Dimensional Analysis and the mathematical steps throughout a process.

1. Apr 3, 2012

Olly_price

One would assume that:

$$t \propto h^\alpha m^\beta g^\gamma$$

Where t = time taken for object to fall, h = height dropped from, m = mass, g = acceleration due to gravity.

By doing some dimensional analysis one can find that:

$$t \propto h^\frac{1}{2} g^\frac{-1}{2}$$ and that t is independant of the objects mass.

From this, one can derive that:

$$t = C \surd\frac{h}{g}$$

Where C is some unknown constant of proportionality.

MY QUESTION:

How does one get from $$t \propto h^\frac{1}{2} g^\frac{-1}{2}$$ to $$t = C \surd\frac{h}{g}$$. I need to know all the mathematical processes and each step in detail.

2. Apr 3, 2012

Integral

Staff Emeritus
x-1/2=$\sqrt{ \frac 1 x}$

How can you not know this?

3. Apr 3, 2012

Olly_price

Probably cos I'm 14 and haven't been taught it...

4. Apr 4, 2012

Olly_price

Besides, that's not even an answer to my question!

I asked for each mathematical step and all you give me is $$x^-1/2=√\frac{1}{x}$$

So come on, what's each mathematical step?