AIM – How do we add vectors?
DO NOW – Where have you heard the word
vector aside from Physics class?
HW - Textbook p. 26 #67(a-d), 68(a-d), 72(a-d)
V ECTOR A DDITION
V ECTORS
Quantities with magnitude (amount, size) and direction.
Example: 20 m North or 20 m West
Vectors
Scalars (no direction)
Displacement
Velocity
Acceleration
Distance
Speed
Time
Mass
D RAWING V ECTORS
Vectors can be drawn to graphically represent magnitude as well as direction.
Length indicates magnitude, and therefore must be
drawn to scale using a ruler and protractor.
length
The angle indicates direction, represented by θ (theta).
θ
Horizontal Axis = +X direction
NEVER FORGET TO
DRAW THE ARROWS!!
R ESULTANT – A DDING
V ECTORS
Resultant – the result of 2 or more displacements (vectors)
20 m West
R = resultant displacement
θ = direction
R
θ
20 m
North
R = 28 m, 45°
determined by measuring with a
ruler and protractor
M ATHEMATICAL T ECHNIQUES
When vectors are at right angles, we can use the Pythagorean
Theorem and SOHCAHTOA: a2 + b2 = c2
20 m West
R2 = (20m)2 + (20m)2
√
R
θ
20 m
North
R = 800 m2
R = 28.2 m
tan θ = opp/adj = 20/20 = 1
θ = tan-1 (1) = 45°
V ECTOR A DDITION ( CONT.)
Same Direction: simply add
= 11 m
4m
7m
Opposite Direction: subtract
5m
9m
=4m
Practice
A plane flies 1500 miles East and 200 miles South. What is the magnitude and
direction of the plane’s final displacement?
A hiker walks 80 m North, 20 m East, 50 m South, and 30 m West. What is the
magnitude and direction of the hiker’s displacement?
P RACTICE P ROBLEM #1
A plane flies 1500 miles East and 200 miles South. What is the magnitude and direction
of the plane’s final displacement?
**not drawn to scale**
1500 miles
θ
200
miles
a2 + b2 = c2
(1500 m)2 + (200 m)2 = R2
R = √ (1500 m)2 + (200 m)2
R = 1513.275 m
tan θ = opp/adj
θ = tan-1 (200/1500)
θ = 7.5946433°
P RACTICE P ROBLEM #2
A hiker walks 80 m North, 20 m East, 50 m South, and 30 m West. What is the
magnitude and direction of the hiker’s displacement?
By subtracting the opposing directions from each
other, we find the hiker’s displacement along the y-axis
to be 30 m North, and the displacement on the x-axis
to be 10 m West.
a2 + b2 = c2
302 + 102 = R2
R = √900 + 100
R = 31.623 m
tan θ = opp/adj
θ = tan-1 (10/30)
θ = 18.435°
AIM – What are the components of the
resultant?
DO NOW – A car drives 4 miles North, 3 miles
East, and 2 miles South, what is its total
displacement?
HW - Textbook p. 53 #50, 51, 53
V ECTOR A DDITION
V ELOCITY V ECTORS
Occur at the same time – concurrent
Displacement vectors occurred sequentially – one
after the other
Boat
velocity
Boat
Stream
velocity
River
How do we find the
resultant velocity?
Resultant velocity found by drawing the vectors head to
tail – just as with displacement
8 m/s
Boat
Boat
6 m/s
8 m/s
θ
6 m/s
VR
Velocity Resultant
VR2 = 82 + 62 = 100
VR = 10 m/s
tan θ = 6/8
θ = tan-1 (6/8) = 37°
V ECTOR C OMPONENTS
If R = A + B, then we can
say that A and B are
components of R
Two or more
components add to
make a resultant
A resultant can also be
resolved back into
components!!
B
R
A
Rectangular Components – components
which lie on the x and y axes
J APANESE V ECTOR V IDEO
Japanese Vector Video - Launching a Ball from a moving truck