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In a made-up physics club, a ball is dropped and its fall is timed…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
In a made-up physics club, a ball is dropped and its fall is timed. After , , , and s it has fallen , , , and m. Find between time and distance, and between time and the square root of the distance, to four decimal places. Which relationship is closer to a straight line?
Need a reminder? The key ideaShow
Growth by an equal factor each step is a straight line on a log scale: , with a factor of per unit of and a doubling time of . A square root straightens a quantity that grows like a square.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The distances. . High, but the points curve upwards.
Step 2. The square roots. With , .
Answer: and ; the square roots lie much closer to a straight line.
Why. For a falling object, the distance grows like the square of the time (). So grows in step with .
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