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Unit 1.5 | Solving Projectile Motion (Motion in 2 Dimensions)

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Jason Kuma

Writer | Coach | USC - Physics B.S & Business B.A. | Fremont, CA

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🎉 Congrats! This is the LAST lesson of Unit 1.

By now you should know how to solve kinematic problems in 1 dimension. In this lesson, we will cover how to solve problems in 2 dimensions, in a quick and simple way!

While watching the videos may only take a few minutes, it is important that you do ALL of the practice questions to test your understanding. This is the second most missed topic on the AP Physics exam! So be sure to be confident with solving kinematic problems before moving onto the next unit.

Unit 1 Breakdown

You are on Lesson 5 of 5

  1. Unit 1.1 | Understanding vectors and the Standard Units used in Physics
  2. Unit 1.2 | The Kinematic (motion) variables: Displacement, Velocity, and Acceleration
  3. Unit 1.3 | Graphing motion
  4. Unit 1.4 | Using Kinematic Equations in 1 Dimension
  5. Unit 1.5 | Projectile Motion: Using Kinematic Equations in 2 Dimensions [Current Lesson]

In this lesson you will learn: 

  • The concepts behind projectile motion
  • Breaking down velocity vectors into their components
  • Labeling components and variables correctly
  • Setting direction on the coordinate plane
  • Framework projectile motion problems
  • Solving several projectile motion problems step by step

LRN Projectile Motion

Watch this video first before moving on to the sections below.

Labeling components

As we saw in the video above it is important to keep track of direction of each variable.

For example, initial velocity in the horizontal direction should be written as vox. Which means the “initial velocity in the x direction.”

Time is the only variable that does not have a direction.

Here is a chart of all their variables and their directions. Note, that this is purely for you to keep track of variables. You can switch them to whatever works best for you.

Horiztonal (x)Vertical (y)
vox (initial velocity in the x-direction)voy (initial velocity in the y-direction)
vfx (final velocity in the x-direction)vfy (final velocity in the y-direction)
ax (acceleration in the x-direction)ay (acceleration in the y-direction)
∆x (horizontal displacement)∆y (vertical displacement)

PS Solving Projectile Problems

In this video we will cover:

  • The easiest way to solve any projectile problem (a framework)
  • Solving an easy, medium, then hard projectile problem

Final Problem In Video

This is the final question given in the video above.

A spider crawling across a table leaps onto a magazine blocking its path. The initial velocity of the spider is 0.91 m/s at an angle of 40° above the table, and it lands on the magazine 0.08 seconds after leaving the table. Ignore air resistance. How thick is the magazine in mm?

Answer: 15.4 mm

To solve this: Make the x and y chart. In this case we have enough variables on the y-side, to solve for the vertical displacement (∆y aka the thickness of the book).

The most commonly made mistake here is setting direction. If we set down as negative, then velocity should be positive and gravity will be negative.

Plugging the y variables into the equation ∆y = voy + 1/2at2 will give a final answer of .00154 meters or 15.4 mm.

Recap and Framework

Let’s create a framework by breaking down all the steps we took above to solve a projectile motion problem:

  1. Draw a diagram
  2. Split any velocity vectors into x and y component
  3. Fill out kinematic variables on your x and y chart
  4. Identify what you’re solving for and see if you will use the x, y, or both sides of the chart to solve it
  5. Pick an equation and solve!

A more detailed outline of the projectile motion frame work can be found here.

Now you can attempt some questions on your own using the framework above.

PQ – Projectile Motion

These problems are much harder. Re-watch the video above to see the step by step process of solving ALL projectile motion problems.

  1. A ball is kicked horizontally at 8.0 m/s from a cliff 80m high. How far from the base of the cliff will the stone strike the ground? (32 m)
  2. A shell is fired from a cliff at an initial velocity of 800 m/s at a 30° angle below the horizontal. How long will it take to reach the ground 150m below? (.37 seconds)
  3. A long jumper leaves the ground at an angle of 20° to the horizontal and at a speed of 11 m/s.
    • How far does he jump? (7.75 m)
    • What is the maximum height he reaches? (.71 m)
  4. A projectile is shot from the edge of a cliff 42 m above ground level with an initial speed of 33.33 m/s at an angle of 37° with the horizontal.
    • Determine the time taken by the projectile to hit point P at ground level. (5.5 seconds)
    • Determine the range X of the projectile as measured from the of the cliff. (147 m)
    • At the instant the projectile hits point P, find the horizontal and the vertical components of its velocity. (vx = 26.7 m/s; vy = -35.2 m/s)
    • Find the speed of the projectile at point P. (44.2 m/s)
  5. A bullet is fired at an angle of 60° with an initial velocity of 200.0 m/s.
    • How long is the bullet in the air? (35.4 seconds)
    • What is the maximum height reached by the bullet? (4601 m)

For more practice, be sure to check out the course materials page.

The Next Unit – Unit 2 Preview

Congrats! You have officially completed the first Unit of AP Physics 1 and many other curriculums. You should be able to solve the most difficult kinematic problems with ease. For more practice be sure to check out the course materials page.

In the next unit (Unit 2: Forces Unpacked), we will a major Physics topic. You may have heard of Newton’s law and now you will be learning and applying it in depth. Further more, everything you have learned so far will also be applied!

Picture of Jason Kuma
Jason Kuma

Writer | Coach | Builder | Fremont, CA


Units in AP Physics 1

Unit 1 – Linear Kinematics

Unit 2 – Linear Forces

Unit 3 – Circular Motion

Unit 4 – Energy 

Unit 5 – Momentum 

Unit 6 – Torque 

Unit 7 – Oscillations 

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