How to find displacement of 400m track

In summary, the question involves a runner running 6.5 laps around a 400m track and finding the displacement. The attempted solution suggests that more details about the track and starting point are needed, and explains that displacement is the shortest line from the starting point to the ending point. It is then mentioned that the correct answer is 160m, which is marked on a diagram provided with the question.
  • #1
Rbraind
10
0

Homework Statement



I know this is basic but I'm stumped

Homework Equations



a runner runs 6.5 laps around a 400m track, what's the displacement. I thought it would be 200m but the answer provided says 160m and I just can't work out how to get to this answer

The Attempt at a Solution

 
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  • #2
You might need some more details about the shape of the track and the runner's starting point.
 
  • #3
Displacement will equal the length of the shortest line possible drawn from the starting point to the ending point. As you can see, if the track has any curvature at all during that half of a lap, the displacement will be less than 200 m.
 
  • #4
Thanks people for your help. However I'm an idiot! Just realized there was a diagram with the question and the displacement marked in...
 
  • #5


To find the displacement of a 400m track, we must first understand the definition of displacement. Displacement is the distance between the initial and final positions of an object, taking into account the direction of movement. In this scenario, the runner is running 6.5 laps around the track, which means they are completing a full circle 6.5 times.

To find the displacement, we can use the formula:

Displacement = Distance x Cosine(angle)

In this case, the distance is the circumference of the track, which is 400m, and the angle is 360 degrees (since the runner is completing a full circle). Plugging these values into the formula, we get:

Displacement = 400m x Cos(360 degrees) = 400m x 1 = 400m

This means that the displacement of the runner after completing 6.5 laps around the track is 400m. It is not 200m as initially thought, as this would only be the distance traveled, not the displacement.

To understand why the answer provided is 160m, we must consider the direction of movement. The runner is completing 6.5 laps in a clockwise direction, which means their displacement is in the opposite direction, counterclockwise. This results in a negative displacement, as the runner ends up 160m behind their initial starting point.

Therefore, the correct answer is a displacement of -160m, taking into account both distance and direction of movement. This is an important concept in understanding displacement and its relationship to distance and direction. I hope this explanation helps to clarify any confusion.
 

1. How do I calculate displacement for a 400m track?

To find the displacement of a 400m track, you will need to measure the distance from the starting point to the finishing point. This can be done using a measuring tape or a measuring wheel. Once you have the distance, you can use the formula: displacement = final position - initial position. In this case, the final position would be 400m and the initial position would be 0m, resulting in a displacement of 400m.

2. What is displacement and why is it important?

Displacement is the shortest distance between the starting point and the finishing point of an object's motion. It is important because it gives us information about the overall movement of an object, regardless of the path it takes. It is also a key component in calculating an object's velocity and acceleration.

3. Can displacement be negative?

Yes, displacement can be negative. This occurs when an object moves in the opposite direction of its initial position. For example, if a runner starts at the 0m mark on a track and finishes at the -400m mark, the displacement would be -400m.

4. How is displacement different from distance?

Displacement refers to the overall change in position, while distance refers to the total amount of ground covered by an object. Displacement takes into account the direction of movement, while distance does not. For example, a runner who runs in a circle and ends up back at their starting point would have a displacement of 0m, but a distance of the circumference of the circle.

5. Can displacement be greater than distance?

No, displacement cannot be greater than distance. This is because displacement is a vector quantity that takes into account both magnitude and direction, while distance is a scalar quantity that only measures the magnitude. In other words, displacement is a more specific and precise measurement of an object's motion, while distance is a more general measurement.

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