What if a ball were thrown sideways off a tower?

Olly stands at the top of a tower with two balls.

He drops one ball. He throws the other ball straight out to the side. Which ball will land first?

Imagine standing at the top of a tall tower. You let one ball simply drop, and at the very same moment you throw a second ball straight out sideways. The thrown ball has a long curved path to travel, out and down, while the dropped ball just falls straight.

So which reaches the ground first? Many people guess the dropped ball, because its path is shorter. Others think the thrown ball, because it is moving faster. Test both ideas in the model.

Two balls leave the same height at the same instant: one released from rest, one launched horizontally. The thrown ball's path is a parabola and its total speed is always greater, yet both are pulled by the same gravity.

OpenStax states the key principle: the horizontal and vertical components of two-dimensional motion are independent, so motion in one direction does not affect motion in the other. This lab tests that claim in the fall model, from a 20 m tower with a sideways push of 5 m/s, and then asks what changes when air resistance is switched on.

First Olly just lets go of a ball. It falls straight down.

It goes faster and faster. It lands in about two seconds.

In the model, a ball dropped from a 20-meter tower falls straight down and lands after about 2.0 seconds. Gravity speeds it up by about 9.8 meters per second every second, so it hits the ground at about 20 meters per second.

The ball has no sideways speed, so it lands right at the foot of the tower. Remember that time: 2.0 seconds. It is the number to beat.

With g = 9.81 m/s², h = 20 m and no air, the dropped ball lands after t = √(2h/g) = 2.02 s at 19.8 m/s, directly below its release point.

Its motion is purely vertical: y = h − ½gt², x = 0. The vertical position at any moment depends only on g and the time since release. Keep that in mind, because the thrown ball's vertical equation will turn out to be exactly the same. In the model, the ruler on the tower and the strobe dots every tenth of a second let you read the height at each moment and compare the two runs directly.

Now Olly throws the ball out to the side.

It flies out in a curve. But it lands at the same time as the dropped ball! Both take about two seconds.

Now give the ball a sideways throw of 5 meters per second. It curves out from the tower and lands about 10 meters away. But look at the timer: it still lands after about 2.0 seconds, exactly like the dropped ball.

The thrown ball does hit the ground a little faster, about 20.4 meters per second instead of 19.8, because it is also still moving sideways. Its falling part, though, is identical. Switch the throw to the other direction, and the same thing happens on the other side.

With v_x = 5 m/s the model gives a landing time of 2.02 s, unchanged, and a landing point x = v_x·t = 10.1 m from the tower. The landing speed rises to √(5² + 19.8²) = 20.4 m/s, because the constant horizontal component adds to the same vertical one.

With air on (the model's default football), the drop takes 2.19 s and the throw 2.21 s, landing 8.9 m out. Quadratic drag depends on the total speed, so it couples the two directions slightly: in real air, independence is an excellent approximation, not an exact law.

Gravity only pulls down. It does not care about moving sideways.

So both balls fall down in the same way, at the same time.

Gravity pulls straight down. It does not push or pull sideways at all. So a ball's sideways motion and its falling motion happen separately, side by side.

NASA's guide to how balls fly explains it: with no sideways force, the sideways speed stays the same, and only the up-and-down speed changes because of the ball's weight. Both balls start with no up-and-down speed, and the same gravity speeds up their falls in the same way, so they reach the ground together. Our model ignores air unless you switch it on, and treats the ball as a dot.

NASA Glenn's ballistic flight equations show why: with no external horizontal force, Newton's first law keeps the horizontal velocity constant, x = U₀t, while weight alone changes the vertical velocity, V = V₀ − gt. Both balls have V₀ = 0, so y(t) = h − ½gt² for each, and they reach y = 0 together.

The model's limits: uniform gravity, a flat non-rotating ground, a non-spinning ball (no lift), and drag only when switched on. On a real tower, wind and spin would push the thrown ball around, which the model leaves out.

Scientists took photos of two balls falling. One was dropped, one was thrown. They fell side by side, all the way down!

Throw something super fast, and it could fall all the way around Earth.

OpenStax shows a strobe photo of two identical balls, one dropped and one thrown sideways at the same instant. The pictures, taken at equal time steps, show both balls at exactly the same height each time.

Now imagine throwing faster and faster from a very high tower. The ball lands farther away each time. OpenStax explains that at about 8,000 meters per second, Earth's surface curves away as fast as the ball falls, so it never lands: it goes into orbit. Satellites in low orbits move at roughly that speed. They are falling sideways all the time.

OpenStax College Physics illustrates independence with a stroboscopic image of two identical balls, one falling from rest and one launched horizontally: their vertical positions and velocities are identical at every flash.

OpenStax University Physics extends the idea with a figure based on a drawing in Newton's Principia: projectiles launched from a very high tower land farther away as their speed rises, because Earth curves away beneath them. Earth's surface drops about 5 m every 8,000 m, and a body falls about 5 m in its first second, so a horizontal speed of about 8,000 m/s gives orbit, roughly the speed of any satellite in low Earth orbit.