1. Calculate the Resultant Force in each case… Extension: Calculate the acceleration if the planes mass is 4500kg. C) B)
1.2 X 103
Thrust A)
1.2 X 103
Thrust
1.2 X 103
Thrust
5.0 X 104
Lift
0.8 X 103
Side-wind
0.2 X 103
Drag
1.2 X 103
Drag
4.5 X 104
Weight
0.2 X 103
Drag

2. Learning Objectives By the end of this lesson you should be able to...
Explain the difference between the terms scalar and vector
List the quantities which are described as either scalar or vectors.
Calculate the resultant force when multiple forces act in parallel and perpendicular to one another.

3. Quantities A scalar is a quantity that has size (number) only.
Learning Objectives
By the end of this lesson you should…
Explain the difference between the terms scalar and vector
List the quantities which are described as either scalar or vectors.
Calculate the resultant force when multiple forces act in parallel and perpendicular to one another.
Quantities
A scalar is a quantity that has size (number) only.
A vector has both size and direction.

4. Scalar Vector Power Acceleration Distance Mass Displacement Energy
Learning Objectives
By the end of this lesson you should…
Explain the difference between the terms scalar and vector
List the quantities which are described as either scalar or vectors.
Calculate the resultant force when multiple forces act in parallel and perpendicular to one another.
Scalar
Vector
Power
Acceleration
Distance
Mass
Displacement
Energy
Speed
Current
Force
Velocity
Momentum
Time

5. Scalar Vector Power Distance Mass Energy Speed Acceleration
Learning Objectives
By the end of this lesson you should…
Explain the difference between the terms scalar and vector
List the quantities which are described as either scalar or vectors.
Calculate the resultant force when multiple forces act in parallel and perpendicular to one another.
Scalar
Vector
Power
Distance
Mass
Energy
Speed
Acceleration
Displacement
Current
Force
Velocity
Momentum
Time?

6. Adding Parallel Vectors
Learning Objectives
By the end of this lesson you should…
Explain the difference between the terms scalar and vector
List the quantities which are described as either scalar or vectors.
Calculate the resultant force when multiple forces act in parallel and perpendicular to one another.
Adding Parallel Vectors 6N
12N 1N
The result of combining vectors is called the resultant (or net)
If the vectors are pointing in the same direction they add up.
If the vectors are pointing in opposite directions they subtract.

7. Vectors at right angles
Learning Objectives
By the end of this lesson you should…
Explain the difference between the terms scalar and vector
List the quantities which are described as either scalar or vectors.
Calculate the resultant force when multiple forces act in parallel and perpendicular to one another.
Vectors at right angles
Now consider this situation. Note that the vectors do not have to be force, they can be velocity or any other vector quantity
Air craft velocity
30 m/s
Due North.
Wind velocity
10 m/s
West

8. Vectors at right angles
Learning Objectives
By the end of this lesson you should…
Explain the difference between the terms scalar and vector
List the quantities which are described as either scalar or vectors.
Calculate the resultant force when multiple forces act in parallel and perpendicular to one another.
Vectors at right angles
What happens? The aircraft will be blown off course.
Actual direction of travel
Air craft velocity
30 m/s
Due North.
Wind velocity
10 m/s
West

9. Vectors at right angles
Learning Objectives
By the end of this lesson you should…
Explain the difference between the terms scalar and vector
List the quantities which are described as either scalar or vectors.
Calculate the resultant force when multiple forces act in parallel and perpendicular to one another.
Vectors at right angles
A scaled diagram will allow you to solve both the length of the actual journey and the direction but it is time consuming.
Actual direction of travel
Air craft velocity
30 m/s
Due North.
Wind velocity
10 m/s
West

10. Vectors at right angles
Learning Objectives
By the end of this lesson you should…
Explain the difference between the terms scalar and vector
List the quantities which are described as either scalar or vectors.
Calculate the resultant force when multiple forces act in parallel and perpendicular to one another.
Vectors at right angles
By re-arranging the arrows (components) we can use Pythagoras theory to find the answer.
Actual direction of travel
Air craft velocity
30 m/s
Due North.
Wind velocity
10 m/s
West

11. Vectors at right angles
Learning Objectives
By the end of this lesson you should…
Explain the difference between the terms scalar and vector
List the quantities which are described as either scalar or vectors.
Calculate the resultant force when multiple forces act in parallel and perpendicular to one another.
Vectors at right angles
By re-arranging the arrows we can use Pythagoras theory to find the answer.
Actual direction of travel
a2 = b2 + c2
A2 =
A = 31.6 m/s
Air craft velocity
30 m/s
Due North.
Wind velocity
10 m/s
West

12. Vectors at right angles
Learning Objectives
By the end of this lesson you should…
Explain the difference between the terms scalar and vector
List the quantities which are described as either scalar or vectors.
Calculate the resultant force when multiple forces act in parallel and perpendicular to one another.
Vectors at right angles
The value for the hypotenuse is the magnitude but as these are vectors we also need the direction. We can use trigonometry for this final step.
a2 = b2 + c2
A2 =
A2 = 31.6 m/s
Actual direction of travel
Air craft velocity
30 m/s
Due North.
Wind velocity
10 m/s
West

13. Vectors at right angles
Learning Objectives
By the end of this lesson you should…
Explain the difference between the terms scalar and vector
List the quantities which are described as either scalar or vectors.
Calculate the resultant force when multiple forces act in parallel and perpendicular to one another.
Vectors at right angles
This provides us with the magnitude but as these are vectors we also need the direction. We can use trigonometry for this final step.
SOH CAH TOA
Identify the 3 sides and label O, H, A.
Find the angle you are looking for.
3. Solve
Actual direction of travel
31.6 m/s
Air craft velocity
30 m/s
Due North. H O
Wind velocity
10 m/s
West A

14. Vectors at right angles
Learning Objectives
By the end of this lesson you should…
Explain the difference between the terms scalar and vector
List the quantities which are described as either scalar or vectors.
Calculate the resultant force when multiple forces act in parallel and perpendicular to one another.
Vectors at right angles
This provides us with the magnitude but as these are vectors we also need the direction. We can use trigonometry for this final step.
SOH CAH TOA
Cosθ = A / H
Cosθ = 10 / 31.6
Cosθ = 0.316
θ = Cos-1 (0.316)
θ = 71.5
Actual direction of travel
31.6 m/s
Air craft velocity
30 m/s
Due North. H O A
Wind velocity
10 m/s
West

15. Worked Example #2 40m 120m First step: Use Pythagoras’ theorem
Learning Objectives
By the end of this lesson you should…
Explain the difference between the terms scalar and vector
List the quantities which are described as either scalar or vectors.
Calculate the resultant force when multiple forces act in parallel and perpendicular to one another.
Worked Example #2
40m
120m
First step: Use Pythagoras’ theorem
a2 + b2 = c2
= c2
C2 = √
C =

16. SOH CAH TOA H O ∂ A 40m 120m Second step – Use trig
Learning Objectives
By the end of this lesson you should…
Explain the difference between the terms scalar and vector
List the quantities which are described as either scalar or vectors.
Calculate the resultant force when multiple forces act in parallel and perpendicular to one another.
SOH CAH TOA H O
40m ∂
120m A
Second step – Use trig
Identify 3 sides and label O, H, A
Find the angle you are looking for

17. SOH CAH TOA H O ∂ A 40m 120m Second step – Use trig Sin∂ = O / H
Learning Objectives
By the end of this lesson you should…
Explain the difference between the terms scalar and vector
List the quantities which are described as either scalar or vectors.
Calculate the resultant force when multiple forces act in parallel and perpendicular to one another.
SOH CAH TOA H O
40m ∂
120m A
Second step – Use trig
Sin∂ = O / H
Sin∂ = 40 /
Sin∂ = 0.3
∂ = Sin-1 (0.316)
∂ = 18.43°

18. Three for you to try… 10km 10km 210m 200m 100ms-1 5ms-1
Learning Objectives
By the end of this lesson you should…
Explain the difference between the terms scalar and vector
List the quantities which are described as either scalar or vectors.
Calculate the resultant force when multiple forces act in parallel and perpendicular to one another.
Three for you to try…
10km
10km
210m
200m
14.1 km and 100.1m/s
100ms-1
5ms-1

19. Further Q’s
A car travels 50 km N and then returns 30 km S. The whole journey takes 2 hours. Calculate:
The distance travelled.
The displacement.
The average speed
The average velocity.
An aircraft pilot wishes to fly north at 800 km/h. A wind is blowing at 80 km/h from the west. What speed and course must he select to fly the desired course?

20. Learning Objectives
By the end of this lesson you should…
Explain the difference between the terms scalar and vector
List the quantities which are described as either scalar or vectors.
Calculate the resultant force when multiple forces act in parallel and perpendicular to one another.
Finding Components
We can use the same process in reverse to work out the vertical and horizontal component forces when given the vector. This 24 N force is acting at an angle of 35 degrees to the horizontal. Some of it effectively acts vertically and some horizontally.

21. We can use sine and cosine to work out components of the force
Learning Objectives
By the end of this lesson you should…
Explain the difference between the terms scalar and vector
List the quantities which are described as either scalar or vectors.
Calculate the resultant force when multiple forces act in parallel and perpendicular to one another.
We can use sine and cosine to work out components of the force

22. Learning Objectives
By the end of this lesson you should…
Explain the difference between the terms scalar and vector
List the quantities which are described as either scalar or vectors.
Calculate the resultant force when multiple forces act in parallel and perpendicular to one another.
Example
A boat sails at 10 km/h on a bearing of 40 degrees from the horizontal. Calculate:
Its velocity due North
Its velocity due East
The distance travelled in 3h.
The displacement North and East from where it started.