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- Scalars, Vectors, and Motion
Vector operations in one dimension
- Intro Lesson: a3:46
- Intro Lesson: b3:26
- Intro Lesson: c2:27
- Intro Lesson: d3:37
- Lesson: 16:04
- Lesson: 25:13
- Lesson: 37:02
- Lesson: 47:51
Vector operations in one dimension
Lessons
In this lesson, we will learn:
Notes:
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How to add, subtract, multiply, and divide vectors
- Graphically (with diagrams)
- Numerically (with math)
Notes:
Just like scalars, vectors can be added, subtracted, multiplied, and divided:
- When vectors are added, the vector diagram is drawn by tip-to-tail addition. To add A and B, draw the vector A, then starting at the tip of A draw B. The tail of B connects to the tip of A.
- Taking the negative of a vector "flips" the vector to point in the opposite direction, while keeping the same magnitude.
- Multiplying or dividing a vector by a positive scalar changes the magnitude of the vector, while keeping the same direction.
- IntroductionIntroduction to vector operations:a)What is the difference between adding scalars and vectors?b)Solving vector problems graphicallyc)Solving vector problems numericallyd)Sign convention for vector problems
- 1.Solve vector addition problems
Solve the following vector additions graphically and numerically:
i. A+B=C, if A=10m [E], B=7m [E].
ii. v1+v2=vres if v1=4.5m/s [E], v2=13.2m/s [W]
- 2.Solve vector subtraction problems
Δd1=1.2km [N], Δd2=0.8km [N]. Solve the equation Δd1−Δd2=Δdres graphically and numerically. - 3.Solve vector multiplication and division problems
D=12m/s [W]. Solve the following graphically and numerically:i. 3D=E
ii. -2D=F
- 4.Create Vector Equation and Diagram from Word Problem
A city block is 50 m long. While doing errands, Tia walks 1 block east, then three fifths of a block west, then two blocks east.
i. Write the displacement vector Δdblock that describes walking 1 block east.
ii. Describe this situation with a vector equation and a vector diagram in terms of Δdblock
iii. Find Tia's overall displacement.