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

2. Vectors and Scalar Quantities
Vector quantities
Position
Velocity
Acceleration
Force
Momentum
Scalar quantities
Time
Mass
Energy
Temperature
(Dr. Hart’s dog)

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

4. Vectors – Graphical addition
Method 1
Sequential movement “A” then “B”.
Etown/Lancaster, Mt. Gretna detour.
Tail-to-tip method.
Right angles, non-right angles.
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
Parallelogram method.
Right angles, non-right angles
Two methods are equivalent C B A C B A

5. Vectors – Graphical subtractionIf
C = A + B
Then
B = C - A
B = C + -A C B A -A B C

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

7. Vectors – Components addition
Components - Simplest method
Break 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

8. Trigonometry For any right triangle Basic trig functions
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒=ℎ𝑦𝑝 ∙ sin 𝜃
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡=ℎ𝑦𝑝 ∙ 𝑐𝑜𝑠 𝜃

9. Mail Carrier Displacement

10. Mail carrier displacement
X-component
Y-component D1
22 km D2
+ 47 km cos(60)
- 47 km sin(60) D km
-18.7 km
Insert sign by inspection
𝐷= 𝐷 𝑥 𝐷 𝑦 2 =30 𝑘𝑚
𝑡𝑎𝑛𝜃= 𝐷 𝑦 𝐷 𝑥 =−.796
𝜃=−38.5° (𝑏𝑒𝑙𝑜𝑤+𝑥 𝑎𝑥𝑖𝑠)

11. Plane Trip

12. Plane Trip 𝐷= 𝐷 𝑥 2 + 𝐷 𝑦 2 =960 𝑘𝑚 𝑡𝑎𝑛𝜃= 𝐷 𝑦 𝐷 𝑥 −1.25
x-component
y-component D1
620 km
0 km D2
+440 km cos(45)
-440 km sin D3
-550 km cos(53)
-550 km sin D
601 km
-750
𝐷= 𝐷 𝑥 𝐷 𝑦 2 =960 𝑘𝑚
𝑡𝑎𝑛𝜃= 𝐷 𝑦 𝐷 𝑥 −1.25
𝜃=−51° (𝑏𝑒𝑙𝑜𝑤+𝑥 𝑎𝑥𝑖𝑠)

13. Other examples
Problem 9
Problem 10
Problems 6-8