Expressing a vector as the scaled sum of unit vectors. This video, which is suitable for high school students, starts with a black screen because the instructor, in his conversational tone, uses it as a 'chalkboard.' Instructor uses different colors ...for clarification.[more]

Solving the second part to the projectile motion problem (with wind gust) using ordered set vector notation. This video, which is suitable for high school students, starts with a black screen because the instructor, in his conversational tone, uses i...t as a 'chalkboard.' Instructor uses different colors for clarification.[more]

More on unit vector notation. Showing that adding the x and y components of two vectors is equivalent to adding the vectors visually using the head-to-tail method. This video, which is suitable for high school students, starts with a black screen bec...ause the instructor, in his conversational tone, uses it as a 'chalkboard.' Instructor uses different colors for clarification. (09:13)[more]

This visually confusing tip-to-tail vector addition problem can be solved just like our previous problems. Give your vectors names, draw a vector diagram, break vectors in to components, redraw the vector diagram, create a data table, add columns an...d solve using basic trig.
Content Times:
0:14 Reading, visualizing, and translating the problem.
1:13 Drawing the vector diagram.
2:06 Breaking vector C in to its components.
3:22 Redrawing the vector diagram (twice).
4:16 Creating the data table.
4:53 Determining the components of the resultant vector, R.
5:33 Solving for vector R.
7:13 Visualizing the entire problem.
7:36 The Review.
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Previous Video: Using a Data Table to Make Vector Addition Problems Easier
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Any vector addition problem can be made easier by using a data table; no matter how many vectors.
Content Times:
0:13 Reviewing the problem.
0:46 Starting the Data Table.
1:13 Filling in the table: Vector A
2:02 Filling in the table: Vector C
...2:33 Filling in the table: Vector B
3:11 Finding the Components of the Resultant Vector, R.
3:59 The Review
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Previous Video: Introductory Vector Addition Problem using Component Vectors
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A simple, introductory vector addition problem that combines the concepts of vectors, cardinal directions, tip-to-tail vector addition and component vectors.
Content Times:
0:14 Reading and understanding the problem.
1:25 Drawing the Vector Diagr...am.
2:28 A common mistake about where to place the arrowhead on the Resultant Vector.
3:39 This is NOT a Vector Diagram!
4:34 How NOT to solve the problem.
5:12 Breaking vector B in to its component in the y direction.
6:02 Breaking vector B in to its component in the x direction.
6:52 Redrawing the Vector Diagram using the components of vector B.
7:30 Finding the direction of our Resultant Vector.
8:35 Finding the magnitude of our Resultant Vector.
9:47 Summarizing the entire problem in 27 seconds.
10:19 The review.
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Next Video: Using a Data Table to Make Vector Addition Problems Easier
Previous Video: Introduction to Vector Components
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Many students struggle with understanding Cardinal Directions. So this is a very basic video describing how to use cardinal directions with vectors. (All “likes” are much appreciated. 😊)
Content Times:
0:12 Previous example summary
0:48 Two sug...gestions for working with Cardinal Directions
1:58 East of North = East “from” North
2:18 The 8 possible directions
3:51 Two equivalent ways to describe the same vector
4:51 NE, SE, SW, and NW
5:24 The review
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Next Video: Introduction to Vector Components
Previous Video: Introductory Tip-to-Tail Vector Addition Problem
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This is a very basic introduction to Tip-to-Tail Vector Addition using a motorized toy car that I made. Also included is an introduction to Vectors and Scalars, their definitions and some variable examples of Vectors and Scalars.
Content Times:
0...:11 Slow Velocity Racer!
0:48 Determining the speed of Slow Velocity Racer!
1:55 Which track for Slow Velocity Racer to move the fastest?
2:54 How fast will Slow Velocity Racer move between the two tracks?
3:18 How fast will Slow Velocity Racer move on the top track?
4:03 Tip-to-Tail Vector Addition
5:45 Defining Vectors
6:15 Defining Scalars
6:38 Variable Examples of Vectors
7:02 Variable Examples of Scalars
7:28 Montage of Examples of Scalars
8:18 Defining Magnitude
9:20 Scalars can be negative
9:56 The Review
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Next Video: Introductory Tip-to-Tail Vector Addition Problem
Previous Video: Don’t Drop Your Camera 5.0 Seconds After Liftoff
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Components of Vectors are an important piece to understand how vectors work. In this video we learn how to “break” or “resolve” vectors in to their component pieces.
Content Times:
0:14 The example displacement vector d
0:44 Finding the y compon...ent of vector d
2:17 Finding the x component of vector d
3:18 What does it mean to be a component of a vector?
4:14 A common question about vector components
4:51 Showing mathematically that the vector components add up to the vector
6:48 Explaining how d in the x direction shows both magnitude and direction
7:57 The Review
Want Lecture Notes?
Next Video: Introductory Vector Addition Problem using Component Vectors
Previous Video: How to use Cardinal Directions with Vectors
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This is a very basic introductory to Tip-to-Tail Vector Addition Problem using a motorized toy car that I made. I don’t just talk about it in a general sense, I actually show the different vectors being added together.
Content Times:
0:16 Problem... introduction
0:36 Determining the velocity of the track
1:43 Defining our givens
3:08 Visual representation of our vectors
3:56 Slow Velocity Racer on the track
4:20 Drawing the resultant vector
5:03 Mathematically finding the magnitude of the resultant velocity vector
6:28 Mathematically finding the direction of the resultant velocity vector
8:45 Summarizing and understanding our results
9:20 49 + 42 = 65?
10:57 The Review
Want Lecture Notes?
Next Video: How to use Cardinal Directions with Vectors
Previous Video: Introduction to Tip-to-Tail Vector Addition, Vectors and Scalars
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