Vectors

Scalars and Vectors Scalar – has only magnitude (or size) Vector – has both magnitude and direction Examples of Scalars: Mass Distance Time Density Work Energy Examples of Vectors: Displacement Velocity Acceleration Force Momentum Angular momentum

Scalars and Vectors Which are scalars? Which are vectors?

Vector Addition - One Dimension Always add vectors “tip-to-tail” Resultant is the sum of the first two vectors

When adding vectors together, the answer is called “The Resultant”.

Vector Addition – One Dimension Always add vectors “tip-to-tail” Place the tip of the first vector next to the tail of the second “Resultant” is the sum of the first two vectors

Vector Addition – Two Dimensions Still add vectors “tip-to-tail” Resultant has both magnitude (the numerical sum of the first two vectors) and direction (typically an angle or direction – north, south, etc.) Example: A hiker travels 4 miles east Which is the magnitude? Which is the direction? Is this a vector?

Vector Addition – Hiker Example Example: A hiker travels 8 miles east then 2 miles north. How far is he from where he started? At what angle? Draw the resultant. Use pythagorean theorem to calculate distance. Use geometry (SOH-CAH-TOA) to calculate angle. 2 mi 8 mi

SOH-CAH-TOA SOH: CAH: TOA: R x y θ

Vector Addition You are in a plane flying east at 45 km/hr when you hit a crosswind moving north at 25 km/hr. What is your resultant velocity? + 25 km/hr north 45 km/hr east V=? 25 km/hr north =? 45 km/hr east

V=? Vy = 25 km/hr =? Vx = 45 km/hr  = 29.050 north of east

Resolving Vectors into components

Resolving Vectors Component – the projection of a vector onto a coordinate axis Vectors are at angles Want the x-component and y-component i.e., the x “piece” and the y “piece” of the vector VECTOR “Y-component” “x-component”

Resolving Vectors You travel 30 meters at an angle that is 250 north of east. Resolve this vector into its components 30 m 250

30 m 250

Positive or Negative Components? y X = pos Y = pos X = neg Y = pos x X = neg Y = neg X = pos Y = neg

“Breaking Vectors down into Components” Practice… (& Walking the Vectors Lab, if time)