Question

Prove Galileo's law of odd numbers

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Answer 1

Galileo’s law of odd number is distance covered by the free falling object is increased by an odd number in successive time interval. Suppose a body is dropped from some height and it falls under the gravity. Again, suppose that body covers 1 unit of distance in 1 sec then according to this law in next second body will cover a distance of 3 units and then 5 units and so on….

Time distance covered in nth second total distance covered form initial point
1sec 1 unit 1 unit
2sec 3 units 1+3=4 units
3sec 5 units 4+5=9 units
4sec 7 units 9+7= 16 units

Galileo's law of odd numbers proved.