# Free Fall Physics Practice Problems

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• 0:01 Physics Math
• 0:26 Types of Free Fall Questions
• 3:02 Free Fall Practice Problem 1
• 5:12 Free Fall Practice Problem 2
• 6:56 Lesson Summary

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Lesson Transcript
Instructor: Angela Hartsock

Angela has taught college Microbiology and has a doctoral degree in Microbiology.

In this lesson, we will dive into doing calculations involving free falling objects. We will begin with a few helpful tips to get started before working through a couple of example problems.

## Physics Math

There is no easy way to break this to you so I'll do it quick, like yanking off a bandage: this lesson is all math. We don't have time for fluffy narrative and exotic example stories - only equations and calculations. Specifically, we're going to go over the key things you need to know to solve problems involving objects in free fall. Once we zip through the background information, we'll work through a couple of problems together.

## Types of Free Fall Questions

To start, let's define free fall motion. Free fall describes any motion involving a dropped object that is only acted on by gravity and no other forces.

Imagine you're outside, you see a rock, pick it up, and throw it straight up in the air. I'm sure you can guess what happens next. The rock flies up, slows down, stops, begins falling, speeds up, and lands close to where you tossed it from. With nothing other than this rock and a stopwatch, you can calculate a lot of information about the flight of this rock. A few examples are how high the rock flew, how fast you tossed the rock, how fast the rock was traveling when it hit the ground, and how high off the ground the rock was when you released it. For a trained physicist like you, you should have already recognized that I'm describing kinematic concepts like displacement and velocity.

## The Big Five Kinematic Equations

And, as a trained physicist about to perform calculations involving kinematics, you know you're going to need your old friends (or enemies?), the Big Five Kinematic Equations. These five equations should be familiar to you. You need these guys when performing any calculations involving uniformly accelerated straight line motion, including free fall problems. Hopefully, you've already memorized these equations, but if not, here's a quick refresher.

These are the Big Five Equations. I'll quickly define each variable.

 Equation 1: Î”y = average v*t Equation 2: v = v sub 0 + at Equation 3: y = y sub 0 + v sub 0*t + ½ at^2 Equation 4: y = y sub 0 + 'v*t - ½ at^2 Equation 5: 'v^2 = v sub 0 ^2 + 2a(y - y sub 0)
• Î” = change in
• y = final position
• y sub 0 = initial position
• v = final velocity
• v sub 0 = initial velocity
• v with a bar over it = average velocity
• a = acceleration
• t = time

There are a couple of things to keep in mind before we get started. With free fall problems, it is best to assume that forces and motion up have a positive vector and forces and motion down have a negative vector. Also, since we're dealing with free fall, you can bet you need to know the acceleration due to gravity, written simply as g.

g = -9.8 m/s^2

The value is negative because gravity always points downward, pulling the object back to earth. Now, some problems might give you a value of g different than -9.8 m/s^2, say if you're dropping objects on another planet, for instance. You should always use the value given for the acceleration and only assume -9.8 m/s^2 if no other number is provided.

Let's work together through two typical free fall problems and I'll give you a few tips along the way that have helped me in the past.

## Free Fall Practice Problem 1

A rock is dropped off a cliff 115 meters high. How long does it take for the rock to reach the ground?

Before I get started on problems like these, I like to draw a little picture to represent what the question is asking. Here is a little man with a rock standing on a cliff 115 meters off the ground.

Next, I like to list all the variables for the problem.

The only piece of information we're given is the height of the cliff: 115 meters. The rock is starting here so it must be the initial position (y sub 0). Since the rock is landing on the ground, let's call that the final position (y). So,

y sub 0 = 115 m

y = 0 m

Since the object is in free fall, we have to make a few assumptions. First, we need to assume the acceleration of the rock is -9.8 m/s^2 due to the force of gravity. Next, since the rock was dropped, we can assume the initial velocity is 0 m/s.

Now, we have the following information:

y sub 0 = 115 m

y = 0 m

a = g = -9.8 m/s^2

v sub 0 = 0 m/s

And the problem is asking for the time it takes to reach the ground (t).

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