3. Vectors

Vector Composition & Decomposition

Vector Components Introduction

Vector Component

<img src="https://media.pearsoncmg.com/aw/aw_knight_physics_5/msa/content/practice-test/img/p03_26_figure.jpg" class="block" alt="Two vectors begin at the origin of a tilted coordinate system."> The figure shows vectors <math display="inline"><mrow><mover accent='true'><mi>A</mi><mo>&#x21C0;</mo></mover></mrow></math> and <math display="inline"><mrow><mover accent='true'><mi>B</mi><mo>&#x21C0;</mo></mover></mrow></math>. What are the x and y components of <math display="inline"><mrow><mover accent='true'><mi>A</mi><mo>&#x21C0;</mo></mover></mrow></math>?

A jet plane taking off from an aircraft carrier has acceleration a = ( 15 m/s², 22° above horizontal). What are the horizontal and vertical components of the jet’s acceleration?

Anderson Video - Vector Components

Calculating Magnitude & Components of a Vector

Vector Components | Physics with Professor Matt Anderson | M3-03

Jack and Jill ran up the hill at 3.0 m/s. The horizontal component of Jill’s velocity vector was 2.5 m/s.

b. What was the vertical component of Jill’s velocity?

Breaking down vectors into components | Vectors | Precalculus | Khan Academy

Let B = (5.0 m, 30 degrees counterclockwise from verically up). Find the x- and y- components of B in each of the two coordinate systems shown in FIGURE EX3.21. <img src="https://lightcat-files.s3.amazonaws.com/problem_images/21159c3a898c4a54-1676584280087.jpg" alt="" />

A toy gun shoots a plastic ball <math display="inline"><mrow><mn>10</mn><mo rspace="thickmathspace">&#x2062;</mo><mrow><mi mathvariant="normal" class="MathML-Unit">m</mi><mo>/</mo><mi mathvariant="normal" class="MathML-Unit">s</mi></mrow></mrow></math> at an angle of 25° above the horizontal. What is the vertical component of the ball's velocity when it left the gun?

Vector A is 2.80 cm long and is 60.0° above the x-axis in the first quadrant. Vector B is 1.90 cm long and is 60.0° below the x-axis in the fourth quadrant (Fig. E1.35). Use components to find the magnitude and direction of (b) A - B In each case, sketch the vector addition or subtraction and show that your numerical answers are in qualitative agreement with your sketch. <img src="https://lightcat-files.s3.amazonaws.com/problem_images/e3db6afd5258018e-1674069416985.jpg" alt="" /><img class="fr-dib" src="https://lightcat-files.s3.amazonaws.com/problem_images/0e5047a454158410-1678204280090.jpg" style="width: 223px;">

Vector Components- Samples (Physics)

If the vector <math display="inline"><mrow><mover accent='true'><mi>E</mi><mo>&#x21C0;</mo></mover></mrow></math> shown in the figure has components <math display="inline"><mrow><msub><mi>E</mi><mi>x</mi></msub><mo>=</mo><mn>3.0</mn></mrow></math> and <math display="inline"><mrow><msub><mi>E</mi><mi>y</mi></msub><mo>&#x2212;</mo><mn>1.3</mn></mrow></math>, what is &#x3b8;? <img src="https://media.pearsoncmg.com/aw/aw_knight_physics_5/msa/content/practice-test/img/ex03_03_figure.jpg" class="block" alt="Vector E falls from the origin into quadrant 4. It is at angle phi to the x-axis, and angle theta to the y-axis.">

Vector components on a grid

Find the magnitude and direction of the vector represented by the following pairs of components: (a) Ax = −8.60 cm, Ay = 5.20 cm:

Your neighbor Paul has rented a truck with a loading ramp. The ramp is tilted upward at 25°, and Paul is pulling a large crate up the ramp with a rope that angles 10° above the ramp. If Paul pulls with a force of 550 N, what are the horizontal and vertical components of his force? (Force is measured in newtons, abbreviated N.)

What are the x- and y-components of the velocity vector shown in FIGURE EX3.20? <img src="https://lightcat-files.s3.amazonaws.com/problem_images/d679ce265717f902-1677790731313.jpg" alt="" />

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Calculating Dot Product Using Components

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Introduction to Vectors

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