2. Scalar and vector quantities 1

3. Starter Put a cross in the centre of your graph paper (landscape)and draw the following movement: (1 pace = 1 cm) From the starting position I walk 5 paces North, followed by 8 paces East, then 11 paces South and finally 14 paces West. How far have I travelled in total? How far from the starting position am I? Write down a simple instruction to get me from the starting point to my finishing position 2

4. 3 Learning objectives: Know what scalar and vector quantities are. Know how to calculate the resultant of two vectors Be able to use scale drawings and/or pythagoras’ theorem to add vectors together

5. Success Criteria Sort quantities into scalar or vector categories (Grade C) Solve vector problems by using scale diagrams. (Grade C) Solve vector problems by using calculations. (Grade A) 4

6. Vector vs. scalar Scalar quantities have size only and no direction. Vector quantities have both size and direction. Scalar or vector??? ScalarVector 1. Mass 2. Distance 3. Displacement 4. Speed 5. Velocity 6. Energy 7. Volume 8. Force 9. Acceleration 5

7. Vector arithmetic We normally represent a vector as an arrow. The direction is shown by the way it is pointing and the length of the arrow denotes the magnitude We sometimes need to add up vectors to get a resultant. When adding up vectors we need to be particularly careful about the directions Do question 1 vector diagram worksheet (P5b2 old course) 6

8. Addition of vectors To work out the resultant of two coplanar vectors we can use a vector triangle. (we can also subtract vectors in this way) 20N 16N Could you solve this using a scale diagram ?

9. N E 4 miles East + 3miles North R = ?  = Bearing of 053.1 0

10. What is the resultant force R ? 6N 8N R  6N 8N

11. Answer question 2 on the worksheet using scale diagrams where necessary.

12. 11 Learning objectives: Know what scalar and vector quantities are. Know how to calculate the resultant of two vectors Be able to use scale drawings and/or pythagoras’ theorem to add vectors together

13. Success Criteria Sort quantities into scalar or vector categories (Grade C) Solve vector problems by using scale diagrams. (Grade C) Solve vector problems by using calculations. (Grade A) 12

14. Vector Calculations 1.A boat leaves a harbour and travels due north for a distance of 3km and then due west for a distance of 8km. What is the displacement of the boat with respect to the harbour? 2.A helicopter rise vertically from the ground for a distance of 600m and then moves horizontally for a distance of 1.6km. What is the displacement of the helicopter from its starting position? 3.A light aircraft travelling at 150m/s due north is suddenly hit by a wind from the east of 40m/s. Find the size and direction of the resultant velocity. Extension 4. After take off an aircraft climbs at a rate of 150m/s at an angle of 30° to the ground. What are the magnitudes of the horizontal and vertical components of its velocity 13

15. Answers 1.8.54km, 69°W of N 2.1.7km, 20.5° above the horizontal 3.155 m/s on a bearing of 345° 4.130m/s horizontal velocity, 75m/s vertical velocity 14