phys 20 lessons unit 2: 2-d kinematics projectiles lesson 1: 2-d vectors adding vectors...
TRANSCRIPT
![Page 1: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/1.jpg)
PHYS 20 LESSONS
Unit 2: 2-D Kinematics
Projectiles
Lesson 1: 2-D Vectors
Adding vectors (Tail-to-tip)
![Page 2: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/2.jpg)
Reading Segment #1:
2-D Vectors
To prepare for this section, please read:
Unit 2: p.2
![Page 3: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/3.jpg)
A. 2-D VECTORS
Recall, when we dealt with 1-D vectors, there were only
two possible directions.
We made one direction positive and the other direction negative.
Now, we will deal with 2-D vectors, where there are many
more than two directions. Expressing its direction is more
complicated.
![Page 4: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/4.jpg)
A1. Direction of 2-D Vectors
- there are two methods to express the direction of 2-D vectors
that we use in Physics 20:
1. NEWS (North, East, West, South)
- acute angles measured with respect to the
nearest axis
2. RCS (rectangular coordinate system)
- angles measured in standard position (from
the positive x-axis)
![Page 5: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/5.jpg)
1. Angles in NEWS N V
= 50W E
S
Method:
The angle is always positive and less than 90 (acute)
The angle is described relative to a nearby axis
i.e.
= 50 N of E
(North of the East Axis)
![Page 6: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/6.jpg)
e.g. V N
60 W E
S
How would express this angle in NEWS?
![Page 7: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/7.jpg)
e.g. V N
60 W E
S
= 60 of
In the NEWS method:
- you always show the acute angle on the diagram
- then, you will place two letters after the angle
(these are shown as spaces)
![Page 8: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/8.jpg)
e.g. V N
60 W E
S
= 60 of W
The second letter is the axis that the angle "touches".
In this case, the angle is touching the West axis.
![Page 9: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/9.jpg)
e.g. V N
60 W E
S
= 60 N of W
The first letter is the direction the angle moves from
the reference axis.
In this case, the angle is moving towards the North.
![Page 10: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/10.jpg)
e.g. V N
60 W E
S
= 60 N of W
We interpret this as:
"60 degrees North from the West axis"
![Page 11: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/11.jpg)
Ex. 1 Express the following angles in NEWS.
a) N b) N
W E W E
40V1 70
S S V2
![Page 12: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/12.jpg)
a) N
W E
V1 70
S
1 = 70 of
![Page 13: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/13.jpg)
a) N
W E
V1 70
S
1 = 70 of S
The second letter is the axis the angle touches.
In this case, it touches the South axis.
![Page 14: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/14.jpg)
a) N
W E
V1 70
S
1 = 70 W of S
The first letter is the direction the angle moves from the
reference axis. In this case, it moves towards the West.
![Page 15: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/15.jpg)
a) N
W E
V1 70
S
1 = 70 W of S
We interpret this as "70 degrees West from the South axis"
![Page 16: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/16.jpg)
b) N
W E
40 V2
S
2 = 40 of
![Page 17: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/17.jpg)
b) N
W E
40 V2
S
2 = 40 of E
The second letter is the axis the angle touches.
In this case, it touches the East axis.
![Page 18: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/18.jpg)
b) N
W E
40 V2
S
2 = 40 S of E
The first letter is the direction the angle moves from the
reference axis. In this case, it moves towards the South.
![Page 19: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/19.jpg)
b) N
W E
40 V2
S
2 = 40 S of E
We interpret this as "40 degrees South from the East axis"
![Page 20: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/20.jpg)
2. Angles in RCS y
-x x
V -y
Method:
The angle is measured in standard position
- starts from the positive x-axis
Counterclockwise angles are positive
Clockwise angles are negative
![Page 21: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/21.jpg)
e.g. V y
60 -x x
-y
How would express this angle in RCS?
![Page 22: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/22.jpg)
e.g. V y
60 start
-x x
-y
RCS angles always start at the positive x-axis.
![Page 23: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/23.jpg)
e.g. V y
60 -x x
-y
If the angle is counterclockwise, then it is positive.
So, = 180 - 60 = 120
![Page 24: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/24.jpg)
e.g. V y
60 -x x
-y
But if the angle is clockwise, then it is negative.
So, = -90 + -90 + -60 = -240
![Page 25: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/25.jpg)
Ex. 2 Express the following angles in RCS.
a) y b) y
-x x -x x
40V1 70
-y -y V2
![Page 26: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/26.jpg)
a) y
Start
-x x
V1 70
-y
RCS angles start from the positive x-axis.
![Page 27: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/27.jpg)
a) y
-x x
V1 70 1
-y
If the angle is clockwise, then it is negative.
So, 1 = -90 + -70
= -160
![Page 28: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/28.jpg)
a) y
1
-x x
V1 70
-y
If the angle is counterclockwise, then it is positive.
So, 1 = 90 + 90 + 20
= 200
![Page 29: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/29.jpg)
b) y
start
-x x
40 V2
-y
RCS angles always start at the positive x-axis.
![Page 30: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/30.jpg)
b) y
-x x
40 V2
-y
Clockwise angles are negative.
So, 2 = -40
![Page 31: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/31.jpg)
b) y
2
-x x
40 V2
-y
Counterclockwise angles are positive.
So, 2 = -90 + -90 + -90 + -50
= -320
![Page 32: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/32.jpg)
Practice Problems
Try these problems in the Physics 20 Workbook:
Unit 1 p. 4 #1
![Page 33: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/33.jpg)
Reading Segment #2:
Adding 2-D Vectors (Tail-to-Tip)
To prepare for this section, please read:
Unit 2: p.3
![Page 34: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/34.jpg)
B. ADDING 2-D VECTORS
A key skill in Physics 20 and 30 is to add 2-D vectors.
There are two methods that we use:
1. Tail-to-Tip
- this is especially good when the vectors
are perpendicular (at 90)
2. Components
- a more tedious, labour-intensive method,
but it works for all cases (including 3-D)
![Page 35: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/35.jpg)
B1. Adding 2-D Vectors (Tail -to-Tip)
Method:
Place the tail of the second vector on the tip of the first
i.e. "place one right after the other"
The resultant (or sum) vector R is drawn from the origin
to the tip of the second vector
i.e. Resultant is the "start to finish" vector
Solve the resulting triangle
If the vectors are at right angles, then you can use
Soh Cah Toa and the Pythagorean formula
![Page 36: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/36.jpg)
Note:
Notice that the resultant vector is a "start-to-finish" vector.
This is the same description for the overall displacement
vector ( d ).
Thus, displacement is a good example of adding 2-D vectors.
![Page 37: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/37.jpg)
Ex. 3 From a hunting lodge, a hiker walks the following path:
1.8 km South
then, 1.10 km East
Find the overall displacement of the hiker.
Include both magnitude and direction in your answer.
![Page 38: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/38.jpg)
Strategy:
Overall displacement is a start-to-finish vector,
just like the resultant vector.
So, we will add the vectors tail-to-tip to get out answer.
![Page 39: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/39.jpg)
1.8 km
1.1 km
Place the tail of the second vector onto the tip of the
first vector.
That is, place one vector right after the other.
![Page 40: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/40.jpg)
1.8 km R
1.1 km
The resultant (displacement) is the "start-to-finish" vector.
Place the angle at the base (origin) of the resultant vector.
![Page 41: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/41.jpg)
1.8 km R
901.1 km
Since it is a right triangle, we can use Soh Cah Toa and
the Pythagorean formula to find R and .
![Page 42: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/42.jpg)
Pythag:
c2 = a2 + b2 1.8 km R c
a
1.1 km
b
Remember, c is always the hypotenuse (the longest side).
![Page 43: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/43.jpg)
c2 = a2 + b2 1.8 km R c
a
R2 = (1.8 km)2 + (1.1 km)2
1.1 km
R2 = 4.45 km2 b
R = 4.45 km2
= 2.1 km
![Page 44: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/44.jpg)
Soh Cah Toa:
1.8 km R hyp
adj
1.1 km
opp
Remember:
- the hypotenuse is the longest side
- the opposite side is the side furthest from (i.e. the one not touching the angle )
- the adjacent side is the side right beside the angle
![Page 45: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/45.jpg)
Toa:
tan = opp 1.8 km R hyp
adj adj
1.1 km
opp
Since we know the opposite and the adjacent sides,
we will use tangent.
![Page 46: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/46.jpg)
Toa:
tan = opp 1.8 km R hyp
adj adj
tan = 1.1 1.1 km
1.8 opp
= tan -1 (0.6111)
= 31
![Page 47: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/47.jpg)
N
W E
31 R = 2.1 km
S
The answer in NEWS:
d = R = 2.1 km at 31 E of S
(or 2.1 km at 59 S of E)
![Page 48: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/48.jpg)
y
-x x
31 R = 2.1 km
The answer in RCS: -y
d = R = 2.1 km at 301
(or 2.1 km at -59)
![Page 49: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/49.jpg)
Animation:
2-D Addition (Tail-to-Tip)
1. http://www.phy.ntnu.edu.tw/java/vector/vector.html
2. http://www.walter-fendt.de/ph11e/resultant.htm
The second animation deals with forces,
but it shows vector addition very well.
![Page 50: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/50.jpg)
Ex. 4 A boat takes the following course:
3.60 km West
then, 5.20 km North
Find the overall displacement of the boat.
Include both magnitude and direction in your answer.
![Page 51: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/51.jpg)
5.20 km
3.60 km
Place the tail of the second vector onto the tip of the
first vector.
That is, place one vector right after the other.
![Page 52: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/52.jpg)
5.20 km R
3.60 km
The resultant displacement vector is the "start-to-finish" vector.
Be certain to show the angle at the base (start) of the
resultant vector.
![Page 53: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/53.jpg)
Pythag:
c2 = a2 + b2 5.20 km R
R2 = (3.60 km)2 + (5.20 km)2 3.60 km
R = 40 km2
= 6.32 km
![Page 54: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/54.jpg)
Soh Cah Toa:
tan = opp 5.20 km R
adj
tan = 5.20 3.60 km
3.60
= tan -1 (1.4444)
= 55.3
![Page 55: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/55.jpg)
N
6.32 km
55.3 W E
S
The answer in NEWS:
d = R = 6.32 km at 55.3 N of W
(or 6.32 km at 34.7 W of N)
![Page 56: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/56.jpg)
y
6.32 km
55.3
-x x
-y
The answer in RCS:
d = R = 6.32 km at 125
(or 6.32 km at -235)
![Page 57: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/57.jpg)
Ex. 5 A person walks the following path:
3.0 km at 20 S of E
then, 5.0 km at 10 W of S
Sketch the resultant displacement vector.
No calculations required.
![Page 58: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/58.jpg)
20
3.0 km
Sketch the first vector:
3.0 km at 20 South from the East axis
![Page 59: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/59.jpg)
20
3.0 km
Next, place new axes at the tip of the vector.
![Page 60: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/60.jpg)
20
3.0 km
10
5.0 km
Add the second vector onto the tip of the first vector.
5.0 km at 10 West of the South axis
![Page 61: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/61.jpg)
20
3.0 km
R
10
5.0 km
The resultant is the "start to finish" vector.
![Page 62: PHYS 20 LESSONS Unit 2: 2-D Kinematics Projectiles Lesson 1: 2-D Vectors Adding vectors (Tail-to-tip)](https://reader035.vdocuments.us/reader035/viewer/2022062217/56649ea05503460f94ba38dd/html5/thumbnails/62.jpg)
Practice Problems
Try these problems in the Physics 20 Workbook:
Unit 2 p. 4 #2 - 7