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Punctuality

Class Rules. Punctuality The last person to come into the class later than me will teach the class for 10 minutes Homework to be returned during the first Theory lesson of the week. Cleanliness Courtesy If you need to speak, raise your hands. Consistency

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Punctuality

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  1. Class Rules • Punctuality • The last person to come into the class later than me will teach the class for 10 minutes • Homework to be returned during the first Theory lesson of the week. • Cleanliness • Courtesy • If you need to speak, raise your hands. • Consistency • You must always have your notes with you.

  2. Kinematics Part 5 Vector Addition & Relative Motion

  3. Learning Objectives • By the end of the lesson, you should be able to: • Add two vectors to determine a resultant (a graphical method will suffice)

  4. Vector Addition • Recall in the earlier lesson, we have learnt how to: • Define kinematics quantities • State the definition of these kinematic quantities mathematically. • Draw s(t) and v(t) graphs from given information. • Interpret information from s(t) and v(t) graphs. • Define free fall. • Interpret situations of non-uniform acceleration. • Calculate kinematics quantities using the Equations of Uniform Acceleration. • There is just one thing left to do to complete the story….

  5. 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-1 100 kmh-1 C

  6. 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

  7. Vector Basics • VECTORS have: • MAGNITUDE and • DIRECTION LENGTH is PROPORTIONAL to MAGNITUDE of vector. 1 ms-1 DIRECTION of arrow represents DIRECTION of vector. 2 ms-1 2 ms-1 3 ms-1

  8. Vector Basics NEGATIVE VECTORS Given that Forward is positive, A vector v of magnitude 2 ms-1can be written as +2ms-1 2 ms-1 A vector u of magnitude 2ms-1 , pointing in the negative direction can be written as -2ms-1 2 ms-1 Hence vector v = -u ie. 2ms-1 = - (-2 ms-1)

  9. 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 3 ms-1 2 ms-1 Resultant Vector Always drawn from the starting point of the first component vector, to the ending point of the last component vector. Starting Point Ending Point

  10. 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 Starting Point 1 ms-1 1 ms-1 2 ms-1 Ending Point Resultant Vector

  11. Vector Addition in One-Dimension • EXAMPLE 3 • 1 ms-1 Westwards + 2 ms-1 Westwards = 3 ms-1 Westwards • - 1ms-1 + (- 2 ms-1) = - 3 ms-1 2 ms-1 3 ms-1 1 ms-1 Resultant Vector Always drawn from the starting point of the first component vector, to the ending point of the last component vector. Ending Point Starting Point

  12. Vector Addition in Two-Dimensions 5 ms-1 Northeast • 3 ms-1 Eastwards + 4 ms-1 Northwards =? Resultant Vector In 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. Ending Point 4 ms-1 ? ms-1 5 ms-1 Starting Point 3 ms-1

  13. Vector Addition in Two-Dimensions 5 ms-1 Northeast • 3 ms-1 Eastwards + 4 ms-1 Northwards =? Sometimes, rearranging the component vectors will help in helping you determine the Resultant Vector. 3 ms-1 4 ms-1 5 ms-1 Ending Point Starting Point

  14. Vector Addition in Two-Dimensions 10ms-1 at 40.5° from horizontal • 5ms-1 Eastwards + 7ms-1 at 68° from horizontal =? 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: ? ms-1 10 ms-1 7 ms-1 112° Ending Point 68° 40.5° 5 ms-1 Starting Point

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