Determining Acceleration g from Slope

[Youngster]

Homework Statement

For my laboratory exercise, I'm given the task of estimating the acceleration due to gravity near the Earth's surface by dropping metal balls from a specified height, and obtaining the time it takes to reach a surface.

I did all that, and plotted the data on some log-log graph paper (since the data seemed to possesses a power law relationship) and calculated the function of my graph:

f(x) = 0.045x^0.497

Where 0.497 is the slope of my graph. I'm not entirely certain how I can use this data to estimate an acceleration. I suppose I don't really know what this slope is, but I'm thinking its a velocity

Homework Equations

I suppose kinematic equations might be of use here.

The Attempt at a Solution

I can't say I really tried... I was thinking that perhaps the slope had some sort of specific dimensions, but after running some test calculations, my results seemed very off.

Any advice on how I can approach this? I'm aware that one can try squaring the times, and then drawing that graph, but my instructions state that I use my calculated slope.

 

[voko]

You can't use this slope to get acceleration. This slope is related to the quadratic nature of the uniformly accelerated motion, not the value of acceleration. Acceleration can be obtained from the slope of a squared time vs height plot.