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AP Physics 1: Exam Prep12 chapters | 136 lessons

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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.

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.

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.

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.

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*).

Looking back at the Big Five Equations, only #3 uses all of these variables only.

Equation 3: *y* = *y* sub 0 + *v* sub 0*t + ½ at^2

Now, all you need to do is sub in the appropriate values, remembering to always include the units and vector signs.

0 m = 115 m + (0 m/s)(*t*) + (½)(-9.8 m/s^2)(*t*^2)

With a little basic algebra you should come up with:

*t* = âˆš(-115 m/-4.9 m/s^2) = 4.8 seconds

So, the rock fell for 4.8 seconds before it hit the ground.

Let's look at a slightly more complicated problem.

You decide to throw that rock straight back up in the air. If you throw it with an initial velocity of 35 m/s, how high will the rock fly?

Let's jump right into jotting down what variables are given for this problem.

*v* sub 0 = 35 m/s

*v* = 0 m/s (The final velocity isn't given, but it must be 0 m/s, because the rock will continue to rise until gravity stops its upward motion.)

*a* = *g* = -9.8 m/s^2

*y* sub 0 = 0 m (We will call the point you released the rock the initial position and designate it 0 m.)

So *y* is the final position, which is what the question is asking for.

There's only one equation that uses only these variables:

Equation 5: *v*^2 = *v* sub 0 ^2 + 2*a*(*y* - *y* sub 0)

Now, simply fill in the values and solve for y.

(0 m/s)^2 = (35 m/s)^2 + 2(-9.8 m/s^2)(*y* - 0 m)

Some algebra should get you to:

*y* = (-1225 m^2/s^2) / (-19.6 m/s^2) = 62.5 m

Your rock will fly 62.5 meters high. The vector sign is positive because the rock is moving upwards.

Let's quickly review.

These were just two basic examples of the kinds of problems you might see. Any of these variables are fair game for calculations. There are a few key points to remember:

Unless the problem provides you with an acceleration due to gravity, assume -9.8 m/s^2.

Always write out the variables that you know, can assume, or are looking to solve.

Always keep your vector signs straight and don't forget to use those signs during every calculation.

Always include the units. If your units are missing, you can get confused about which value belongs where in the equation.

Memorize, then get familiar working with, the Big Five Kinematics Equations. The more practice you have, the easier these problems will become. And you will not be provided with these equations for any of your exams.

Always select the Big Five equation that uses all the variables provided in the problem, without any leftovers.

Finally, if you're having trouble with the algebra, go back and brush up on these crucial concepts. There are many additional videos that can walk you through the rules for solving algebraic equations and provide many more algebra example problems for practice.

Once you have completely reviewed this lesson you should be able to

- State the basic value for gravity for use in calculating acceleration
- Recall the Big Five Kinematic Equations
- Solve a free fall physics problem

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AP Physics 1: Exam Prep12 chapters | 136 lessons

- What is Kinematics? - Studying the Motion of Objects 3:29
- Scalars and Vectors: Definition and Difference 3:23
- What is Position in Physics? - Definition & Examples 4:42
- Distance and Displacement in Physics: Definition and Examples 5:26
- Speed and Velocity: Difference and Examples 7:31
- Acceleration: Definition, Equation and Examples 6:21
- Significant Figures and Scientific Notation 10:12
- Uniformly-Accelerated Motion and the Big Five Kinematics Equations 6:51
- Representing Kinematics with Graphs 3:11
- Ticker Tape Diagrams: Analyzing Motion and Acceleration 4:36
- What are Vector Diagrams? - Definition and Uses 4:20
- Using Position vs. Time Graphs to Describe Motion 4:35
- Determining Slope for Position vs. Time Graphs 6:48
- Using Velocity vs. Time Graphs to Describe Motion 4:52
- Determining Acceleration Using the Slope of a Velocity vs. Time Graph 5:07
- Velocity vs. Time: Determining Displacement of an Object 4:22
- Understanding Graphs of Motion: Giving Qualitative Descriptions 5:35
- Free Fall Physics Practice Problems 8:16
- The Acceleration of Gravity: Definition & Formula 6:06
- Projectile Motion: Definition and Examples 4:58
- Projectile Motion Practice Problems 9:59
- Kinematic Equations List: Calculating Motion 5:41
- Go to AP Physics 1: Kinematics

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