1. Chapter 3: Vectors EXAMPLES

2. Example 3.1
The Cartesian coordinates of a point in the xy plane are (x,y) = (-3.50, -2.50) m, as shown in the figure. Find the polar coordinates of this point.
Solution: From Equation 3.4,
and from Equation 3.3,

3. Example 3.1, cont. Change the point in the x-y plane
Note its Cartesian coordinates
Note its polar coordinates
Please insert active fig. 3.3 here

4. Example 3.2 V = Vector Displacement 500 m, 30º N of E.
Find components of V (Vx and Vy )

5. Example 3.3 Sum of Two vectors (Example 3.3 Text Book)
Find the Resultant vector: R = A + B
If: and
Using Eqn: (3.14)
Or: Rx = 4.0m and Ry = – 2.0m
Magnitude and direction of R will be:
–27o means clockwise from + x axis. Or 333o from +x axis counterclockwise

6. Example 3.4 Taking a Hike (Example 3.5 Text Book)
A hiker begins a trip by first walking 25.0 km southeast from her car. She stops and sets up her tent for the night. On the second day, she walks 40.0 km in a direction 60.0° north of east, at which point she discovers a forest ranger’s tower.

7. Example 3.4 cont,
Find the resultant displacement (graphically and analytically) for the trip: R = A + B
Select a coordinate system
Draw a sketch of the vectors
Find the x and y components of A & B (Decomposition) y Bx B By Ax x Ay A

8. Example 3.4 cont,
Draw each component with its magnitude and direction
Find Rx and Ry components of the resultant:
Rx = Σx components
Ry = Σy components
Given by Equation 3.15:
Rx = Ax + Bx = 17.7 km km
Rx = 37.7 km
Ry= Ay + By = –17.7 km km
Ry = 16.9 km
In unit-vector form, we can write the total displacement as y By Ry Bx x Ax Rx Ay

9. Example 3.4 cont,
Draw Rx and Ry components with its magnitude and direction
Use the Parallelogram system to find the resultant graphically
Use the Pythagorean theorem to find the magnitude of the resultant (R)
And the tangent function to find the direction (θ ) y Ry R  x Rx

10. Example 3.5 Conceptual Questions
Q1: Two vectors have unequal magnitudes. Can their sum be Zero?
NO!
The sum of two vectors are only zero if they are in opposite direction and have the same magnitude!!!
Q9: Can the magnitude of a vector have a negative value?
The magnitude of a vector is always positive. A negative sign in a vector only means DIRECTION!!!!

11. Material for the Midterm
Material from the book to Study!!!
Objective Questions:
Conceptual Questions: 2-3-4
Problems: