Runner A & B Paths Cross: Displacement of B from Flagpole

[AdnamaLeigh]

Runner A is initially 4.54 mi West of a flagpole and is running with a constant velocity of 7.06 mi/h due East. Runner B is initially 4.34 mi East of the flagpole and is running with a constant velocity of 6.82 mi/h due West. Consider East to be in the positive direction. What is the displacement of runner B from the flagpole when their paths cross? Answer in units of mi.

Thanks.

 

[quantumdude]

Please show how you started, and where you got stuck.

 

[AdnamaLeigh]

I figured out that it will take A .643hr to reach the flagpole but B .636hr so I know that when the two cross, it's going to be on the left side of the pole, with negative displacement. At .636hrs, A will be 0.05mi away from the pole so they should cross soon. That's where I'm stuck; I think I'm making this too confusing.

 

[quantumdude]

You should try to write down the displacement of each runner as a function of time, like this:

$$x(t)=vt+x_0$$,

where $x(t)$ is the displacement, $v$ is the velocity, $t$ is the time, and $x_0$ is the initial displacement. To find out when the runners meet, simply equate the two functions and solve for time.

 

[SGT]

What is the initial distance between the two runners?
What is their relative velocity?
Dividing the distance by the velocity you find the time they take to cross each other.