# Solving Velocity Formula: Runner A & B Crossing Paths

• razored
In summary: Runner A and Runner B are both moving towards each other, so their individual distances from the flagpole are decreasing. In order to find when their paths cross, we need to find the time when the sum of their individual distances is equal to the distance between them (11km). Using the formula V = d / t, we can set up an equation where the velocities of Runner A and Runner B are multiplied by the same time t, and when added together, equal 11km. We can then solve for t, which will give us the time when their paths cross. Once we have the time, we can plug it back into the equation to find the distance each runner has traveled in that time, giving us the answer of 3km
razored
[SOLVED] Velocity Formula

## Homework Statement

"Runner A is initially 6.0km west of a flagpole and is running with a constant velocity of 9.0km/h due east. Runner B is initially 5.0km east of the flagpole and is running with a constant velocity of 8.0km/h due west. What will be the distance of the two runners from the flagpole when their paths cross? (Leave answer in km)"

## Homework Equations

Solve this only using V = d / t

## The Attempt at a Solution

I've tried too many.

well first you need to find when their paths cross. This is when the sum of their individual distances is equal to 11 (the distance between them). Once you have this time you can figure out how far each person ran in that time because you have their velocities.

Tricky.
Here's what I did.
Set up a co-ordinate axis with your runners on the x-axis and flag pole at origin.
Now express the distance each runner runs in terms of the original distance from the flag pole given and the equal final distance $$d_f$$.
Once you have this see if it doesn't pop out at you.

D1 would be the position of Runner A; D2 would be the position of Runner B.

|D2 - D1| = 11

I don't know what to do from here.

if you think about it runner a runs 9kms in an hour and runner b runs 8kms in an hour.

9t+8t=11 gives you a way to find when they pass each other

Okay, I've figured it out. I solved for D in the equation I gave and got the answer. Before, for some unknown reason, I simply could not figure it out. Thanks!

Last edited:
Both ways work, spoon's may be a bit easier.

<--- said:
Both ways work, spoon's may be a bit easier.

It is essentially the same thing.

## 1. What is the velocity formula for calculating the speed of Runner A and B crossing paths?

The velocity formula is distance divided by time (v=d/t). In this case, the distance would be the distance between Runner A and B when they cross paths, and the time would be the time it takes for them to cross paths.

## 2. How do you determine the distance between Runner A and B in the velocity formula?

The distance can be measured in any unit of length, such as meters or kilometers. It is important to ensure that the units for distance and time are consistent when using the velocity formula.

## 3. Can the velocity formula be used for any type of motion?

Yes, the velocity formula can be used for any type of motion as long as the distance and time are known. It is commonly used for calculating speed in linear motion, but can also be applied to rotational motion.

## 4. How do you calculate the time in the velocity formula?

The time can be calculated by dividing the distance by the velocity. In the case of Runner A and B crossing paths, the time would be the time it takes for them to reach the point where they cross paths.

## 5. Is there a different formula for calculating velocity when there are multiple objects in motion?

No, the velocity formula remains the same regardless of the number of objects in motion. However, the distance and time may need to be adjusted to account for the paths of each object and when they cross paths.

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