Help with showing that two variables are proportional in a discussion

[VCE247]

Hey guys

I started writing a discussion for a prac about incline motion. basically we showed that the speed at the bottom of the incline is affected by height and not mass.
So in my discussion I've said:
From the analysis calculations, it can be further deduced that the G.P.E and KE are proportional to each other which indicates that the height and velocity are also related.  By plotting the graphs of Height vs Velocity, the curved shape shows that the height is indeed proportional to v2. The straight line obtained when height is plotted against velocity2 further proves this and supports the hypothesis that the height is indeed proportional to the velocity.

Is that all i need to say to show that it is proportional? just talk about the graphs? or do i need to explain more in detail..

[xZero]

just a question, was friction ignored?

[VCE247]

yep we assumed it was a closed system

[schnappy]

By conservation,
0.5mvv = mgh
0.5vv = gh

vv [prop to] h

Nothing else to really say?

[VCE247]

ah thought so, thanks

just one more question
How would you do the uncertainty values for GPE, Velocity and KE, since you will be rounding the answer off?
e.g if i was calculating the velocity for something like this 0.3 m / 0.24 s

[xZero]

the uncertainty will be half of the smallest value on the device you're using. So if you use a ruller to measure the 0.3m, the uncertainty will be 0.5mm, and time will be the smallest value of the device you're using eg. stopwatch will be like milisecond?

From there the uncertainty of velocity will the the percentage of uncertainty of length + time