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The hill people measure heights using the top of the highest peak as a reference point and down as the positive direction. Valley people use the river bottom as the reference point and up as the positive direction. If they both observed a stone falling, would they agree on its velocity? speed? displacement? distance?

User Suhas Gosavi
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1 Answer

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15 votes

ANSWER and EXPLANATION

To be able to answer this question, we need to understand the difference between a scalar quantity and a vector quantity.

A scalar quantity is one that has only magnitude. This means that we can measure "how large" its value is but we cannot measure its direction. Speed and distance are scalar quantities.

A vector quantity is one that has both magnitude and direction. Velocity and displacement are vector quantities.

For a stone falling, both hill people and valley people will be able to measure the distance it travels to be the same since the distance is simply the measure of how far an object travels between two points. Hence, they will also measure its speed to be the same, because speed is simply the measure of how fast an object is traveling without measuring the direction it travels.

However, the hill people will measure the stone's displacement differently from the valley people. The hill people will measure the displacement of the stone to be positive since the stone falls from up to down (positive direction) but the valley people will measure the displacement of the stone to be negative (since up is the positive direction in their view).

The same applies to the stone's velocity. Its velocity will be positive for the hill people (positive direction) while it will be negative for the valley people (negative direction).

Therefore, they will agree on the stone's speed and distance but they will disagree on the stone's velocity and displacement.

User Alisso
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