The Vector Lecture Or Whats Our Vector Victor

The Vector Lecture Or What’s Our Vector Victor?

Vectors vs. Scalar Quantities • Vector quantities have both a magnitude (measure) and direction. • Vector quantities add geometrically • Can be broken into components • E. G. displacement, velocity, acceleration, force • Scalar quantities have magnitude only • Scalar quantities add algebraically (simply add values) • Can have positive and negative values. • E. G. mass, time

Check Question 1 Which of the pictured vectors are in the same direction? A. A and B B. B and C C. A and C Which of the pictured vectors are equal in magnitude? A. A and B B. B and C C. A and C A B C

Vector Addition • For vectors in same or opposite direction simply add or subtract. • For vectors at right angles use pythagorus to add and get resultant. • For vectors at angles other than right angle break up vector(s) into components, add and then use pythagorus. • Graphically can always use tip to tail and using scaling for magnitude.

Check Question 2 Which of the following represents the resulting vector for the two vectors to the right? A B C

Vector Decomposition • Dividing one vector into two component vectors • Components are amount of vector quantity in that direction • Perpendicular components do not affect one another – Parallel Component = R cosine angle – Perpendicular Component = R sine angle • Opposite of vector addition R sine angle Angle R cosine angle R

Vector Addition Revisited • To add vectors not in same direction or at right angles. – Decompose each vector into perpendicular components – Add components in same direction – Find resultant using Pythagorean theorem – Find angle using tangent or other trig function and components • This is where the law of sines and cosines came from Px Qx Qy Py Q P

Use of Velocity Vectors: Wind and Wave Power • Fastest point of sail is nearly perpendicular to wind – Running with wind means you can only go as fast as the wind – Running sideways to the wind means that wind continues to push on you even when you are going the same speed as wind Wind A B C