High SchoolCorePhysicsGravityKinematicsAcceleration

How does free fall work?

Q: What is the acceleration of free fall?

About 9.81\ \text{m/s}^2 downward at Earth's surface, often rounded to 10. It varies slightly with latitude and altitude, and it is very different on other bodies: 1.62 on the Moon, 24.79 on Jupiter.

Q: How long does it take to fall a given height?

t = \sqrt{2h/g}, ignoring air. From 10 m on Earth that is about 1.43 s; from 100 m about 4.5 s (air resistance makes real falls from that height slightly longer).

In free fall every object accelerates at g ≈ 9.81 m/s², whatever its mass. Equations, gravity on other worlds, and how air resistance sets terminal velocity.

How does free fall work?

An object in free fall has gravity as the only force acting on it, so it accelerates downward at a constant rate: $g \approx 9.81\ \text{m/s}^2$ on Earth. Its speed grows by about $9.81$ m/s every second, and — the surprising part — the acceleration is the same for a bowling ball and a feather, because a heavier object is pulled harder but is also harder to accelerate.

Key fact

In free fall

v = gt

and the distance fallen is

d = \tfrac12 g t^2

, for any mass. Only air resistance makes light, broad objects fall more slowly.

What are the equations of free fall?

Drop an object from rest at height $h$ and take up as positive. Constant acceleration gives:

\begin{aligned}v(t) &= -g\,t \\[2pt] y(t) &= h - \tfrac{1}{2}g\,t^2 \\[2pt] v^2 &= 2\,g\,d\end{aligned}

The last one says the landing speed depends only on the distance fallen $d$ , not on the mass. A ball dropped from $10$ m hits the ground at about $14$ m/s (50 km/h), whether it is a ping-pong ball or a bowling ball — in a vacuum.

Drop height	Time to ground	Impact speed
1 m (table)	0.45 s	4.4 m/s (16 km/h)
5 m (second floor)	1.01 s	9.9 m/s (36 km/h)
10 m (third floor)	1.43 s	14.0 m/s (50 km/h)
50 m	3.19 s	31.3 m/s (113 km/h)

Galileo on the Moon

On 2 August 1971 Apollo 15 astronaut David Scott dropped a hammer and a falcon feather together on the Moon. With no air, they hit the surface at the same instant — Galileo's idea confirmed live on television.

How does gravity change on other worlds?

Surface gravity comes from Newton's law, $g = GM/R^2$ . It depends on the planet's mass and radius, which is why small, dense bodies can pull harder than their mass alone suggests. Same drop, different worlds:

World	$g$ (m/s²)	Time to fall 10 m	Impact speed
Moon	1.62	3.51 s	5.7 m/s
Mars	3.71	2.32 s	8.6 m/s
Earth	9.81	1.43 s	14.0 m/s
Jupiter	24.79	0.90 s	22.3 m/s

Try it

In the simulation pick a different world from the gravity menu and drop the ball from the same height. The timing changes exactly as

t = \sqrt{2h/g}

predicts.

What does air resistance do?

Real objects push air out of the way, and the air pushes back. At everyday speeds that drag force grows with the square of the speed:

F_{\text{drag}} = \tfrac{1}{2}\,C_d\,\rho\,A\,v^2

Drag equation · formula card →

Here $C_d$ is the shape-dependent drag coefficient (about $0.47$ for a sphere), $\rho \approx 1.225\ \text{kg/m}^3$ is air density and $A$ is the area facing the flow. As a falling object speeds up, drag grows until it equals the weight. Then the net force is zero, the acceleration stops, and the object falls at constant terminal velocity:

v_{\text{terminal}} = \sqrt{\dfrac{2\,m\,g}{C_d\,\rho\,A}}

Terminal velocity · formula card →

A belly-down skydiver tops out around $55$ m/s (200 km/h); tucked head-down, above $80$ m/s.
A raindrop falls from kilometres up but hits at only about $9$ m/s.
An ant has such a small mass for its surface area that its terminal speed is a few m/s — it survives a fall from any height.

The simulation ignores air drag

The Ball Gravity simulation models gravity, wind, floor friction and bounce — not air resistance — so its ball never reaches a terminal velocity. The drag section above describes the real-world extension.

How does wind change the fall?

In the simulation, wind (active while you hold the mouse button) is a constant horizontal acceleration $a_w$ . Gravity acts only vertically and wind only horizontally, so the two motions are independent and you can solve each separately:

\begin{aligned}x(t) &= x_0 + v_{x0}\,t + \tfrac{1}{2}a_w\,t^2 \\[2pt] y(t) &= y_0 + v_{y0}\,t - \tfrac{1}{2}g\,t^2\end{aligned}

Combined, the path curves like a tilted parabola. It is the same independence that makes projectile motion work, with wind supplying the sideways acceleration instead of a launch speed.

Frequently asked questions

Do heavier objects fall faster?

Not in free fall. Gravity pulls a heavier object harder, but its greater inertia cancels that exactly, so all objects accelerate at

g

. In air, drag slows light and broad objects more — that is why a feather falls slower than a hammer, but not on the Moon.

What is the acceleration of free fall?

About

9.81\ \text{m/s}^2

downward at Earth's surface, often rounded to 10. It varies slightly with latitude and altitude, and it is very different on other bodies: 1.62 on the Moon, 24.79 on Jupiter.

What is terminal velocity?

The constant speed a falling object reaches when air drag equals its weight, so the net force — and the acceleration — is zero. For a skydiver it is roughly 55 m/s in a belly-down position.

How long does it take to fall a given height?

t = \sqrt{2h/g}

, ignoring air. From 10 m on Earth that is about 1.43 s; from 100 m about 4.5 s (air resistance makes real falls from that height slightly longer).

Why do astronauts float if gravity still acts on them?

Because they are in continuous free fall around the Earth: the station and everything in it fall together, so nothing pushes on anything else. Weightlessness is falling with nothing to stop you.

Keep exploring

Drop a ball on any world, add wind and friction: Ball Gravity simulation.
What the floor does next: How a bouncing ball works.
Add a launch speed and angle: How projectile motion works.
Code the drag and check it against the exact solution: Simulating a falling object with air resistance.

How does free fall work?

How does free fall work?

What are the equations of free fall?

How does gravity change on other worlds?

What does air resistance do?

How does wind change the fall?

Frequently asked questions

Do heavier objects fall faster?

What is the acceleration of free fall?

What is terminal velocity?

How long does it take to fall a given height?

Why do astronauts float if gravity still acts on them?

Keep exploring

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