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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.

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Chapter 3 vectors examples l.jpg

Chapter 3:Vectors EXAMPLES


Example 3 1 l.jpg
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,


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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


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Example 3.2

  • V =VectorDisplacement 500 m, 30º N of E.

  • Find components of V (Vxand Vy )


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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


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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.


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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


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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


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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


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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!!!!


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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


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