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# 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.

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### Chapter 3:Vectors EXAMPLES

• 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,

• Change the point in the x-y plane

• Note its Cartesian coordinates

• Note its polar coordinates

Please insert active fig. 3.3 here

• 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.

• 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

• 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

• 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 from the book to Study!!!

• Objective Questions: 3-8-10

• Conceptual Questions: 2-3-4

• Problems: 6-7-15-23-29-45-57