1. Unit 1 Our Dynamic Universe Vectors - Revision
CfE Higher Physics
Unit 1
Our Dynamic Universe
Vectors - Revision

2. Learning Intentions
Can I calculate the equivalent vector by scale diagram or otherwise for vectors in a non-right angled triangle?

3. Vectors Vector quantities have both a magnitude and direction.
e.g. 12 mph North
25N at 45° to the horizontal
Velocity and displacement are vector quantities.
velocity =
displacement
time

4. Scalars Scalar quantities have a magnitude only.
e.g kg
45 s
Speed and distance are scalar quantities.
speed =
distance
time

5. Vector or Scalar ?
Which of the following quantities are vectors and which are scalars?
velocity
energy
power
weight
acceleration
force
time
temperature
displacement
work done
mass
distance
speed
frequency

6. Vector or Scalar ? Vectors Scalars displacement distance velocity
speed
acceleration
time
mass
force
temperature
weight
energy
work done
power
frequency

7. Adding Vector Quantities
Vector quantities should be added “nose to tail”.
30N
40N
resultant
40 N
30 N
Use either scale drawing or trigonometry to find the magnitude and direction of the resultant.
magnitude = √(a2+ b2)
direction, θ = tan-1(a/b) a b θ

8. e.g. horizontal and vertical or North-South and East-West
Vector Components
Any vectors can be replaced by two other vectors at the same point acting at right angles to one another.
e.g. horizontal and vertical or North-South and East-West
70 N
60°
70N
60°
70sin60°
70cos60°
Use either scale drawing or trigonometry to find the magnitude of the components.

9. Worked Example
A yacht sails 4 km North, 6 km East and finally 1 km South. Calculate the final displacement of the yacht.
magnitude = √(a2+ b2)
6 km
= √(62+ 32)
1 km
4 km
= 6.71 km
resultant q
direction, θ = tan-1(a/b)
= tan-1(6/3)
= 63.4°
displacement = 6.71 km at 063°