LearningPhysics one last runner problem

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Homework Help Overview

The problem involves two runners, A and B, moving towards each other from different starting points relative to a flagpole. Runner A starts 6.0 km west of the flagpole and runs east at a velocity of 8.4 km/h, while Runner B starts 4.3 km east of the flagpole and runs west at a velocity of 7.1 km/h. The objective is to determine how far each runner is from the flagpole when their paths intersect.

Discussion Character

  • Exploratory, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Participants discuss the equality of time for both runners and the total distance between them, which is 10.3 km. There are inquiries about the relationship between the distances traveled by each runner and how to set up the equations to find the intersection point.

Discussion Status

The discussion has progressed with participants exploring the relationship between the distances traveled by the runners and the total distance apart. Some have suggested drawing a sketch to visualize the problem, while others have confirmed the equation setup for finding the time of intersection. There is an acknowledgment of the correct approach to solving for the distances after determining the time.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the depth of exploration into the problem-solving process. There is a sense of urgency as one participant mentions working ahead to avoid problems over the weekend.

anglum
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Homework Statement


Runner A is initially 6.0km west of a flagpole and is running with a constant velocity of 8.4km/h east. Runner B is initially 4.3km east of flagpole and is running with a constant velocity of 7.1km/h west

how far are the runners from the flagpole when their paths cross?

The Attempt at a Solution



so again the time for both are the same and the distance apart is 10.3 km
do i solve for t since t is equal for both runners?
 
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anglum said:

Homework Statement


Runner A is initially 6.0km west of a flagpole and is running with a constant velocity of 8.4km/h east. Runner B is initially 4.3km east of flagpole and is running with a constant velocity of 7.1km/h west

how far are the runners from the flagpole when their paths cross?

The Attempt at a Solution



so again the time for both are the same and the distance apart is 10.3 km
do i solve for t since t is equal for both runners?

Yes, t is equal... how do the distances the two runners travel relate?
 
well since the time is equal then wouldn't the distance of runner A be 1.18309 times more than runner B?
 
anglum said:
well since the time is equal then wouldn't the distance of runner A be 1.18309 times more than runner B?

Yes, but you don't really need that relationship... how does the 10.3km come into play here?
 
im not sure how that comes into play since its where do they intersect
 
anglum said:
im not sure how that comes into play since its where do they intersect

draw a sketch... they start at 10.3km apart... they run towards each other... draw a line for the path one runner travels... draw a line for the other...

what is the relationship between the length of the two lines?
 
i see that they intersect i just don't know what formula or what i try and solve for to get this problem
 
anglum said:
i see that they intersect i just don't know what formula or what i try and solve for to get this problem

Well, I was getting at... the distance traveled by one runner + distance traveled by the other = 10.3 km
 
ahhhhh damn i knew that ... i thought u meant something more complex... its gettin late here and I am bucklin down to finsih this last one
 
  • #10
so if the Time is equal and the Distance is D of 1 + D of 2 = 10.3 how do i solve for that?
 
  • #11
do i get 8.4t + 7.1t = 10.3 km?

which give me a time of intersect at .6645 hours?
 
  • #12
anglum said:
do i get 8.4t + 7.1t = 10.3 km?

which give me a time of intersect at .6645 hours?

yup. how far are they from the flagpole.
 
  • #13
so after that time runner A has gone 5.581935484 km and he was initially 6km away

so he is now .4180645161 km away from the pole
 
  • #14
AWESOME THAT WAS CORRECT

YOU ARE THE MAN AND A SAVIOR... this should be all my problems until next week... i was workin ahead to avoid them over the weekend
 
  • #15
anglum said:
AWESOME THAT WAS CORRECT

YOU ARE THE MAN AND A SAVIOR... this should be all my problems until next week... i was workin ahead to avoid them over the weekend

cool. :smile: no prob.
 

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