What you are describing is actually a variation of the Galileo's Leaning Tower of Pisa Experiment, and we all know how you feel about Galileo

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Your experiment is actually not a good experiment because there would be too many other factors that would ruin the results. At best, it would just be a decent eyeball test.

Now it's correction time....

1. The derivative of speed is not velocity. The derivative of position(displacement) is velocity. The first derivative of velocity is acceleration.

2. You wrote,

*"Once you have computed (approximated) velocity, you’ve effectively determine gravity..."* Actually, no. I'd explain it to you, but since you don't understand derivatives, it would be pointless.

NOTE: This is high school stuff.

Suppose you knew nothing about gravity, aerodynamics, friction and blah blah blah. Take 10 iron balls of varying weights: 10KG, 20KG, etc… 100KG. Climb up the tallest building in your village (the church). Suppose this church is 10m high thus your distance = 10m. Now take these iron balls of varying weight and drop it from 10m. Did the heavy one fall faster than the lighter one? If no, then the final speed = distance/time. So we can at see objectively through measured data they have the same speed. Now suppose, you graphed this at varying heights 10, 15m, 20m, etc..., you’ll notice that the speed is not constant and the higher you go the faster the speed is. Thus, the derative (rate of change) of speed is velocity. Once you have computed (approximated) velocity, you’ve effectively determine gravity, and know things fall at the sate rate (e.g. rate of change).

NOTE: This is high school stuff.