Chapter 3: Vectors EXAMPLES

1 / 11

# Chapter 3: Vectors EXAMPLES - PowerPoint PPT Presentation

Chapter 3: Vectors EXAMPLES. 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,. Example 3.1, cont.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Chapter 3: Vectors EXAMPLES' - anthony

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Chapter 3:Vectors EXAMPLES

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,

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

Example 3.2
• V =VectorDisplacement 500 m, 30º N of E.
• Find components of V (Vxand Vy )
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
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.
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

0

x

Ay

A

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 + 20.0 km

Rx=37.7 km

Ry= Ay + By= –17.7 km + 34.6 km

Ry=16.9 km

• In unit-vector form, we can write the total displacement as

y

By

Ry

Bx

0

x

Ax

Rx

Ay

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

0

x

Rx

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?

NO!

• The magnitude of a vector is always positive. A negative sign in a vector only means DIRECTION!!!!

Material for the Midterm

• Material from the book to Study!!!
• Objective Questions: 3-8-10
• Conceptual Questions: 2-3-4
• Problems: 6-7-15-23-29-45-57