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Motion & Forces · Question 18 of 20

Projectile motion

A thrown ball is running two completely separate programs at once — and neither one knows the other exists.

Plate IV — Two motions, one arc constant vₓ · g downward · parabola
Fire at different angles and hunt for the longest throw.
20 m 40 m 60 m 80 m 100 msideways speed never changes · gravity only pulls down
FIG. IV — TWO MOTIONS, ONE ARC
Launch angle 45°
Launch speed 24 m/s
Range
58.7m
Peak height
14.7m
Flight time
3.5s
Fire at different angles and chase the longest throw — it's always near 45°. Steeper buys airtime but wastes speed going up; flatter is fast but lands early. Watch the two arrows on the ball: the sideways one never changes.
The short answer

Throw a ball and two things happen at once: it coasts forward steadily while gravity pulls it down. Together they curve its path into a graceful arc.

What's actually happening

The key insight is independence. Once a ball leaves your hand, its horizontal motion and vertical motion stop talking to each other. Horizontally, nothing pushes or pulls (ignoring air), so the ball coasts at whatever sideways speed you gave it — inertia, pure and simple. Vertically, gravity accelerates it downward at 9.8 m/s², utterly indifferent to the sideways travel. The graceful arc is just those two boring motions superimposed: steady drift plus accelerating fall equals a parabola.

Independence produces a result most people refuse to believe: a bullet fired perfectly level and a bullet dropped from the same height hit the ground at the same instant. The fired bullet covers enormous sideways distance, but its vertical story — start at rest (vertically), fall under gravity — is identical to the dropped one's. Sideways speed buys you no extra airtime.

Aim is where the trade lives. Launch steeply and you buy airtime but waste speed going up; launch flat and you have pace but no time before the ground arrives. The optimum, in a vacuum, is 45°. In real air, drag taxes the long high path more, so shot-putters, golfers, and artillery officers all settle lower — typically 30–43° depending on what they're throwing. A basketball's high arc, a water fountain's curve, a long-jumper's flight: all the same two independent programs, tuned to different goals.

Try it at home The two-coin verdict
  1. 1Place one coin at a table's edge and a second coin next to it, ready to be flicked.
  2. 2In one motion, flick the second coin horizontally off the table while nudging the first straight off the edge.
  3. 3Listen: one click, not two. The flicked coin lands metres away but at the same moment — sideways speed cannot delay a fall.