Components of a vector Objectives Resolve a vector into two perpendicular components. Understand the independent nature of perpendicular components of.

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Presentation transcript:

Components of a vector Objectives Resolve a vector into two perpendicular components. Understand the independent nature of perpendicular components of a vector.

Imagine walking 4m/s 30˚ N of E Imagine walking 4m/s 30˚ N of E Look at the birds eye view. Look at the birds eye view. How fast are you moving North? How fast are you moving North? What is the component of the vector in a Northerly direction? What is the component of the vector in a Northerly direction?

Scale drawing Make a scale drawing on graph paper as shown Make a scale drawing on graph paper as shown Measure the Northerly component. Measure the Northerly component.

Component of velocity towards the east = 3.45 ms –1 Component of velocity towards the east = 3.45 ms –1 At the same time, you can see from the diagram that AB represents the component of the velocity towards the north. Its magnitude is 2 ms –1. At the same time, you can see from the diagram that AB represents the component of the velocity towards the north. Its magnitude is 2 ms –1.

Calculation So you have: So you have: Re-arranging gives: Re-arranging gives: OA = 4.0 ms –1 × cos 30° OA = 4.0 ms –1 × cos 30° and calculation gives: and calculation gives: OA = 3.46 ms –1 OA = 3.46 ms –1 OA = 3.5 m s –1 (2sf) OA = 3.5 m s –1 (2sf)

General Rule Starting from the vector; find the angle θ between it and the direction of interest. Starting from the vector; find the angle θ between it and the direction of interest. Then the component of L in this direction is L cos θ. Then the component of L in this direction is L cos θ.