Can you please Discuss the "Galileo's Concept of Motion"?

Question

I have some diagrams that illustrates the Galileo's Concept of Motion but I can't get the initia and final positions of an object. I can't also explain it. It's so complicated. I need the formulas related to it.

Answer 1

According to Galileo, the motion of a falling object is independent of mass. Meaning two objects of unequal masses will fall to the ground when dropped from a set height in equal times

The reason why objects did not always fall in the same time was because of a retarding force called friction.

If friction is negligible, the following formulae apply:

Motion(upward):

Vf=0

S=-1/2gt^2

Motion(downward):

Vo=0

S=1/2gt^2