Calculating Distance and Position of Two Moving Objects in 2D Space

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In summary, two soccer players, Sherman and Malissa, start from the same point at the same time. Sherman runs east at 4.00 m/s, while Malissa runs north of east at 5.40 m/s. The questions ask how long it takes for them to be 25.0 m apart and how far apart they are after 4.00 s. To answer these, we need to find their position vector and the difference between them. We can also show their positions at any time and find the modulus of the vector difference.
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7282
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HELP! I have no clue how to figure out how far apart they are! How would I figure out how far the 2 soccer players are?


Two soccer players, Sherman and Malissa , begin running from approximately the same point at the same time. Sherman runs in easterly direction at 4.00 m/s, while Malissa takes off in a direction 60.0˚ north of east (i.e. [N 30.0˚ E]) at 5.40 m/s.
(a) How long is it before they are 25.0 m apart?
(b) How far apart are they after 4.00 s?
 
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  • #2
Find the position vector of both the player at any instant. Then the the displacement vector at any instant will be the difference in the position vectors.
 
  • #3
Show the position of the two players at any time.Then find the modulus of the vector difference between their position.
 

FAQ: Calculating Distance and Position of Two Moving Objects in 2D Space

How do you measure the distance between two points?

To measure the distance between two points, you can use a measuring tool such as a ruler, tape measure, or measuring wheel. You can also use mathematical equations, such as the Pythagorean theorem, to calculate the distance between two points on a coordinate plane.

What is the difference between distance and displacement?

Distance refers to the total length traveled between two points, while displacement refers to the straight-line distance between the starting and ending points. Displacement takes into account direction, whereas distance does not.

How does the distance between two points affect the time it takes to travel?

The distance between two points can affect the time it takes to travel in several ways. For example, the greater the distance, the longer the journey will take. Additionally, factors such as mode of transportation, speed, and route can also impact the time it takes to travel between two points.

Is there a limit to the distance that can be measured between two points?

There is no limit to the distance that can be measured between two points. With advancements in technology, scientists are able to measure distances that are extremely large, such as the distance between planets and stars in the universe.

How does the curvature of the Earth affect distance measurements?

The curvature of the Earth can affect distance measurements, especially when measuring large distances. This is because the Earth is not a perfect sphere, and as the distance increases, the curvature becomes more significant. To account for this, scientists use mathematical equations and tools such as GPS to accurately measure distances on a curved surface.

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