Relative velocity of two cars

In summary, the question is how long it takes for a car traveling at 60.0 km/hr in the left lane to catch up to a car traveling at 40.0 km/hr in the right lane, when the cars' front bumpers are initially 100 m apart. The key is to find the velocity of the left car in relation to the right car, which is 20 km/hr. Using the given distance of 100 m, we can calculate the catchup time in seconds by converting from km/hr to m/s. The final answer is 18.0 seconds.
  • #1
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How long does it take an automobile traveling in the left lane at 60.0 km/hr to pull along side a car traveling in the right lane at 40.0 km/hr if the cars' front bumpers are initially 100 m apart?

I know the velocity of the car in the left is 60 and the velocity of the car on the right is 40. I also know it's imperative to find the velocity of the left car in relation to the right car in order to compare their distances. I found this to be 20 km/hr. What I don't know, however, is how to find out how far the car on the right goes before the car on the left reaches it. I know time is distance divided by velocity, so I figure that if I can find this distance and divide it by 20 km/hr, I'll have the time.

I also know the answer in the back of the book .. 18.0 seconds. The question is, how do I get it?
 
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  • #2
catchup time in hrs = 100 m/(20 km/hr) = .1 km/(20 km/hr) = ?

catchup time in secs = ?
 
  • #3
What I don't know, however, is how to find out how far the car on the right goes before the car on the left reaches it.
You don't need to know that. The whole point of finding the speed of one car relative to another is to be able to use the distance between them as the distance- and you are given that. You just have to be careful to convert from km to m and from hr to sec.
 

1. What is relative velocity and how is it calculated?

Relative velocity refers to the speed and direction of an object in relation to another object. It is calculated by subtracting the velocity of the first object from the velocity of the second object.

2. How does the distance between the two cars affect their relative velocity?

The distance between two cars does not directly affect their relative velocity. However, the distance between them can impact the perception of their relative velocity. For example, two cars traveling at the same speed may appear to have a higher relative velocity if they are closer together, compared to if they are further apart.

3. Can two cars have the same relative velocity?

Yes, two cars can have the same relative velocity if they are traveling at the same speed and in the same direction. However, if they are traveling at different speeds or in opposite directions, their relative velocity will be different.

4. How is the relative velocity affected if the two cars are traveling in different directions?

If two cars are traveling in different directions, their relative velocity will be the sum of their individual velocities. For example, if one car is traveling at 50 km/h east and the other car is traveling at 30 km/h west, their relative velocity will be 80 km/h east.

5. How does the angle of the cars' motion affect their relative velocity?

The angle of the cars' motion will affect their relative velocity if they are not traveling in the same direction. In this case, their relative velocity will be calculated using trigonometric functions to determine the horizontal and vertical components of their velocities. The magnitude and direction of their relative velocity will be determined by combining these components.

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