Kinematics Chasing Problem: Correct Answer and Explanation

[jerad908]

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

 

[kuruman]

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.

 

[hmmm27]

I got 26.6 seconds (as measured from the second car going through the intersection).

 

[Andrew Mason]

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

 

[hmmm27]

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 ?

 

[Andrew Mason]

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

 

[hmmm27]

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)

 

[haruspex]

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.

 

[hmmm27]

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)