How projectile motion works
Throw something and it stops being your problem. Gravity pulls down at a constant rate while it keeps drifting sideways at the speed you gave it — and those two independent facts draw the whole arc.
How projectile motion works — the interactive part
Range is 63.7 metres. Highest point is 15.9 metres. Time in the air is 3.60 seconds.
Two motions that ignore each other
Sideways, nothing acts on the object at all, so it covers equal distance every second. Downwards, gravity pulls at a constant rate, so it gains speed steadily. Neither motion knows about the other, and the curve is just those two independent stories plotted against each other. That is why a bullet fired horizontally and one dropped from the same height hit the ground at the same moment.
Why 45 degrees, and when it stops being true
Range depends on staying airborne long enough and travelling fast enough sideways. Steep buys time and loses speed; shallow buys speed and loses time. From flat ground the trade balances exactly at 45. Raise the launch height and it stops balancing: you are given extra hang time for free, so the best angle drops and shallower throws win.
Check your understanding
On the Moon, gravity is about a sixth of Earth's. What happens to the range?
Pick one to check yourself.