Galileo's Theory of falling bodies problem

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SUMMARY

Galileo's Theory of falling bodies states that the distance fallen by an object during successive time intervals is proportional to the sequence of odd numbers. In the first interval, an object falls a distance of 1x, followed by 3x in the second interval, and 5x in the third. Given that the object falls five meters in the first interval, the total distance fallen at the end of the second interval is 12 meters, which is incorrect. The correct approach involves determining the value of x based on the initial distance fallen.

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  • Understanding of kinematic equations
  • Familiarity with sequences and series, particularly odd numbers
  • Basic knowledge of physics principles related to motion
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Ki-nana18
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Homework Statement


If an object falls five meters during the first interval of time, what is the total distance fallen at the end of the second interval of time? (Galileo's Theory of falling bodies)


Homework Equations



The Attempt at a Solution


I know that at successive intervals of time the distance fallen is proportional to the odd numbers. So I suspect it to be 12, but apparently I'm wrong.
 
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Use you kinematic equations to help you out here.
 


Ki-nana18 said:

The Attempt at a Solution


I know that at successive intervals of time the distance fallen is proportional to the odd numbers.
That's right. Another way to say that is
  • The object falls a distance 1x in the 1st time interval.
  • The object falls a distance 3x in the 2nd time interval.
  • Then 5x in the 3rd time interval, etc. etc.
So the question is, what is x, given what they tell you about the 1st time interval?

So I suspect it to be 12, but apparently I'm wrong.
Yes, that's wrong. Again, what is the value of x here?
 

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