Question

Galileo's law of odd numbers: The distance traversed during equal intervals of time, by a body falling from rest,stand to one another in the same ratio as the odd number beginning with unity(namely 1:3:5:7.....)prove it


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Answer 1

Explanation:

Let a ball freely fall from some height

Initial Velocity = 0

At the end of 1st second, its Velocity will be given by

v= u+gt => v = 9.8m/sec

And the Distance travelled during the 1 st second is given by

s= ut+ 1/2*g*t^2

=> s= 4.9 m

From t=0 to t=2 sec

Distance travelled will be 1/2gt^2. = 1/2*9.8*4 = 19.6 m

Hence from t=1 to t=2, Distance travelled = 19.6-4.9 = 14.7m

similarly in First 3 seconds, Distance = 44.1 m

Hence Distance in 3 second= 44.1-19.6 = 24.5

Hence Distance traveled in 1st:2nd:3re second= 4.9:19.6:24.5 = 1:3:5

Hence proved