Vectors vs. Scalars
Pop Quiz: Which of these do you think
are vector quantities?
Mass, Temperature, Distance,
Displacement, Speed, Velocity,
Acceleration, Force, Work, Energy,
Power, Momentum, Time
• A vector is an arrowed line.
• A vector has a tail and a head.
• The head points in the direction
of the vector.
• The length represents the size
(magnitude) of the vector.
Represent these displacements
as vectors on your book
Use scale 1:100 (i.e. 1cm on your book
is equivalent to 1m in real)
1. Jimmy travels 13 m west.
2. Bobby travels 3 m south.
3. Timmy travels 6 m, 45o north of east.
4. Libby travels 5 m, 80o north of west.
Bearing
o
030
A=
B = 300o
C = 110o
D = 260o
o
048
o
240
o
140
o
290
The bearing of A from B is 065o.
The bearing of B from A is 245o.
Vector Addition
Vector A = 7 m towards east
Vector B = 4 m towards north
Vector A + B = ???
Adding Vectors
(to find the resultant vector)
Q1. A car travels 3 km east, then 4 km
south. Find the car’s total displacement by
drawing a scaled vector diagram.
Q2. During a tug-of-war, the rope is pulled
with a force of 250 N towards left and a
force of 300 N towards right. Find the
resultant force acting on the rope.
Negative Vector
Vector A = 7 m towards east
Question: What would be the
negative vector A?
Answer: 7 m towards west
Vector Subtraction
Vector subtraction is the same as the
vector addition, only adding a negative
vector.
A–B = A+ B
Vector A = 7 m towards east
Vector B = 4 m towards north
Vector A – B = ???
Vector Subtraction
(to find the change, Δ = f – i)
Q1. A car initially travelling at 15 ms-1 east
turns a 90o corner and ends up travelling at
10 ms-1 north. Determine the change in
velocity by using a vector diagram.
Q2. A ball initially travelling towards a
batman at 5 ms-1 collides with him and
rebounds at 4 ms-1 in the opposite
direction. Find the ball’s change in velocity.
Do all questions from
Activity 8A (green textbook,
pg. 98) except for Q9.
Do now
Vector A = 4 cm east
Vector B = 4 cm north
Vector C = 6 cm west
Vector D = 5 cm bearing 45O
Draw vector diagrams to show:
1. A + B
5. A – B
2. C + D
6. A – D
3. A + B + C
7. A – C
4. A + C
8. D – B
Components of a Vector
Any vector can be broken down into
two components – Horizontal and
Vertical
Any vector can be drawn as the sum of
two other vectors drawn at right angles
to each other. The two vectors are
called components of the first vector.
Vector A = 4 cm north
Vector B = 3 cm east
Vector C = 5 cm bearing 37o
Draw a vector diagram to show that:
A+B=C
•
Vector A is the vertical component
of Vector C
•
Vector B is the horizontal
component of Vector C
1. Complete Activity 8A
2. Worksheets (pages 37 ~ 39)
3. Homework Booklet Sheet #1
Finish by Friday