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.

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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.

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.

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

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

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

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

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

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

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

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

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;

Scalars and Vectors Resolving vectors

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

Scalars and Vectors Resolving vectors

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

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

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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