Kinematics Chasing Problem: Correct Answer and Explanation

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Homework Help Overview

The discussion revolves around a kinematics problem involving two cars, one traveling faster than the other, and the timing of their passage through an intersection. Participants are analyzing the time it takes for the second car to catch up to the first, given the initial conditions and speeds of both vehicles.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants present different calculated times for when the second car passes the first, with values such as 27.3 seconds, 33.9 seconds, and 26.6 seconds being discussed. There are questions regarding the interpretation of the problem's timing reference point and whether both answers can be correct based on different assumptions.

Discussion Status

There is an ongoing exploration of the problem's ambiguity, with participants questioning the assumptions made about the timing of the cars' passage through the intersection. Some have provided algebraic approaches to derive their answers, while others express confusion over the discrepancies in results. No consensus has been reached, but various interpretations are being examined.

Contextual Notes

Participants note that the problem does not clearly specify the reference point for time, leading to different interpretations of when to start measuring. There is also mention of potential errors introduced by unit conversions and rounding in the calculations.

jerad908
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Homework Statement
A car passes through an intersection travelling at 56 km/hr. A second car travelling at 70 km/h passes the same intersection 6.65 seconds later. How long will it be before the second car passes the first?
Relevant Equations
big 5 equations
I solved this and got 27.3 seconds so basically what I did was found the headtsart of the slower car (15.6 m/s times 6.65 seconds) but the answer given is 33.9 seconds and it uses the second (faster cars speed) to find the head start distance. Which answer is correct and why? Thanks so much
 
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jerad908 said:
Homework Statement:: A car passes through an intersection traveling at 56 km/hr. A second car traveling at 70 km/h passes the same intersection 6.65 seconds later. How long will it be before the second car passes the first?
Relevant Equations:: big 5 equations

I solved this and got 27.3 seconds so basically what I did was found the headtsart of the slower car (15.6 m/s times 6.65 seconds) but the answer given is 33.9 seconds and it uses the second (faster cars speed) to find the head start distance. Which answer is correct and why? Thanks so much
Is it a coincidence that your answer is 6.65 seconds less than the given answer? The problem asks how long will it be before the second car passes the first? OK, how long after which of the two cars passes through the intersection? Considering that the problem does not specify, I would say both answers are correct as long as you explain when t = 0 is.
 
I got 26.6 seconds (as measured from the second car going through the intersection).
 
Last edited:
Neither appear to correct. It is just a two equation algebra problem.
D1 = v1t
D2 = v2(t-6.65)
D1 = D2
So:
(56000/3600)t = (70000/3600)(t-6.65)
(14000/3600)t = 465500/3600
14t = 465.5
t = 465.5/14 = 33.25 s.

AM
 
Andrew Mason said:
t = 465.5/14 = 33.25 s.
That minus 6.65 is my 26.6s.

Sooooo... how did the OP and the book get their answers ?
 
Last edited:
Hmmm27: The question is ambiguous. It should ask "how long after the _____ car passes the intersection will the second car pass the first?" On your interpretation your answer is correct.

AM
 
My reading of it says ##t_0## is when the second car goes through, just from the way it's phrased.

I'm more interested in how both the book and the OP got consistent wrong answers :

26.6 / 33.25 sec (our answers, not too smugly correct)

vs.

27.3 / 33.9 sec (OP and source)
 
Last edited:
hmmm27 said:
My reading of it says ##t_0## is when the second car goes through, just from the way it's phrased.

I'm more interested in how both the book and the OP got consistent wrong answers :

26.6 / 33.25 sec (our answers, not too smugly correct)

vs.

27.3 / 33.9 sec (OP and book)
By unnecessarily converting to m/s and rounding 15.55... to 15.6, thereby introducing a 3% error.
 
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haruspex said:
By unnecessarily converting to m/s and rounding 15.55... to 15.6, thereby introducing a 3% error.
Quite the difference ; admittedly, dividing by 14km/h as a single step seemed suspiciously convenient. (at a guess, the OP's version was a reprint from an old book that didn't give the answers in the back)
 

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