# Practice Applying Free Fall & Air Resistance Formulas

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• 0:03 Free Fall and Air Resistance
• 1:08 Free Fall Distance
• 2:40 Free Fall Velocity
• 5:12 Air Resistance
• 8:43 Lesson Summary

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Lesson Transcript
Instructor: Laura Foist

Laura has a Masters of Science in Food Science and Human Nutrition and has taught college Science.

In this lesson, we'll go through some practice problems to determine the velocity and acceleration of an object in free fall and when applying air resistance.

## Free Fall and Air Resistance

According to the laws of gravity, all objects should fall at the same rate, regardless of their weight, right? Then why does a flat piece of paper fall to the ground much slower than a rock? The key here is understanding the relationship between free fall and air resistance. Everything falls at the same rate under free fall, but air resistance can slow the fall of objects: that's why a piece of paper will experience more air resistance than a rock and fall more slowly.

The formula for acceleration due to gravity is 9.8 m/s2, so if an object is in free fall (which is no air resistance), the only force acting on that object will be gravity, and the acceleration of the object will be 9.8 m/s. Using this information, we can determine the velocity of an object at any given point and how far it will travel after a given amount of time.

Air resistance acts as a counter force: one force (gravity) pulls an object down, while another force (air resistance) pushes the object up. We can calculate the total force on an object by adding these forces together.

## Free Fall Distance

Let's say you drop a rock weighing 2 kilograms (or kg in our formulas) and a piece of paper weighing 0.5 kg from an airplane 1000 meters (or m) above the ground. Without any air resistance, they would drop at the same speed. After 2 seconds, how far would the objects have traveled? The equation for distance (or displacement) is:

In this formula:

• d (or displacement) is what we are trying to determine
• vi (or initial velocity) = 0 m/s (because it started at rest)
• t (time) = 2 seconds
• g (or acceleration due to gravity) = 9.8 m/s2

Let's calculate the displacement the objects have traveled:

In free fall, the rock and the paper will travel -19.6 m. The negative sign indicates that they're traveling downward.

## Free Fall Velocity

We can also determine how fast the rock and piece of paper are traveling at that moment. Right before each object was released, the potential energy was equal to the height times acceleration due to gravity times the mass of the object, while the kinetic energy was equal to one half times the mass times velocity squared:

When we add the kinetic and potential energy together, we get the total energy, which is always the same as the objects are falling. This allows us to calculate kinetic and potential energy at any given point.

Let's look at the rock. The potential energy right before it is dropped is:

The kinetic energy of the rock right before it's dropped is 0 N because the velocity is equal to 0 m/s. This means that, based on our calculations, the total energy is equal to 19600 N (the potential energy just before it is dropped).

Now, let's determine what the kinetic energy would be after 2 seconds of free fall. Earlier we determined that the height at this point is -19.6 m, so the current height is 1000 - 19.6 = 980.4 m.

Total energy = 19600 N

PE = m * g * h (the new height)

KE = Total energy - PE

KE = 19600 - (2 * 9.8 * 980.4)

KE = 19600 - 19215.8

KE = 384.2 N

Once we know the kinetic energy, we can rearrange the equation to solve for velocity:

We can plug in our information to determine the velocity:

So, after 2 seconds of free fall, our rock is traveling 19.6 m/s.

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