Finding when two runners cross

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In summary: We can use this value to find the distance traveled by each runner at the time of crossing:xA = vA*tA = (4.8 km/h)*(0.698 hours) = 3.35 kmxB = vB*tB = (-8.6 km/h)*(0.698 hours) = -5.99 kmSince the distances are equal, we know that the runners will be 3.35 km from the flagpole when their paths cross. In summary, Runner A and Runner B will be 3.35 km from the flagpole when their paths cross. I hope this helps! If you have any further questions, please don't hesitate to ask for clarification. Best
  • #1
gotpink74
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Homework Statement


Homework Statement
Runner A is initially 6.0 km west of a flagpole and is running with a constant velocity of 4.8 km/h due east. Runner B is initially 6.6 km east of the flagpole and is running with a constant velocity of 8.6 km/h due west. What will be the distance of the two runners from the flagpole when their paths cross?


2. Homework Equations
i have no clue

3. The Attempt at a Solution
i don't even know where to start
HELP!
 
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  • #2
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Thank you for your question. I can help you solve this problem using the principles of physics. Let's start by defining some variables:

xA = distance of Runner A from the flagpole (in km)
vA = velocity of Runner A (in km/h)
xB = distance of Runner B from the flagpole (in km)
vB = velocity of Runner B (in km/h)

We know that Runner A is initially 6.0 km west of the flagpole, so we can write xA = -6.0 km. Similarly, Runner B is initially 6.6 km east of the flagpole, so xB = 6.6 km. We also know that Runner A is running with a constant velocity of 4.8 km/h due east, so vA = 4.8 km/h. Similarly, Runner B is running with a constant velocity of 8.6 km/h due west, so vB = -8.6 km/h. The negative sign for vB indicates that Runner B is moving in the opposite direction of Runner A.

Now, let's think about what happens when the two runners cross paths. At this point, the distance of Runner A from the flagpole (xA) will be equal to the distance of Runner B from the flagpole (xB). We can write this as an equation:

xA = xB

We can also use the equation for distance (d = vt) to find the distance traveled by each runner at the time of crossing:

xA = vA*tA
xB = vB*tB

where tA and tB are the times it takes for Runner A and Runner B to reach the crossing point, respectively. Since we know that the distances are equal, we can set these two equations equal to each other:

vA*tA = vB*tB

Now, we can solve for tA or tB. Let's choose tA:

tA = (vB*tB)/vA

Substituting this into the equation for xA, we get:

xA = vA*(vB*tB)/vA

Simplifying, we get:

xA = vB*tB

Now, we can substitute the values we know into this equation:

-6.0 km = (-8.6 km/h)*tB

Solving for tB, we get tB =
 

Related to Finding when two runners cross

1. How do you determine when two runners will cross paths?

The exact timing of when two runners will cross paths can be determined by calculating their individual speeds and distances. By dividing the distance between the two runners by the difference in their speeds, you can find the time it takes for them to meet at the same point.

2. What factors can affect when two runners will cross paths?

The main factors that can affect when two runners will cross paths are their individual speeds, distances, and starting points. Other factors such as terrain, weather, and obstacles can also impact the timing of their meeting.

3. Can you use a formula to find when two runners will cross paths?

Yes, there is a formula that can be used to find when two runners will cross paths. This formula is Distance = Speed x Time, which can be rearranged to Time = Distance/Speed. By plugging in the distances and speeds of the two runners, you can solve for the time it takes for them to cross paths.

4. What if the two runners are not running at a constant speed?

If the two runners are not running at a constant speed, then it becomes more difficult to determine when they will cross paths. In this case, you can use an average speed by calculating the total distance traveled and total time taken by each runner. Then, use the same formula (Time = Distance/Speed) to find the estimated time of their meeting.

5. Can you predict when two runners will cross paths if they are running in different directions?

Yes, it is still possible to predict when two runners will cross paths if they are running in different directions. In this case, you will need to consider their relative distances and speeds from each other. By using the formula Time = Distance/Relative Speed, you can find the estimated time of their meeting.

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