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