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Chapter 3: Vectors EXAMPLES

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

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  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 =VectorDisplacement 500 m, 30º N of E. • Find components of V (Vxand 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 0 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 + 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

  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  0 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? NO! • 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: 3-8-10 • Conceptual Questions: 2-3-4 • Problems: 6-7-15-23-29-45-57

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