Punctuality

1. Punctuality

a. The last person to come into the class later than me will teach the class for 10 minutes

b. Homework to be returned during the first Theory lesson of the week.

2. Cleanliness

3. Courtesya. If you need to speak, raise your hands.

4. Consistencya. You must always have your notes with you.

Class Rules

Kinematics Part 5Vector Addition & Relative Motion

Learning Objectives

By the end of the lesso

n, you should be

able to:

i)Add tw

o vectors to determine a

resultant (a graphical m

ethod will

suffice)

Vector Addition

•Recall in the earlier lesson, we have learnt how to:

a) Define kinematics quantitiesb) State the definition of these kinematic quantities mathematically.c) Draw s(t) and v(t) graphs from given information.d) Interpret information from s(t) and v(t) graphs.e) Define free fall.f) Interpret situations of non-uniform acceleration.g) Calculate kinematics quantities using the Equations of Uniform

Acceleration.

•There is just one thing left to do to complete the story….

Vector Addition

•Consider the following situation in the video:• http://www.youtube.com/watch?v=yPHoUbCNPX8

(..\..\Videos\RealPlayerDownloads\Vector Addition.flv )•Vehicle is travelling at 100 kmh-1 forward.•Ball is shot backwards at 100 kmh-1.• If both happened together, what will be the velocity of the ball?

100 kmh-1C 100 kmh-1

Vector Addition

• The last part of the jigsaw is to learn how to add or subtract the same kinematics quantities together.

• Unlike scalars, vectors have direction. Not only must we add its magnitude, we must also add its direction.

SCALARS• Eg. mass• 1 kg + 1kg = 2kg• 2kg – 1kg = 1kg

VECTORS• Eg. velocity• 1 ms-1 Eastwards + 1 ms-1 Northwards ≠

2 ms-1

• 2 ms-1 Southwards – 1 ms-1 Westwards ≠ 1 ms-1

Vector Basics

VECTORS have:• MAGNITUDE and• DIRECTION

1 ms-1

2 ms-1

3 ms-1

LENGTH is PROPORTIONAL to

MAGNITUDE of vector.

2 ms-1

DIRECTION of arrow represents DIRECTION of vector.

Vector Basics

NEGATIVE VECTORS

2 ms-1

2 ms-1

Given that Forward is positive,A vector v of magnitude 2 ms-1

can be written as +2ms-1

A vector u of magnitude 2ms-1 , pointing in the negative direction

can be written as -2ms-1

Hence vector v = -uie. 2 ms-1 = - (-2 ms-1)

Vector Addition in One-Dimension

• Let’s use velocity as an example, of course there are many other vector quantities that we may use such as displacement or acceleration.

• EXAMPLE 1• 1 ms-1 Eastwards + 2 ms-1 Eastwards = 3 ms-1 Eastwards

1 ms-1 2 ms-1

Starting Point Ending Point

3 ms-1

Resultant VectorAlways drawn from the starting

point of the first component vector, to the ending point of

the last component vector.

Vector Addition in One-Dimension

EXAMPLE 2• 1 ms-1 Eastwards + 2 ms-1 Westwards = 1 ms-1 Westwards• If we take Eastwards as positive, then Westwards will be

negative.. Hence, the above statement may be simplified as:• 1 ms-1 + (- 2 ms-1) = -1 ms-1

1 ms-1

2 ms-1

Starting Point

Ending Point

1 ms-1

Resultant Vector

Vector Addition in One-Dimension

EXAMPLE 3• 1 ms-1 Westwards + 2 ms-1 Westwards = 3 ms-1 Westwards• - 1 ms-1 + (- 2 ms-1) = - 3 ms-1

1 ms-12 ms-1

Starting PointEnding Point

3 ms-1

Resultant VectorAlways drawn from the starting

point of the first component vector, to the ending point of

the last component vector.

Vector Addition in Two-Dimensions

• 3 ms-1 Eastwards + 4 ms-1 Northwards = ?

3 ms-1

4 m

s-1

? ms-1

5 ms-1 Northeast

5 ms-1

Resultant VectorIn the case of 2D vector addition, the Magnitude of the Resultant Vector can only be calculated using Pythagoras Theorem if the two components are at right angles.

Starting Point

Ending Point

Vector Addition in Two-Dimensions

• 3 ms-1 Eastwards + 4 ms-1 Northwards = ?

3 ms-1

4 m

s-1

5 ms-1

Sometimes, rearranging the component vectors will help in helping you determine the Resultant Vector.

Starting Point

Ending Point

5 ms-1 Northeast

Vector Addition in Two-Dimensions

• 5ms-1 Eastwards + 7ms-1 at 68° from horizontal = ?

5 ms-1

7 ms-1

? ms-1

Starting Point

Ending Point

10ms-1 at 40.5° from horizontal

112°

68°

10 ms-1

In this situation, we may not be able to use Pythagoras Theorem. If given the angle between the component vectors, we can apply Cosine Rule:

40.5°

abCosCbac 2222