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Lesson_1.3_Printable

# Lesson_1.3_Printable - Vectors and Vector Addition A vector...

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Vectors and Vector Addition A vector is a physical quantity that has both magnitude and direction . The displacement of an object from position A to position B is a vector A B x θ 2.0 m A vector is represented by drawing an arrow, its length represents the magnitude and the arrow represents the direction. If the distance measured from A to B is 2.0 m, the magnitude of the vector is 2 m The direction of a vector is given by specifying the angle the vector makes with the positive x-axis The displacement vector has a magnitude 2 m and its direction is specified by the angle θ . The displacement vector makes an θ with the positive x-axis 1

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Vector Components The displacement from A to B can be achieved by first moving from A to C and then from C to B A B Vector AC is along the x-axis. x θ 2.0 m Vector AB is obtained by adding vector AC to vector CB C AB AC CB = + Vector CB is along the y-axis. It is called the y-component of vector AB It is called the x-component of vector AB 2
A B x θ In the right triangle ABC, side AC is the adjacent side and BC is the opposite side for angle θ . AB is the hypotenuse. C AB AC CB = + cos AC θ = cos AC AB θ = If v is a vector that makes an angle θ with the x-axis, v x = v cos θ AB sin CB AB θ = sin CB AB θ = Its y-component is given by: v y = v sin θ Its x-component is given by: 3

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Unit Vectors It is represented by i A unit vector in the y-direction is a vector of magnitude 1 along the y-direction.
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