4 Vectors vs. Scalarsscalars: only magnitude (size) ex. distance, time, speed, mass, temperaturevectors: magnitude and a directionExamples of vectorsdisplacement, s or x : distance and directionvelocity, v : speed and directionacceleration, a: change in speed and direction
5 Vector BasicsVectorsdisplacement vectors d = d (displacement), q (direction)length proportional to amountdirection measured by angle
6 Co-linear Vectors Combining Vectors resultant: vnet= v1+ v2 Collinear vectors:v v v v2resultant: vnet= v1+ v2ex: A plane flies 40 m/s E into a 10 m/s W headwind. What is the net velocity?ex: A plane flies 40 m/s W with a 10 m/s W tailwind. What is the net velocity?
7 Non Co-linear Vectors Perpendicular vectors: resultant’s magnitude: resultant’s direction:
8 Graphical Method Tail to tip method +yTail to tip methodPlace first vector on graph with tail starting at the originPlace the second vector with the tail at the tip of the first vectorRepeat step two for multiple vectorsDraw a line from the tail of the first vector to the tip of the final vector. This final vector is called the resultant.The order that you add vectors doesn’t matter (commutative property)+x-x-y