How Long Before Runners A and B Meet at the Starting Point on a Circular Track?

In summary, the problem involves two runners, A and B, moving on a circular track of circumference 100m at speeds of 3m/sec and 1m/sec respectively. The question is asking for the time it takes for both runners to reach the starting point at the same time, assuming they are running in the same direction. The solution involves finding the time it takes for B to complete one lap and then multiplying it by 3 for A to complete 3 laps.
  • #1
Benjamin_harsh
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5
Homework Statement
What is the time taken by A & B to reach starting point for first time?
Relevant Equations
Relative speed = 3-1; 1m/sec since it is same direction.
Circular track: Both are in same direction.A = 3m/sec, B = 1 m/sec. Circumference of track= 100m.

What is the time taken by A & B to reach starting point for first time?
 
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  • #2
Benjamin_harsh said:
Homework Statement: What is the time taken by A & B to reach starting point for first time?
Homework Equations: Relative speed = 3-1; 1m/sec since it is same direction.

Circular track: Both are in same direction.A = 3m/sec, B = 1 m/sec. Circumference of track= 100m.

What is the time taken by A & B to reach starting point for first time?
Let's see your attempt at a solution.
Also, please give some meaningful equations, and/or definitions.
 
  • #3
SammyS said:
Also, please give some meaningful equations, and/or definitions.
... and a clearer problem statement.
Benjamin_harsh said:
What is the time taken by A & B to reach starting point for first time?
Is this asking how long will it take for both A and B to cross the finish line at the same time?
 
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  • #4
I guess we also assume both A, B run a circle of equal perimeter? These tracks usually have concentric rings and outer rings have larger perimeters than inner ones.
 
  • #5
B moves at 1 m/sec.

The track is 100 m in length. T =100/1 = 100 sec for B to complete one lap on the track.

In that time, A will complete 3 laps.

So answer will be 100 sec?
 
  • #6
Just to clarify a bit more. You want to see when they will meet/coincide in the starting line?
 
  • #7
WWGD said:
You want to see when they will meet/coincide in the starting line?
Give me answers in both cases: meet/coincide in the starting line
 
  • #8
Benjamin_harsh said:
Give me answers in both cases: meet/coincide in the starting line
No, that's not what we do here. Providing complete answers to posted homework questions is against the rules at this site.

Since you still haven't given us a clear explanation of what the problem is asking for, I am closing this thread. Please start a new thread with a clear problem statement.
 
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Related to How Long Before Runners A and B Meet at the Starting Point on a Circular Track?

What is the circular track problem?

The circular track problem is a physics problem that involves calculating the position, velocity, and acceleration of an object moving in a circular path. It is often used to test understanding of concepts such as centripetal force and angular velocity.

What are the key equations used to solve the circular track problem?

The key equations used to solve the circular track problem are the equations for centripetal force, centripetal acceleration, and angular velocity. These are:
Fc = mv2/r
ac = v2/r
ω = v/r
where Fc is the centripetal force, m is the mass of the object, v is the velocity, r is the radius of the circular path, ac is the centripetal acceleration, and ω is the angular velocity.

What are some real-life examples of the circular track problem?

Some real-life examples of the circular track problem include a car driving around a race track, a satellite orbiting around the Earth, and a roller coaster going around a loop. In each of these cases, the object is moving in a circular path and the equations for centripetal force, acceleration, and angular velocity can be used to calculate its motion.

What happens to the motion of an object on a circular track when the radius is changed?

When the radius of a circular track is changed, the motion of the object on the track also changes. If the radius is increased, the object will have a larger radius and therefore a smaller angular velocity. This means it will take longer to complete one full revolution around the track. If the radius is decreased, the object will have a smaller radius and a larger angular velocity, causing it to complete one full revolution in a shorter amount of time.

How does the speed of an object on a circular track affect its motion?

The speed of an object on a circular track affects its motion in several ways. In general, a higher speed will result in a larger centripetal force and acceleration, causing the object to move in a larger radius and complete more revolutions in a given time. Additionally, a higher speed may also cause the object to experience a higher frictional force, which can affect its overall motion. However, the angular velocity of the object will remain the same regardless of its speed, as long as the radius of the circular path remains constant.

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