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Applications of Vectors

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Definition: Resultant: The result of two vectors acting on a point at the same time. Equilibrant: The opposite vector of the resultant. Find the resultant by ADDING vectors.

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Two Methods to solve Application Problems. A). Resolve the vectors into component form. Then add. Two forces act on a point. Vector A has direction angle = 30 o and magnitude = 50 Vector B has direction angle = 135 o and magnitude = 20 1. Write each vector in Component form – start with trig form 2.Add the components to find the Resultant Vector 3.Find the magnitude and Amplitude of the Resultant

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Two forces act on a point. Vector A has direction angle = 30 o and magnitude = 50 Vector B has direction angle = 135 o and magnitude = 20 Mag= amp = resultant

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Two Methods to solve Application Problems. A). Resolve the vectors into component form. Then add. Two forces act on a point. Given the angle between the angles Vector A has magnitude = 15 Vector B has magnitude = 23 The angle between the two angles is 70 o. Make one the x-axis Resultant has a magnitude of and amplitude of

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Two Method to solve Application Problems. B). Parallelogram Method - Law of Cosines. Two forces act on a point. Given the angle between the angles Vector A has magnitude = 15 Vector B has magnitude = 22 The angle between the two angles is 100 o. 1)Draw a Parallelogram. 2)Find the angle opposite the resultant – using the Law of Cosines 3)Use the Law of Sines to find the angles.

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Two forces act on a point. Given the angle between the angles Vector A has magnitude = 15 Vector B has magnitude = 22 The angle between the two angles is 100 o. 100 ⁰ 1)Draw a Parallelogram. 2)Find the angle opposite the resultant – using the Law of Cosines 3)Use the Law of Sines to find the angles. x

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Two Method to solve Application Problems. B). Parallelogram Method - Law of Cosines. Two forces at on a point. Vector A has direction angle = 75 o and magnitude = 45 Vector B has direction angle = 310 o and magnitude = 27

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Two forces act on a point. Vector A has direction angle = 75 o and magnitude = 45 Vector B has direction angle = 310 o and magnitude = 27 x y

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Assignment: Applications 1: Methods

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