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Physics problems: kinematics

 

Problem 11.

From the dimensional analysis find the time t it takes for a ball to fall from a height h.

 

Solution:

We know that the time should depend on the height, h, and free fall acceleration, g. So we can write:

Where a is a dimensionless constant (we cannot find this constant) and x, y are constant, which can be found from dimensional analysis.

The units of t is seconds. The units of h is meter, the unit of g is . Then we have:

From this equation we have:

Then

Then

 

 

 

 

 

 

 

 

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