Vertical Drop

Introduction

Vertical drop — or free fall — is the simplest case of motion under gravity: an object released from rest and pulled straight downward. It is the baseline experiment that connects everyday experience (dropping things) to Newton's second law and the concept of gravitational acceleration. Understanding free fall is essential before tackling any more complex trajectory, because it isolates the one force that dominates most of classical mechanics.

The Physics Explained

In a vacuum, every object falls at exactly the same rate regardless of its mass. This was the great insight of Galileo, who challenged the Aristotelian belief that heavier objects fall faster. The reason is elegant: while a heavier object experiences a greater gravitational force, it also has more inertia resisting that force. The two effects cancel perfectly, leaving the same acceleration — 9.8 m/s² — for every object near Earth's surface.

In reality, air is present, and it exerts a drag force that opposes motion. Drag depends on velocity (faster objects experience more drag), the cross-sectional area of the object, and a drag coefficient that captures shape and surface texture. As an object accelerates downward, drag grows until it exactly balances gravity. At that point, acceleration reaches zero and the object falls at a constant speed called terminal velocity. A feather reaches terminal velocity almost immediately; a cannonball barely feels it.

Mass matters in the presence of drag: a heavier object of the same size has the same drag but more gravitational force, so it takes longer to reach terminal velocity and falls faster than a lighter one. This is why a heavy and a light ball of the same size land at different times in air, but simultaneously in a vacuum.

Key Equations

v(t) = g · t (velocity in free fall, no drag)

y(t) = ½ · g · t² (distance fallen in free fall, no drag)

F_drag = ½ · ρ · Cd · A · v² (aerodynamic drag force)

F_net = m·g − F_drag (net downward force with drag)

a = F_net / m (acceleration at any instant)

v_terminal = sqrt(2·m·g / (ρ·Cd·A)) (terminal velocity)

Key Variables

Symbol	Name	Unit	Meaning
g	Gravitational acceleration	m/s²	9.8 m/s² near Earth's surface
m	Mass	kg	Mass of the falling object
v	Velocity	m/s	Speed of the object downward
t	Time	s	Time elapsed since release
y	Distance fallen	m	How far the object has dropped
F_drag	Drag force	N	Air resistance opposing the motion
ρ	Air density	kg/m³	Density of the surrounding air (~1.225 at sea level)
Cd	Drag coefficient	dimensionless	Shape-dependent resistance factor
A	Cross-sectional area	m²	Projected area of the object facing the airflow
v_terminal	Terminal velocity	m/s	Constant speed reached when drag equals gravity

Real-World Examples

Skydiving: A skydiver in a spread-eagle position reaches terminal velocity around 55 m/s (~200 km/h). Tucking into a dive reduces drag and raises terminal velocity to over 90 m/s.
Raindrop speed: Raindrops fall at terminal velocity — typically 6–9 m/s — determined by their size. Without drag, a drop falling from 2 km would hit you at over 200 m/s.
Apollo 15 hammer and feather drop: On the airless Moon, astronaut David Scott dropped a hammer and a feather simultaneously. Both hit the ground at the same time, confirming Galileo's prediction in the most dramatic setting possible.

How the Simulation Works

The simulation drops an object from 50 m. You control two sliders: mass (kg) and air resistance. The air resistance slider adjusts the drag coefficient — at zero, you get perfect free fall; higher values introduce increasingly strong drag, slowing the fall and making terminal velocity visible. Watch the velocity readout: in free fall it climbs steadily at 9.8 m/s every second; with drag it climbs then levels off at terminal velocity. Comparing a heavy and a light object at the same drag setting illustrates how mass shifts the terminal velocity without changing the physics.