Scalar and
vector
quantities
1
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
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
3
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
Vector vs. scalar
Scalar quantities have size only and no direction.
Vector quantities have both size and direction.
Scalar or vector???
Scalar
7. Volume
Vector
2. Distance
1. Mass
6. Energy
9. Acceleration
3. Displacement
8. Force
4. Speed
5. Velocity
5
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
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
Could
you
solve
this
using a
scale
diagram
?
16N
N
R  4  3  5 miles
2
2
R=?

+ 3miles
North
E
4 miles East
 3
  tan    36.90
 4
1
= Bearing of 053.10
6N
What is the resultant
force R ?
8N
6N

R
R  82  62 10 N
tan  
8
 1.333
6
  53.1
0
Answer question
2 on the
worksheet using
scale diagrams
where necessary.
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
11
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
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
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