Determining Throwing Height: Dimensional Analysis

[Firben]

Throwing height:

A rock is thrown straight up with initial speed v. Determine a expression for the maximum height h the rock reach.The air resistance is neglected and the throwing height are dependent on the gravity.

Variable list:

Speed: V, LT^-1
Height h, L
gravity g, LT^-2

My matrix:

---L T--
V |1 -1|
L |1 0 |
g |1 -2|

After reduction i got

(k=constant)

k = h*g*v^2

It should be h = k*v^2/g

Any ideas ?

 

[BruceW]

I think you did the reduction wrong. The matrix is right though. It doesn't involve many variables, so you could do the problem without using a matrix.

 

[Firben]

Yes, but how?

 

[BruceW]

Well, you can assume that each variable is raised to some power, and you know that the equation including them must be dimensionally correct, so then you can solve for what those powers are.

This is effectively the same as what you should be doing with the matrix. Using the matrix can make the answer easier to find when there are a lot of variables. But since there's only 3 variables, the matrix isn't really that useful.

 

[Firben]

yes. But is the formula right?

 

[BruceW]

(k=constant)

k = h*g*v^2

It should be h = k*v^2/g

Any ideas ?

Their formula is right. (The one that 'it should be').