt} + Q\dfrac{dQ}{dt}
We already know DS/dt (52 kmh) and DQ/dt (-65 kmh) and D (1300 m) and S (500 m) and Q (1200 m). Substitute and solve for dD/dt.

Granted, it is a complicated problem and it required some assumptions. Welcome to the REAL world!! You just have to dig in and see where it leads. Don't give up because you cannot see the end from the beginning.
 
Please go away. First you post the problem. Then you say you solved it. Then you say you'll learn if you are shown how to do it. Then you say that you don't understand something. Then you say that you want a helper to give you the answer just to confirm it is what you got. Please go away.
 
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