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

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

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.

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.

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)

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!

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.

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

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

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

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.