LearningPhysics one last runner problem

  • Thread starter anglum
  • Start date
In summary, Runner A and Runner B are initially 6.0km and 4.3km from a flagpole respectively, with constant velocities of 8.4km/h east and 7.1km/h west. When their paths cross, they will be 0.4180645161 km and 5.581935484 km from the flagpole respectively. The time of intersection is 0.6645 hours and the total distance traveled by both runners is 10.3km.
  • #1
anglum
275
0

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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  • #2
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?
 
  • #3
well since the time is equal then wouldn't the distance of runner A be 1.18309 times more than runner B?
 
  • #4
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?
 
  • #5
im not sure how that comes into play since its where do they intersect
 
  • #6
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?
 
  • #7
i see that they intersect i just don't know what formula or what i try and solve for to get this problem
 
  • #8
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
 
  • #9
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.
 

Related to LearningPhysics one last runner problem

1. What is the "LearningPhysics one last runner problem"?

The "LearningPhysics one last runner problem" is a hypothetical scenario in which there are three runners on a track, each with different speeds. The first runner has a constant speed, the second runner starts at the same time but accelerates at a constant rate, and the third runner starts at the same time and decelerates at a constant rate. The problem asks for the distance between the first and second runners when the third runner catches up.

2. What is the purpose of this problem in learning physics?

The "LearningPhysics one last runner problem" is often used as a practice exercise in physics classes to help students understand and apply the concepts of uniform motion, acceleration, and distance-time graphs.

3. How do you solve the "LearningPhysics one last runner problem"?

To solve the problem, you need to use the equations of uniform motion and acceleration to determine the distance each runner has covered at a specific time. Then, set the distances of the first and second runners equal to each other to find the time at which the third runner catches up. Finally, use this time to calculate the distance between the first and second runners.

4. What are the key assumptions in the "LearningPhysics one last runner problem"?

The problem assumes that the runners are moving in a straight line, and there is no external force acting on them except for the acceleration and deceleration of the second and third runners. It also assumes that the speeds and rates of acceleration and deceleration remain constant throughout the race.

5. What are some real-life applications of the "LearningPhysics one last runner problem"?

The "LearningPhysics one last runner problem" can be applied to real-life situations, such as analyzing the motion of vehicles on a highway or the movement of objects on a conveyor belt. It can also be used to understand the concept of relative motion and how it affects the distance between two moving objects.

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