Vectors

Scalars A scalar is a quantity that has magnitude only (no direction) Examples of Scalar Quantities: Distance Area Volume Time Mass

Vectors A vector quantity is a quantity that has both magnitude and a direction in space (has both x and y components) Examples of Vector Quantities: Displacement Velocity Acceleration Force Weight

Magnitude and direction 20 m/s at 125o (if no direction is given, it is the angle with horizontal) 40 N at 25o north of west

Direction 90 o North y + - + 0 o East x West 180 o 360 o

To find x and y components given magnitude and direction Use trig!! Each vector is made up of an x component and a y component To find the x component, multiply the magnitude by cos θ To find the y component, multiply the magnitude by sin θ A Asinθ θ Acosθ

Example Find the components of a vector with magnitude of 30 m/s at 40o

Example Find the components of a vector with magnitude of 120N at 25o west of north

To find magnitude and direction given components Magnitude can be found using the pythagorean theorem!! Direction is found using trig! If vector is not in 1st quadrant, you will need to change the answer your calculator gives you y θ x

Vector Addition When you add vectors, the answer is called the resultant To find the resultant, simply add the components

An airplane is flying 200m/s at 50o N of E Wind velocity is 50 m/s due S. What is the velocity of the plane? N 50 200 ? W E VR = 164.9 m/s @ 38.7° S