Throw anything — a ball, a stone, a droplet of water — and it follows the same curved path. That path is called a projectile trajectory, and it is one of the cleanest examples in all of physics: two independent motions happening at the same time.
Projectile Motion
Change speed, angle and gravity, then watch the pathWhat the simulation shows
Once an object is launched, only one force acts on it (we ignore air resistance here): gravity, pulling straight down. That single fact splits the motion in two:
- Horizontally: no force at all, so the horizontal velocity never changes. The object keeps drifting sideways at a constant rate: x = v cos θ × t.
- Vertically: gravity accelerates the object downwards at 9.8 m/s² on Earth, so the height follows a parabola: y = v sin θ × t − ½ g t².
Put those together and you get the arc. Two results fall straight out of the equations:
- Flight time = 2 v sin θ / g
- Range = v² sin(2θ) / g
Notice the sin(2θ) in the range formula. It peaks at θ = 45°, which is why 45° gives the longest throw — and it has the same value at 30° and 60°, which is why those two angles land in exactly the same place.
Try this
- Set the angle to 45° and note the range. Now try 30°, then 60°. The range should be identical, even though one arc is flat and fast and the other is tall and slow.
- Switch gravity to the Moon (1.6 m/s²). The same throw now travels about six times as far and stays in the air six times as long.
- Drop the speed to its minimum and watch how quickly the curve collapses.
Why it matters
Projectile motion is the reason a basketball arc, a water fountain and an artillery shell are all described by the same three equations. Engineers use it to aim sprinklers and design ramps; athletes use it intuitively every time they judge a catch. The key idea — that horizontal and vertical motion are independent — shows up again in orbital mechanics, in electric fields, and anywhere else that a constant push acts on a moving object.