Chapter 3 2D Motion and Vectors. Introduction to Vectors Vector Operations Projectile Motion Relative Motion.

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Presentation transcript:

Chapter 3 2D Motion and Vectors

Introduction to Vectors Vector Operations Projectile Motion Relative Motion

Scalar vs. Vector ScalarVector DefinitionA quantity that has magnitude but no direction A quantity that has both magnitude and direction Examples Notation vv -Distance -Speed - -Displacement -Velocity -

Walk 7 squares east Walk 5 squares south Walk 3 squares west Walk 2 squares north

Start End

While driving through the city, you drive 3 blocks south, 5 blocks east, 5 blocks north, 7 blocks east, 4 blocks south, 2 blocks east, and 2 blocks north. What is your total displacement? What is the total distance traveled? 14 blocks 28 blocks

Which vectors have the same direction? Which vectors have the same magnitude? Which vectors are identical? A, HB, FD, EC, I A, B, D, HC, G, IE, F A, HC, I

Multiplying and Dividing by a Scalar

Adding Vectors

Subtracting Vectors – “Add negative”

Subtracting Vectors – “Fork”

Trig Review a=4 b=3 Pythagorean Theorem Angles c θ

x y Resultant Vectors A=7 cm B=5 cm Magnitude Direction θ R

While following a treasure map, a pirate walks 7.50 m east and then turns and walks 45.0 m south. What single straight-line displacement could the pirate have taken to reach the treasure? x y θ 45.0 m 7.50 m R

Components of Vectors A AyAy A x = ? A y = ? x y AxAx

A Practice:A = 5.0 cm, θ = 53.1° θ x y AyAy AxAx “Squished” → sin “Collapsed” → cos ↑ Not always the case!

B x y θ ByBy BxBx

x y θ 1500 km A plane flew 25.0° west of south for 1500 km. How far would it have traveled if it flew due west and then due south to get to its destination?

Adding Non-perpendicular Vectors Break down each vector into its x- and y- components Add all of the x-components Add all of the y-components Calculate the resultant vector

BxBx ByBy A B x y A B A+B R θ

BxBx ByBy AxAx AyAy A B x y –3 5 2 A B A+B R θ

x y AxAx AyAy A B θAθA R A B A+B θ θBθB BxBx ByBy

A pilot’s planned course is to fly at 150 km/hr at 30° SW. If the pilot meets a 25 km/hr wind due east, how fast does the plane travel, and in what direction? x y θ plane wind x y plane wind total x y θ