UB PHY 101 - Components of a Vector (3 pages)

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Components of a Vector

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Components of a Vector


Dr Zhang's Lecture of sections 3.2 and 3.3

Lecture number:
Lecture Note
University at Buffalo, The State University of New York
Phy 101 - College Physics

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PHY 101 1nd Edition Lecture 7 Outline of Last Lecture I Free Falling Objects II Problem Solving Strategies III 3 1 Vectors and Properties IV Adding Vectors Outline of Current Lecture V 3 2 Components of a Vector VI Vector Addiction Algebraically VII 3 3 Displacement Velocity Acceleration in 2 Dimensions a Average Velocity b Instantaneous Velocity c Average Acceleration d Instantaneous Acceleration Current Lecture 3 2 Components of a Vector A vector can be decomposed into components o Each component by itself is a vector A two dimensional vector has 2 components o A Ax Ay o 1D Vector 1 components o 3D Vector 3 components The magnitude of the components o Ax Acos o Ay Asin o A is the magnitude of the vector A Using the Pythagorean theorem we have o A Ax2 Ay2 1 2 o The angle can also be calculated o tan Ay Ax o tan 1 Ay Ax o The calculated angle is correct only if the vector lies in the 1st or 4th quadrant These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute Example o Superman flies from the top of a building along a path The magnitude of the displacement of superman is 100m o A 30 0 because it is clockwise from the axis Find the x and y components Ax Acos 30 0 Ax 100 0 866 Ax 86 6m Ay Asin 30 0 Ay 100 0 5 Ay 50m Vector Addition Algebraically o Graphically tip to tail method o Vector Addition can be done numerically o Suppose R A B o Then R Rx Ry where Rx Ax Bx and Ry Ay By o The x and y components are added separately o Graphically and algebraic methods should give the same answer Example o A hiker travevls 25 km 45 south of east on the first day then travels 40km 60 north of east on the second day o A Determine the components of the hikers displacement on the first and second day day 1 A day 2 B Draw the coordinate vectors Ax Acos 45 Make sure the angle is negative Ax 25 0 707 17 7 km Ay Asin 45 Ay 25 0 707 17 7km Bx Bcos 60 Bx 40 0 5 20 km By Bsin 60 By 40 0 866 34 6

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