Vectors Questions Vectors vs Scalars Vectors Graphical addition

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Vectors • Questions • Vectors vs. Scalars • Vectors – Graphical addition • Vectors

Vectors • Questions • Vectors vs. Scalars • Vectors – Graphical addition • Vectors – Components addition • Example 3 -2. • Example 3 -3. • Quiz next week (10 -15 min)

Vectors and Scalar Quantities • Vector quantities – Position – Velocity x, v, a,

Vectors and Scalar Quantities • Vector quantities – Position – Velocity x, v, a, F, etc – Acceleration – Force – Momentum • Scalar quantities – Time – Mass – Energy – Temperature – https: //www. youtube. com/watch? v=f. Vq 4_Hh. BK 8 Y – (Dr. Hart’s dog) 10 t, m, E, etc.

Vector Addition – why? • • Multiple-leg trip Boat velocity + stream velocity Multiple

Vector Addition – why? • • Multiple-leg trip Boat velocity + stream velocity Multiple forces on object Accelerated circular motion Momentum Electric Forces Magnetic Forces

Vectors – Graphical addition • Method 1 – Sequential movement “A” then “B”. C

Vectors – Graphical addition • Method 1 – Sequential movement “A” then “B”. C – Etown/Lancaster, Mt. Gretna detour. B – Tail-to-tip method. – Right angles, non-right angles. A • Method 2 – Simultaneous little-bit “A” and little bit “B” – Velocity, paddling across the current – Force, pulling a little in x and a little in y B C – Parallelogram method. – Right angles, non-right angles • Two methods are equivalent A

Vectors – Graphical subtraction • If C C = A + B B A

Vectors – Graphical subtraction • If C C = A + B B A -A • Then B = C - A B = C + -A B C

Vectors - components • If C = A + B (vector C is sum

Vectors - components • If C = A + B (vector C is sum of vectors A and B) B C A • Then C = Cx + Cy ( C can be broken into components Cx and Cy) Cy C Cx • Method 3 - Break all vectors into components, add components, reassemble result

Visualizing components • x component C Cx • y component Cy C

Visualizing components • x component C Cx • y component Cy C

Vector components • C can be broken into components Cx and Cy Cy C

Vector components • C can be broken into components Cx and Cy Cy C Cx

Vectors – Components addition • Components - Simplest method – Break all vectors into

Vectors – Components addition • Components - Simplest method – Break all vectors into x and y components – Add components like accounting sheet – Recombine to form final vector • Trig definitions – Break up - right triangle, sin, cos, tan – Combine - Pythagorean theorem, arctan • Example 3 -2 • Example 3 -3

Trigonometry • For any right triangle • Basic trig functions

Trigonometry • For any right triangle • Basic trig functions

Mail Carrier Displacement

Mail Carrier Displacement

Mail carrier displacement X-component Y-component D 1 0 22 km D 2 + 47

Mail carrier displacement X-component Y-component D 1 0 22 km D 2 + 47 km cos(60) - 47 km sin(60) D + 23. 5 km -18. 7 km Insert sign by inspection

Plane Trip

Plane Trip

Plane Trip x-component y-component D 1 620 km D 2 +440 km cos(45) +311

Plane Trip x-component y-component D 1 620 km D 2 +440 km cos(45) +311 -440 km sin 45 -311 D 3 -550 km cos(53) -330 -550 km sin 53 -439 D 601 km -750

Other examples • Problem 9 • Problem 10 • Problems 6 -8

Other examples • Problem 9 • Problem 10 • Problems 6 -8