Motion of bodies under the Earth’s gravity
A body thrown horizontally with an initial velocity υ₀ takes part in two motions. Horizontally no force acts on it (ignoring air resistance), so it moves uniformly: x = υ₀t. Vertically gravity makes it move as if falling freely from rest: h = gt²/2. Hence the time of fall t is found from h = gt²/2 (t² = 2h/g), and the range is L = υ₀t. The two motions are independent: a horizontally thrown body and one simply dropped from the same height land at the same time. The trajectory is a parabola-shaped curve; in problems we take g = 10 m/s². If the horizontal speed is very large (about 7.9 km/s near the Earth’s surface — the first cosmic speed), the body no longer falls back but starts circling the Earth.
“Two balls”: push one ball horizontally off a low table edge while dropping another at the same moment (with an adult): they land at about the same time. Safety: never throw towards people.