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7.5 Vectors and Applications Day 1

7.5 Vectors and Applications Day 1. Do Now Find the absolute value of the complex number. HW Review: p.644 #63-97. Magnitude and Displacement. Some quantities are measured only by their magnitude Time, length, mass, etc Other quantities are measured by a magnitude and a direction

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7.5 Vectors and Applications Day 1

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  1. 7.5 Vectors and ApplicationsDay 1 Do Now Find the absolute value of the complex number

  2. HW Review: p.644 #63-97

  3. Magnitude and Displacement • Some quantities are measured only by their magnitude • Time, length, mass, etc • Other quantities are measured by a magnitude and a direction • Displacement, velocity, force

  4. Vectors • When both magnitude and direction are measured, together they describe a vector • A vector in the plane is a directed line segment. • Two vectors are equivalent if they have the same magnitude and direction

  5. Properties of Vectors • Each vector has an initial point and a terminal point • The direction of the vector goes towards the terminal point • We can compare slopes of vectors to determine if the direction is the same • The length, or magnitude, of a vector is expressed with absolute value lines • Use the distance formula to find the magnitude

  6. Ex • Ex1 on p.647 of book

  7. You try • Given the points D(-1,-1) J(3,1) O(0,0) F(2,1) sketch each vector and determine if they are equivalent

  8. Closure • Given the points C(-2,5) G(-4,4) O(0,0) F(2,1) Sketch the pair of vectors and determine whether they are equivalent • HW: p.652 #1-11 odds

  9. 7.5 Vector AdditionDay 2 • Do Now • Solve the triangle ABC given A = 90 deg, b = 25, c = 15

  10. HW Review: p.652 #1-11

  11. Vector Addition • The sum of two vectors is the vector needed to travel both vectors in order • The sum is also called the resultant of the vectors

  12. Ex • Forces of 15 newtons and 25 newtons act on an object at right angle to each other. Find their sum, giving the magnitude of the resultant and the angle that it makes with the larger force

  13. Ex • An airplane travels on a bearing of 100 deg at an airspeed of 190 km/h while a wind is blowing 48km/h from 220 deg. Find the ground speed of the airplane and the direction of its track

  14. Components • Given a vector W, the vectors U and V are called components of W if U + V = W • Finding the components is called resolving, or representing a vector • To find components, we usually want to look for perpendicular components, then use trig equations to find the vectors

  15. Ex • A vector W has a magnitude of 130 and is inclined 40 degrees with the horizontal. Resolve the vector into horizontal and vertical components

  16. Ex • A wooden shipping crate that weights 816lb is placed on a loading ramp that makes an angle of 25 deg with the horizontal. To keep the crate from sliding, a chain is hooked to the crate and to a pole at the top of the ramp. Find the magnitude of the components of the crate’s weight (disregarding friction) perpendicular and parallel to the incline

  17. Closure • Two forces of 50N and 60N act on an object at right angles. Find the magnitude of the resultant and the angle that it makes with the larger force • HW: p.652 #13-37 odds

  18. 7.5 Vectors and ApplicationsDay 3 • Do Now • Two forces of 255N and 325N act on an object. The angle between the forces is 64 deg. Find the magnitude of the resultant and the angle that it makes with the smaller force

  19. HW Review: p.652 #13-37 odds

  20. Closure • What is a vector? What do they measure? • HW: none

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