A projectile does two independent things at the same time: it moves sideways at constant speed
(nothing pushes it horizontally) and it accelerates downward under gravity. Splitting the launch into
those two components — horizontal v·cosθ and vertical v·sinθ — is the whole trick.
Press launch to watch them combine into the familiar arc.
Throw a ball at 20 m/s and 45° from ground level. It flies for 2.9 s, peaks at 10.2 m, and lands 40.8 m away — and hits the ground at the same 20 m/s it left, just angled downward.
The neat result: on flat ground, 45° gives the maximum range, and any two angles that add to 90° (say 30° and 60°) land in the same spot.
Range depends on the product of horizontal speed and hang time. Lower angles have more horizontal speed but less hang time; higher angles the reverse. 45° balances them — on level ground. Launch from a height and the best angle drops below 45°.
Not here. Without air resistance, all projectiles follow the same path regardless of mass — a cannonball and a pebble launched identically land together. Add drag and that changes.
For dense, slow, heavy objects over short distances, barely. For light objects, high speeds, or long ranges, very — real range can be a fraction of the ideal. Treat this as the frictionless ideal.
Gravity is about ⅙ of Earth's, so the same throw goes roughly six times farther and stays up about 2.5× longer. Switch the gravity buttons to see it.