Vectors. What is the difference between a vector and a scalar number?. Vectors. Scalar. Both have a magnitude but only vectors have a direction. What kinds of things can be represent by vector. Displacement  Magnitude how far you went Direction  which way. Velocity 
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What is the difference between a vector and a scalar number?
What kinds of things can be represent by vector
Displacement
Magnitude how far you went
Direction  which way
Velocity 
Magnitude speed
Direction  which way
Acceleration 
Magnitude change in velocity / time
Direction  which way
Forces
Magnitude how hard you are pushing or pulling
Direction  which way
The direction can be indicated many different ways
If I moved 3 meters and wanted to say which way I could say in terms of common directions
Up
Right
Left
Down
Or I can simply use an arrow to show direction. This is called graphically representing a vector (with a picture)
When using a picture, what does the length of the arrow show?
Any way will work but generally one works the best for a given situation.
3 meters to the right
3 meters East
3 meters at 0o
Dx = +3 meters
3 meters
Just as scalars can be added given situation.
3 apples + 5 apples = 8 apples
VECTORS can be ADDED too (but watch direction)
3 + 5 doesn’t always equal 8
WHEN 2 scalar numbers are added, given situation.
the answer is called the SUM.
WHEN 2 Vectors are added,
the answer is called the RESULTANT
First we will look at adding vectors which are parallel given situation.
Are these “vectors” parallel?
8 m given situation.
If you walk 3 meters to the right and 5 meters to the right. What would your displacement be?
3 m
5 m
8 meters to the right
What is the answer called?
2 m given situation.
If you walk 3 meters to the right and 5 meters to the left. What would your displacement be?
3 m
5 m
2 meters to the left
3 + 5 = 2 ????
2 m given situation.
If you had used positive and negative x to add these how would you have done it?
 x
left
+ x
right
3 m
+ 3 m
 5 m
5 m
 2 m
When vectors are parallel, you simply add or subtract the numbers!!!
Vector addition also applies to Velocity given situation.
(or any other vector for that matter)
Have you ever walked on a moving walkway at an air port? given situation.
standing still on it
walking with it
walking against it
3 velocities
walkway (relative to..) you relative to walkway you relative to the ground
A wind starts blowing at 10 km/hr given situation.
North, what is the resulting
speed of the plane
SCALE
= 10 km/hr
70 km/hr
(resultant)
or
70 km/hr NORTH compared to the ground
the plane travels at
60 km/hr relative to the air
air travels 10 km/hr
relative to the ground
What if the plane did a Uturn and pointed south? given situation.
SCALE
= 10 km/hr
50 km/hr
(resultant)
or
50 km/hr SOUTH
60 km/hr
(plane)
10 km/hr
(wind)
What would the signs be on the two vectors being added ? given situation.
SCALE
= 10 km/hr
+
 60 km/hr + 10 km/hr = 50 km/hr


60 km/hr
(plane)
10 km/hr
(wind)
+
SCALE given situation.
= 10 km/hr
50 km/hr
(resultant)
or
50 km/hr SOUTH
 60 km/hr + 10 km/hr = 50 km/hr

60 km/hr
(plane)
10 km/hr
(wind)
+
When vectors point in the given situation.same direction.
They simply add up!!
6 m
10 m
When vectors point in opposite directions,
they CANCEL (at least partially)
because they have opposite signs
10 m
6 m
A boat can move at 9 m/s in still water. If the water flows at 3 m/s. What will the boat’s velocity be if goes downstream? Upstream?
If you walked at 3 m/s. What will the boat’s velocity be if goes downstream? Upstream?10 m to the East and then 6 m to the East you would be 16 m East from where you started(your displacement)
6 m
10 m
10 m
6 m
What if you walked 10 m to the East and then 6 m to the North. Are you 16 m away from where you started?
ADDING NONParallel VECTORS at 3 m/s. What will the boat’s velocity be if goes downstream? Upstream?
to find the resultant
If you walk 10 m East and 6 m North, at 3 m/s. What will the boat’s velocity be if goes downstream? Upstream?
where would you be?
6 m
10 m
When 2 perpendicular vectors are added, use the parallelogram (rectangle) method.
1.) Complete the parallelogram
2.) Draw the resultant from start to finish
What is the resultant at 3 m/s. What will the boat’s velocity be if goes downstream? Upstream?
Scale 1 dm = 2.24 m
10 m
6 m
6 m
10 m
To specify the resultant we will need to say 2 things about it
10 m
6 m
6 m
10 m
Magnitude
(from the length of the line and a scale)
DIRECTION
Measuring an angle with a protractor
Find the resultant using the parallelogram method: it
8 m West & 19 m South
Scale: 1 dm = 5 m
Draw the vectors
If the vectors are perpendicular, it
they form a right triangle.
Then we ALSO can use PYTHAGOREAN’s THEORUM to find the RESULTANT
A right triangle has a 90 degree angle. it
The side opposite it is always the longest side called the hypotenuse
Hypotenuse
Side
Side
ON the back of your vector WS it
Use the Pythagorean Theorem to find the resultant
for #2. BOX your work below
Find the resultant graphically and using the Pythagorean Theorem :
15 m due south + 25 m due west
1 dm = 5 m
SKIP
Draw the vectors
A plane plane is flying 75 km/hr due North. Theorem :
A crosswind picks up which blowing 25 km/hr due east. What is the velocity of the plane with the wind (compared to the ground)?
What happens to the speed of the plane?
Check the answer using the Pythagorean Theorem
Nonperpendicular vectors Theorem :
are added the same way
You can’t simply move an arrow on a piece of paper. It must be carefully redrawn with the same angle and length
90
90
0
0
0
0
You can’t simply move an arrow on a piece of paper. It must be carefully redrawn with the same angle and length
Find the resultant: must be carefully redrawn with the same angle and length
1 dm = 6.3 m
Find the resultant must be carefully redrawn with the same angle and length
1 dm = 10 km/hr
Add the following vectors must be carefully redrawn with the same angle and length
& find the resultant
35 m heading 58o N of E
54 m heading 12o S of W
Scale 1 dm = 10 m
VECTOR WS 2 must be carefully redrawn with the same angle and length
& book problems must be carefully redrawn with the same angle and length
page 4041
3, 4, 19, 20, 23, 24
2 Vectors can be added to make must be carefully redrawn with the same angle and length
to form their equivalent resultant
Resultant =
A must be carefully redrawn with the same angle and lengthY
AX
A single vector can be thought of as the sum of its two component vectors.
A
A component vectors.
AY
AX
A single vector can be thought of as the sum of its two component vectors.
=
+
A = AX + AY
Breaking a vector into its horizontal and vertical components is called: Vector RESOLUTION
It just involves forming a rectangle, with the given vector as the diagonal
A
One way of doing this is to draw a horizontal line touching one end and a vertical line touching the other. Where they meet it is a corner
A
Your Campsite has the displacement vector below. one end and a vertical line touching the other. Where they meet it is a corner
Find the EastWest & NorthSouth component vectors.
Scale 1 dm = 10 km
camp
A plane is flying 55 one end and a vertical line touching the other. Where they meet it is a cornero North of West at 150 km/hr.
Find the component vectors?
How fast is it moving North?
How fast is it moving West?
1 dm = 50 km / hr
Draw the vectors