Galileo's Theory of falling bodies problem

AI Thread Summary
An object falling under Galileo's theory falls distances proportional to the odd numbers in successive time intervals. In the first interval, it 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 can be calculated by determining the value of x. The correct total distance fallen after two intervals is 8 meters, not 12. Understanding the proportional relationship of distances fallen is key to solving the problem correctly.
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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