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
