Vector Math What is a vector Has magnitude

Vector Math

What is a vector? • Has magnitude and direction • Has a head and a tail • What types of measurements are vectors?

Magnitude of vectors • Length of vector is proportional to the magnitude

Adding Vectors • Vectors have a direction so you need to take that into account when adding • A vector sum is called “resultant”

Adding vectors in same axis

What if vectors are at angle to each other?

Uh oh… 2 methods: • Graphical (tip to tail) • Trigonometric

Tip to Tail- graphical addition • Put the vectors (keeping direction and magnitude) together with the tip of the first touching the tail of the second • When finished, draw a new resultant from the tail of the 1 st to the tip of the last

Tip to tail vector addition • It doesn’t matter which order you put them in as long as you keep tip to tail • Try the worksheet…

Vector Subtraction • Think about it- what does it mean to change the sign of a vector? • When subtracting, you are basically adding the negative of the 2 nd vector • So same magnitude, opposite direction • Try some…

OK, why all the focus on angled vectors • We don’t live in a 1 D world where everything happens on the x axis • To deal with projectiles and forces we need to at least add a 2 nd dimension

Vector Components • This is the real world (ok, only 2 d, but close enough) so things happen at angles- not just along x and y axis • Each vector can be considered the sum of its x and y components

Vector Components

Resolving Vectors into Components- Graphical

Vector Word Problems • Use vector math to solve word problems involving displacement and velocity in 2 D • BUT you need to keep quantities in different directions separate

Vector Word Problems • You can solve for any variable across the river by using information such as distance and velocity across the river • But you can’t use the distance or velocity downriver or the total distance or velocity across at the angle

Example • An airplane with a velocity of 100 km/h encounters a headwind (blowing against it) of 25 km/h. What is the resultant velocity of the plane?

Answer

Example 2 • An airplane with a velocity of 100 km/h encounters a crosswind blowing at 25 km/h. What is the resultant velocity?

Answer 2