Iveria

throw it. watch what the air does.

pick a ball, a stick, a flat stone or a beach ball from the pile and drag to throw it into the sea, and the dog fetches it back: each projectile flies its own arc, because the air slows each by a different amount -- the ball goes farthest near 45 degrees, the beach ball stops dead in the sea breeze, and the stone only skips when it is thrown low

Without air, any projectile flies the same curve, a parabola, and 45 degrees goes farthest from level ground (a little lower from a height, like this ridge). With air, each thing is slowed by air resistance, a drag that grows with the square of its speed, and how much that matters depends on its terminal speed: how fast it would fall for ever in still air. A tennis ball is about 22 m/s, so at a beach throw of 10 m/s it flies nearly the whole parabola. A tumbling stick, about 13, comes down noticeably short and steeper. A beach ball, about 6, is slower than the throw itself, so the air stops it within a couple of metres and it drops almost straight down -- and a sea breeze of a few metres a second, nothing to a ball, carries it back to the beach. A flat stone hardly notices the air, but it is the water it has to beat: it bounces only if it meets the surface at a shallow enough angle and fast enough, which is why skimmers crouch and throw low. The drag here uses real terminal speeds and the card is drawn to one scale, 25 px to the metre, the same scale the waves are built on. The skip rule is simplified: a well-spun flat stone at up to about 45 degrees, in the spirit of the lab results of Clanet, Hersen and Bocquet (2004), losing speed at every bounce until it goes in.

Concepts: trajectory, gravity, drag.

An interactive you play with one thumb, on Wundr.