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Published byDerek Simon Modified over 5 years ago

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Scalars and Vectors (a)define scalar and vector quantities and give examples. (b) draw and use a vector triangle to determine the resultant of two vectors such as displacement, velocity and force. (c) Use trigonometry to determine the resultant of two vectors.

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Scalars and Vectors Scalar Quantities – A quantity with magnitude but no direction Vector Quantity - A quantity with magnitude and direction ( can be represented on a diagram by an arrow ) mass, displacement, force, length, acceleration, speed, velocity, energy, momentum, time, temperature.

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Scalars and Vectors Liam walks 100m due North and then 20m due south. He has walked 120m but is not 120m from his starting point – how far is he from his starting point? 100m Due North 20m Due South Now add Tip to Tail = 80m Due North Vectors acting in the Same Direction

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Scalars and Vectors Liam walks 100m due North and then 40m due East. He has walked 120m but is not 120m from his starting point – how far is he from his starting point ( his displacement)? 100m Due North 40m Due East Now add Tip to Tail = Vectors acting in a different Direction

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Scalars and Vectors Use a scale drawing or Pythagoras to find the resultant displacement 100m Due North 40m Due East Vectors acting in a Different Direction

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Scalars and Vectors Use trigonometry to find the bearing. 100m Due North 40m Due East Tan Θ = 40/100 =0.4 Θ = 21.8 o Vectors acting in a Different Direction

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Scalars and Vectors Aircraft and a cross wind The next example of vector addition shows an aircraft flying on an initial bearing of 0 o at 350 ms -1 with a wind blowing west-east at 50 ms -1. Vectors acting in a Different Direction Aircraft flying south-north (bearing 0 o ) at 350 ms -1 Wind blowing west-east (bearing 270 o )at 50 ms -1

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Aircraft flying south-north (bearing 0 o ) at 350 ms -1 Wind blowing west-east at 50 ms -1 Scalars and Vectors 350 m/s 50 m/s

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Scalars and Vectors Scale Diagram Trigonometry 350 m/s 50 m/s 350 m/s Final path of aircraft is N 8.1 o E moving with a speed of 354 ms -1

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Scalars and Vectors Scale Diagram Trigonometry 350 m/s 50 m/s 350 m/s Final path of aircraft is N 8.1 o E moving with a speed of 354 ms -1

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Scalars and Vectors Resolve a velocity vector into two perpendicular components. Apply the equations of constant acceleration to describe and explain the motion of an object due to a uniform velocity in one direction and a constant acceleration in a perpendicular direction. By the end of the lesson you should be able to;

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Scalars and Vectors Resolving vectors

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Scalars and Vectors What is similar and what is different for these two projectiles ?

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Scalars and Vectors Resolving vectors

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Scalars and Vectors How does resolving vectors help us to analyse projectile problems? Vertical Motion

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Scalars and Vectors How does resolving vectors help us to analyse projectile problems? Horizontal Motion

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Scalars and Vectors How does resolving vectors help us to analyse projectile problems? Jan 03 Jan 07 June 08 v = u +at V 2 = u 2 +2as S= ut + ½at 2 g = 9.81ms -2

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