How Fast Was the Car from City B Initially?

[PITPin]

Homework Statement

Two cars leave at the same time (one from city A and the other from city B) and drive toward each other. They first meet d=45 km far from B . Both cars reach their destination (B for the former, A for the latter) and then start driving to their initial cities.The cars have constant acceleration. They meet a second time after t=3 hours from their first meeting. What is the speed of the vehicle which (initially) leaves from B?

Homework Equations

x=vt

The Attempt at a Solution

I tried fragmenting the problem. First I wrote the equations for the first meeting of the cars (d=v_B*t₀, D-d=v_A*t₀, where D is the distance between A and B) then the equations for the arrival of car B (the one which leaves from B) while car A has not yet arrived (I considered B to be faster). Then the equations for the arrival of car A and finally, the equations for the second meeting. I got 9 equations including the one for the time and I am not sure this is the right way to solve the problem. I also thought about considering the cars to be moving in a circle,but couldn't get enough equations.

I am sorry for any translation mistakes. I, myself, have found the original problem statement to be ambiguous, but I tried to translate it as accurate as possible.

 

[PeroK]

If you have not already done so, can you derive the equation

$Dv_b = 45(v_a + v_b)$

where $D$ is the distance between the cities.

 

[WrongMan]

well.. 9 equations? that's a lot...
what equations and unknowns did you get?
You need to conceptualize the problem, draw out the important moments ofthe problem and do the minimum equations and the minimum unknowns possible.
start by writing out the equations for the stated moments(first meet, reach city, second meet, reach city)
this has multiple possible answers!

 

[PeroK]

well.. 9 equations? that's a lot...
what equations and unknowns did you get?
You need to conceptualize the problem, draw out the important moments ofthe problem and do the minimum equations and the minimum unknowns possible.
start by writing out the equations for the stated moments(first meet, reach city, second meet, reach city)
this has multiple possible answers!

There's only one answer for $v_b$.

 

[WrongMan]

There's only one answer for $v_b$.

oh right my mistake

 

[PeroK]

oh right my mistake

There are multiple solutions for $D$ and $v_a$, though.

 

[WrongMan]

There are multiple solutions for $D$ and $v_a$, though.

ah yes... not crazy after all... its just when i see these kind of problems i have to find all unknowns and forget i was only supposed to find one... and i don't allways write everything on paper...
now that i think (more) about it D can't change that much... carB has to get to A in at least 3 hours, right?

 

[PeroK]

Yes, there must be upper and lower limits on $D$.

 

[PITPin]

If you have not already done so, can you derive the equation

$Dv_b = 45(v_a + v_b)$

where $D$ is the distance between the cities.

Can you please tell me more about this equation? I have just started using derivatives in physics and I'm having trouble understanding where this equation came from and what it means. Is D a function? If so, I think the result would be 45.

 

[PeroK]

Can you please tell me more about this equation? I have just started using derivatives in physics and I'm having trouble understanding where this equation came from and what it means. Is D a function? If so, I think the result would be 45.

As I said, $D$ is just the distance between the cities. I was using your notation from post #1!