1. NM Unit 2 Vector Components, Vector Addition, and Relative Velocity
Learning Goals:
Solve/Calculate the horizontal and vertical components of a vector
Solve (Mathematically) vector addition that results in a 1-D resultant
Apply the Pythagorean Theorem to calculate the magnitude of a 2-D resultant
Apply tangent to calculate the direction of a 2-D resultant
Adapt vector addition techniques to solve relative velocity problems

2. Vector Notation 3m, 65 degrees 100 m/s, SW 50 km, 30 degrees N of W
25 kgm/s, South

3. Angles Based off of +x axis equalling 0 degrees
In 2-D space we consider the following
East (+x axis) = 0 degrees
North (+y axis) = 90 degrees
West (-x axis) = 180 degrees
South (-y axis) = 270 degrees
NE, NW, SE, and SW all have specific angle values.

4. Graphical Representation
Length of vector is the magnitude
Angles need to be drawn in a manner that corresponds with the given coordinate system
Let’s draw the 4 vectors from the 2nd Slide in the notes.

5. Vector Components Vectors can be 1-D (horizontal or vertical)
Vectors can be 2-D (a mix of horizontal and vertical)
Horizontal component determines left-ness and right-ness of a vector.
Vertical component determines up-ness and down-ness of a vector
Up is positive, Right is positive, Left is negative, and Down is negative
Vector components are also vectors (but they are always 1-D)

6. Calculating Components
Frequently (not always) the horizontal component is associated with using cosine and the vertical component is associated with using sine.
Drawing the vector or looking at a provided diagram will allow you make the correct trig function choice.
The magnitude of the vector is the hypotenuse and the component we need to find will either be adjacent or opposite the angle of the vector.
Let’s Calculate some components!

8. Adding Vectors
1-D Resultant: All vectors are horizontal or vertical, resultant calculated via “normal” math, direction can be compass direction or +/-
2-D Resultant (Vectors are perpendicular): Use pythagorean theorem to find magnitude, use tangent to find direction (+/- will not work)
2-D Resultant (vectors not perpendicular): must break vectors into components, combine components into two 1-D perpendicular vectors, follow adding perpendicular vector steps
We will work these out later on.

9. Relative Velocity
Relative velocity is the velocity of an object as seen by an observer (the observer may or may not be stationary)
This relative motion could be 1-D or 2-D
Based on your sketch you will apply vector math.
You may want to use subscripts to help keep track of all of the velocities.
Examples…
We now shift from math class to physics.
Relative velocity is an application of vector math

10. A person is walking at 3 m/s with respect to the moving sidewalk
A person is walking at 3 m/s with respect to the moving sidewalk. The moving sidewalk is moving at 1.5 m/s with respect to the ground. How fast does a stationary observer see the person walking?
Work out in notes

11. A swimmer can swim at 4 m/s in still water
A swimmer can swim at 4 m/s in still water. Suppose they swimming north across a river, and the river has a current of 2 m/s to the east. What is the magnitude and direction of the swimmer with respect to the shore?
Work out in notes

12. A dog walks 1000 m north and then turns to a heading that is 30 degrees west of north. The dog continues on this heading for 1500m. What is the magnitude and direction of the dog’s displacement.