Scalars and Vectors
(a) define scalar and vector quantities and give
examples.
(b) draw and use a vector triangle to
determine the resultant of two vectors such
as displacement, velocity and force.
(c) Use trigonometry to determine the
resultant of two vectors.
Scalars and Vectors
Scalar Quantities – A quantity with magnitude but
no direction
Vector Quantity - A quantity with magnitude and
direction ( can be represented on a diagram by an
arrow )
mass , displacement, force, length, acceleration,
speed, velocity, energy, momentum, time,
temperature.
Scalars and Vectors
Vectors acting in the Same Direction
Liam walks 100m due North and then 20m due south. He has
walked 120m but is not 120m from his starting point – how far
is he from his starting point?
20m
Due
South
100m
Due
North
Now add
Tip to Tail
=
80m
Due
North
Scalars and Vectors
Vectors acting in a different Direction
Liam walks 100m due North and then 40m due East. He has
walked 120m but is not 120m from his starting point – how far
is he from his starting point ( his displacement)?
100m
Due
North
40m
Due
East
Now add
Tip to Tail
=
Scalars and Vectors
Vectors acting in a Different Direction
Use a scale drawing or Pythagoras to find the resultant displacement
40m Due East
100m Due North
Scalars and Vectors
Vectors acting in a Different Direction
Use trigonometry to find the bearing.
40m Due East
100m Due North
Tan Θ = 40/100 =0.4
Θ = 21.8 o
Scalars and Vectors
Vectors acting in a Different Direction
Aircraft and a cross wind
The next example of vector addition shows an aircraft flying on an
initial bearing of 0o at 350 ms-1 with a wind blowing west-east at 50
ms-1.
Wind blowing west-east
(bearing 270o)at 50 ms-1
Aircraft flying south-north (bearing 0o) at 350 ms-1
Scalars and Vectors
50 m/s
Wind blowing west-east
at 50 ms-1
350 m/s
Aircraft flying south-north
(bearing 0o) at 350 ms-1
Scalars and Vectors
50 m/s
350 m/s
Scale Diagram
50 m/s
350 m/s
Trigonometry
Final path of aircraft is N 8.1o E moving with a speed of 354 ms-1
Scalars and Vectors
50 m/s
350 m/s
Scale Diagram
50 m/s
350 m/s
Trigonometry
Final path of aircraft is N 8.1o E moving with a speed of 354 ms-1
Scalars and Vectors
By the end of the lesson you should be able to;
• Resolve a velocity vector into two
perpendicular components.
• Apply the equations of constant acceleration
to describe and explain the motion of an
object due to a uniform velocity in one
direction and a constant acceleration in a
perpendicular direction.
Scalars and Vectors
Resolving vectors
Scalars and Vectors
What is similar and what is different for these two
projectiles ?
Scalars and Vectors
Resolving vectors
Scalars and Vectors
How does resolving vectors help us to analyse
projectile problems?
Vertical Motion
Scalars and Vectors
How does resolving vectors help us to analyse
projectile problems?
Horizontal Motion
Scalars and Vectors
How does resolving vectors help us to analyse
projectile problems?
Jan 07
v = u +at
Jan 03
V2 = u2 +2as
June 08
S= ut + ½at2
g = 9.81ms-2