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Chapter 3: Vectors EXAMPLES

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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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example 3 1
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
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
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
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
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
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 cont8
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 cont9
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
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!!!!
slide11

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