He first reasoned that a projectile is composed by two motions and not just one. The object is also moving forward while gravity is pulling down on the object. He was able to show that a projectile is controlled by two independent motions, which work together to get a mathematical curve. He actually found that the curve has an exact mathematical shape. The conclusion that Galileo reached was that the path of any projectile is a parabola.
Projectile motion is applied today in jobs and other things too.
People can use projectile motion in hunting animals so the know what angle to shot so it will hit the animal. Many sports use projectile motion everyday. In soccer, the players need to understand projectile motion so they know the angle and force to kick the soccer ball to reach a certain distance. Without projectile motion they would be missing targets and their distances would be off too. People can use projectile motion to determine a lot of things.