# What is Terminal Velocity? - Definition, Formula, Calculation & Examples

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• 0:01 Why Do Objects Fall at…
• 0:36 Gravity
• 2:16 Drag Force
• 3:28 Terminal Velocity
• 5:00 Calculating Terminal Velocity
• 7:17 Lesson Summary

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Lesson Transcript
Instructor: Betsy Chesnutt

Betsy teaches college physics, biology, and engineering and has a Ph.D. in Biomedical Engineering

In this lesson, we will learn about terminal velocity and why it is better to jump out of a plane with a parachute than without one. We will explore why objects fall at different speeds and how to calculate the maximum speed of a falling object.

## Why Do Objects Fall at Different Speeds?

Imagine you are about to jump out of an airplane. At the last minute, you have to decide whether to take a parachute or not. What would you choose? I'm guessing that you would choose the parachute! Most people would make the same choice, because it causes you to have a much slower terminal velocity, or maximum falling speed, than if you were to fall without it. Although we all know that it is better to jump from a plane with a parachute than without it, have you ever thought about why? What factors determine the terminal velocity of a falling object like a person jumping from a plane?

## Gravity

Hundreds of years ago, people thought that the mass or weight of an object was the main thing that determined how fast it would fall. This idea was put forth by the Greek philosopher Aristotle, who said that the speed of a falling object was directly proportional to how heavy it was. Although this seems reasonable at first glance, there are some big problems with this idea. Try dropping a baseball and a crumpled up piece of paper at the same time. You will see that although the baseball weighs much more, they hit the ground at about the same time.

The scientist Galileo Galilei (1564-1642) disproved this idea by showing that objects of the same size and shape but with different masses would hit the ground at the same time when dropped from the same height. Later, Isaac Newton (1643-1727) demonstrated that the Earth exerts a force on all objects near it, which causes falling objects to speed up as they fall. He called this force gravity and calculated that all objects would speed up at a rate of 9.8 m/s as they fall towards Earth. The force of gravity on every object is the product of its mass and the gravitational constant (g = 9.8 m/s^2). This force of gravity is what we know as weight. Force of gravity = mass * g.

So, when you jump out of that airplane, you immediately start speeding up at a rate of 9.8 m/s every second. If there was no air in the atmosphere, you would keep speeding up at that rate until you hit the ground. However, the air you are falling through exerts a force on you, too.

## Drag Force

While it is true that the Earth exerts a gravitational force on every falling object, there is another very important force that also affects the terminal velocity of a falling object. As objects fall through air, they experience drag or air resistance forces that act upward and oppose the force of gravity. The air drag force depends on several factors, including the speed at which the object is falling (v), the surface area of the object (A), the density of the air (d) and something called the drag coefficient (C), which is determined by how aerodynamic the object is: Drag Force = 0.5 * d * v^2 * A * C. The most important factor in determining the air drag force is the velocity of the object. As it speeds up, the drag force gets bigger and bigger.

After you jump from the airplane, you start speeding up, and the faster you go, the more air drag force is exerted on you. Eventually you will be going so fast that the air drag force will be equal to the force of gravity that was causing you to speed up. At that point, you will not speed up any more but will continue to fall at the same constant velocity.

## Terminal Velocity

As the object falls, the force of gravity initially causes it to continuously speed up as predicted by Isaac Newton. As it gets faster and faster, the air drag force increases until eventually, the air drag force is exactly equal to the force of gravity, and there is no net force acting on the object. If these two forces are exactly balanced, the object will no longer speed up or slow down but will continue falling at a constant velocity, called the terminal velocity.

Since the air drag force depends heavily on the size and shape of the object, objects with a large surface area (like a parachute) will have a much lower terminal velocity than objects with a smaller surface area (like a person falling from a plane). The weight of the object does affect the air drag force on the object and, therefore, its terminal velocity.

However, it is not the most important factor. This explains why a flat piece of paper will fall more slowly than the same paper after it has been crumpled into a ball. The paper weighs the same, but the air drag forces have decreased because its surface area and drag coefficient have changed. This causes the crumpled paper to have a higher terminal velocity than the flat paper. This also explains why a parachute can lower your terminal velocity when you jump from an airplane. The parachute has a very large surface area and drag coefficient and a relatively small mass, so it experiences much higher air drag forces than you would without a parachute.

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