3. Vectors

Unit Vectors

Unit Vector Notation Physics

The position of a particle as a function of time is given by 𝓇 = ( 5.0î ＋4.0ĵ )t² m where t is in seconds.

c. What is the particle’s speed at t = 0, 2, and 5 s?

You are given two vectors A = -3i + 6j and B = 7i + 2j. Let Counterclockwise angles be positive (a) What angle does A make with the +x-axis?

Given two vectors A = 4i + 7j and B = 5i - 2j, (a) find the magnitude of each vector;

In each case, find the x- and y- components of vector A: (b) A = 11.2j - 9.91i

The position of a particle as a function of time is given by 𝓇 = ( 5.0î ＋4.0ĵ )t² m where t is in seconds.

b. Find an expression for the particle’s velocity v as a function of time.

A cannonball leaves the barrel with velocity v = (75î ＋ 45ĵ). At what angle is the barrel tilted above horizontal?

Vector Notation

What are the x- and y-components of vector shown in FIGURE EX3.3 in terms of the angle and the magnitude E? <img src="https://lightcat-files.s3.amazonaws.com/problem_images/21cab74126559561-1676333891254.jpg" alt="" />

Let E = 2i + 3j and F = 2i - 2j. Find the magnitude of (c) -E - 2F

Trevon drives with velocity v₁ = (55î ─ 10ĵ) mph for 1.0 h, then v₂ = (20î ＋ 50ĵ) mph for 2.0 h. What is Trevon’s displacement? Write your answer in component form using unit vectors.

C = (9 m) i + (10 m) j = 13.5 m @ 48° above the +x-axis

C = -(9 m) i + (10 m) j = 13.5 m @ 48° above the -x-axis

C = (9 m) i + (10 m) j = 13.5 m @ 0.83° above the +x-axis

C = -(9 m) i + (10 m) j = 13.5 m @ 0.83° above the -x-axis

A = (4.0 m)i + (3.0 m)j and&nbsp;B = (−13.0 m)i&nbsp;+ (7.0 m)j. You add them together to produce another vector&nbsp;C. (a) Express this new vector&nbsp;C in unit-vector notation. (b) What are the magnitude and direction of&nbsp;C?

Let E = 2i + 3j and F = 2i - 2j. Find the magnitude of (a) E and F

Adding 3 Vectors in Unit Vector Notation

Unit vector notation | Vectors and spaces | Linear Algebra | Khan Academy

Anderson Video - Cartesian Coordinates

The position of a particle as a function of time is given by 𝓇 = ( 5.0î ＋4.0ĵ )t² m where t is in seconds.

a. What is the particle’s distance from the origin at t = 0, 2, and 5 s?

Anderson Video - Unit Vectors

Given two vectors A = -2i + 3j + 4k and B = 3.00î+1.00ĵ − 3.00k (a) find the magnitude of each vector;

Unit Vectors | Physics with Professor Matt Anderson | M3-06

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