TDK - Vectors

Vectors

Most motion takes place in more than one dimension. Objects on the surface of the earth, or traveling through the air, move in two or even three dimensions. To deal with objects moving in two dimensions we need to be able to deal with them as vectors. Vectors have both a magnitude and direction. Vectors are treated as right triangles, allowing us to use the laws of sines and cosines to break vectors into their components. This means that we mathematically calculate what the length of the vector is along each axis of a coordinate grid. Pythagorean's Theorem and the law of tangents allows us to take the components of vectors to determine the magnitude and direction of the vectors they represent. The direction is given as an angle from the positive x-axis, or from the East. Watch the following presentation that will give you more insight into what a vector is and how we can resolve vectors and calculate the values of vector components. 

Vectors Practice

We will now practice solving problems using the equations and concepts you learned in the presentation. This is one of the few times in physics that you simply follow the steps to get the right answer. Be sure to stay in the habit of showing all work as you solve physics problems. The presentation will give you time to work through the problems, find a solution, and check your work. 

Vectors Self-Assessment

Now it is your turn. Complete the self-assessment questions to verify that you can calculate the components of vectors and can resolve the components of vectors into a single, overall magnitude and direction.

  1. A car travels with a velocity of 27 m/s at -76 degrees .
    1. What is the x-component of the velocity?
    2. What is the y-component of the velocity? 

SOLUTIONS

 

  1. A man walking his dog has a displacement of 152m at 18 degrees West of South.
    1. What is the x-component of his displacement?
    2. What is the y-component of his displacement?

SOLUTIONS

 

  1. The x and y-components of a vector are 28m and -45m respectively.
    1. What is the magnitude of the vector? 
    2. What is the direction of the vector? 

SOLUTIONS

 

  1. The x-component of an acceleration vector is -5.0 m/s2. If the angle of the acceleration is 119 degrees. what is the magnitude of the acceleration? 

SOLUTION

Vectors Practice Problems

Download more Vectors Practice Problems.

Download Solutions to practice problems. 

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