1. Starter (5 minutes): 1) A + B = 2) A + C = 3) B – D = 4) C – B =
5) A – D = 6) D – A =
7) D – B = 8) B – C =
Vector A
5 →
Vector B
11 ←
Vector C
3 →
Vector D
5 ←

2. A cricket ball is thrown and it travels straight towards the batsman at a speed of 28 ms-1.
The batsman hits the ball and it travels straight back towards the bowler at a speed of 22 ms-1.
If the ball was in contact with the bat for 0.01 seconds, calculate the ball’s acceleration.

3. Vectors in 2D

4. Vector Diagrams
When dealing with problems with vector quantities in 2D, you MUST use Vector Diagrams.

5. How to draw vectors A vector is an arrowed line
The head points in the direction of the vector
The length represents the size (magnitude) of the vector

6. Draw these displacement vectors:
Jimmy travels 13 m west.
Bobby travels 3 m south.
Timmy travels 6 m, 45o north of east.
Libby travels 5 m, 30o north of west.

7. Adding Vectors in 2D
A man walks 6 m east then 8 m north. What is the man’s total displacement?
Vector A = 6 m to east
Vector B = 8 m to north
Vector A + B = ?

9. Vector Addition Draw: 1) A + C 4) C + D 2) B + D 5) A + C + B
3) A + B ) B + A + C
Vector A
5 m →
Vector B
2 m ←
Vector C
4 m ↑
Vector D
7 m ↓

11. A car travels 3 km west, then 4 km south
A car travels 3 km west, then 4 km south. Calculate the car’s total displacement.
A man walks 300 m south, then 200 m west, then 400 m south. Calculate the man’s total displacement.

12. Example – net force 3N 9N
Box

13. Example – net force 5N
10N
Box 2N

14. Example – net force 3N 7N
Box 2N

15. Example – net force (extension*)
(angle: 45o)
Box 3N 4N

16. There is an airplane flying in the sky and there are four forces acting upon the plane.
Weight force: 6000 N
Thrust force: 5000 N
Friction force: 2000 N
Lift force: 9000 N
Draw a force diagram to show all forces
Draw a vector diagram to show the net force
Extension*: Describe the plane’s motion

18. Worksheet: Vector Diagrams (addition only)

19. Starter (5 mins): SHOW ALL WORKING
Bradley is pushing a box with a force of 7 N →. There is also a friction force (3 N) which opposes Bradley’s push. What is the net force applied on the box?
A bouncy ball travelling straight at 9 ms-1 → hits a wall and bounces back in the exact opposite direction at 6 ms-1. What is the change in velocity of the ball?
A truck travelling at 14 ms-1 ← slows down to 4 ms-1. Assume the direction is not changed. What is the change in velocity of the truck?
A box is being lifted by a crane with a force of 15 N. There is also a very strong wind which pushes the box from the side with a force of 10 N →. Draw a vector diagram to show the net force applied on the box.

20. Subtracting Vectors in 2D
There is an airplane travelling East at a speed of 70.0 ms-1. Moments later, it changes its direction and travels South, but at the same speed of 70.0 ms-1.
Find the change in velocity (Δv)

21. A – B = A + -B Subtracting Vectors in 2D
Just like in 1D, vector subtraction is adding a negative vector. (i.e. reverse the second vector around then add it)
A – B = A + -B
7 – 2 = 5 is same as = 5

22. Draw and label Δv = vf – vi
There is an airplane travelling East at a speed of 70.0 ms-1. Moments later, it changes its direction and travels South, but at the same speed of 70.0 ms-1.
Draw and label vi
Draw and label vf
Draw and label Δv = vf – vi

24. Try these: Draw vector diagrams to show the change in velocity:
A car travels west at 17 ms-1, then south at 11 ms-1.
A man walks north at 2.0 ms-1, then east at 1.4 ms-1.
A dog runs east at 7 ms-1, then in the opposite direction at 6 ms-1.

25. Worksheet: Vector Diagrams (ALL)