
How did Galileo quantify motion in 2 dimensions? Well, he was a good scientist so he did an experiment.

This experiment involved rolling balls off of a the table and controlling

the speed with which they rolled off the table and measuring where the ball landed.

Galileo controlled the speed of the ball by adjusting the height from which it rolled.

If he wanted it to go faster, he will roll it from higher up.

We'll talk later about how exactly he can know where to put the ball.

Galileo controlled the speed of the ball by adjusting where in the plane he released it from.

Higher up of course meant it would be going faster by the time it got to the edge of the table.

Like in his previous experiments, he didn't know

the units of his velocity, but he knew their relative sizes.

For example, he knew he can make the velocity twice as big as it was originally

or three or four times bigger and look what he found.

Again these are unit list distances but look at this correspondence.

When the ball had a velocity of 1 unit, represented here, the trajectory looks something

like this. With a velocity of 2 units, the ball went twice as far.

Likewise with 3 and 4 units of initial horizontal velocity.

Galileo called this Vx. This x indicates an x direction.

When we label axis, we usually called the horizontal direction x and the vertical y

and so this x is just here to remind us that we're talking about a velocity in the horizontal direction.

Okay, this is pretty interesting. What's the conclusion that we can draw from this data?

Is it that the horizontal velocity is equal to the motion in the x direction?

That horizontal velocity is somehow proportional to the motion in the x direction?

Or that horizontal velocity and x direction motion are totally unrelated?

What's the best answer?