how to prove Galileo's law of odd numbers?
Answers
Answer:
The Galileo's law of odd numbers states that the distances traveled are proportional to the squares of the elapsed times. In other words, in equal successive periods of time, the distances traveled by a free-falling body are proportional to the succession of odd numbers(1,3,5,7, etc.).
Galileo observed that the distance traveled by falling objects is proportional to the square of the time elapsed. He discovered the equivalent fact that the sequence of distances traveled between equal times are in the proportions 1, 3, 5, 7, 9, etc, through the odd numbers.
In other words, if you are watching something fall from a great height and it falls distance d in the first second, then it will fall by 3d in the next second, 5d in the next and so on.
The reason that is equivalent to the other way of saying it is because the numbers
1,
1+3,
1+3+5,
1+3+5+7,
etc,
are the perfect squares of all the integers in order.
Hope it helped
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