# PHYS 1021 Lecture Notes - Lecture 2: Relative Velocity, Projectile Motion, Pythagorean Theorem

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13 Feb 2017

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Kinematics in Two or Three dimensions: vectors

3-1 Vectors and Scalars

1. Vector: quantity including direction and magnitude

a. Ex. displacement, force, momentum

2. Scalar: quantity have no direction associated

a. Mass, time, temperature

3-2 Addition of Vectors- Graphical Methods

1. Resultant displacement: displacement after adding vectors

2. Using pythagorean theorem if the vectors at right angle

3. When vectors are not along the same line, the resulting magnitude will be less than the

raw addition

4. Parallelogram method: make a parallelogram with two vectors, draw a vector to

the other end of the parallelogram

5. The daigonal attaching teh two vectrors is their difference

3-3 Subtraction of Vectors and Multiplication of a Vector by a Scalar

6. Negative vectors run in the opposite direction

7. Scalar multiplication

3-4 Adding Vectors by Components

1. Components: the vectors a + b that make up vector c when added

a. Usually done in the y and x direction

2. Resolving the vector into its components: find the components of the vector

3. Add the x components and the y components of two different vectors.

4. Use x and y components to construct a triangle and SOLVE

3-5 Unit Vectors

1. Unit vectors: magnitude of 1

2. i, j, k are the vector that point along the x, y, or z axis

3-6 Vector Kinematics

1. Displacement vector Δr: the vector that is drawn between the two tips of two other

vectors.

a. Represents change in position

b. Over a specific time interval: t2 - t1

2. Average velocity vector: Δr / Δt

3. Instantaneous velocity: limit of the average velocity as Δt approaches 0

a. v = lim Δt → 0 (Δr / Δt) = dr / dt

4. Average acceleration vector: (v2 - v1) / (t2 - t1)

5. Instantaneous acceleration vector: dV / dT

a. Also refers to a change in direction

6. 3-7 Projectile Motion

a. Projectile motion

i. Air resistance is usually declared negligible

b. Gravity acceleration

c. Analyse horizontal and vertical motions separately

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