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Unit 3.3
Vectors Problems/
Graphing
Example #1:
A plane flies 30 m/s directly south and a 60 m/s wind is blowing
east. Find the magnitude and direction of the planes resultant
velocity.
Example #2:
What is the velocity of a speed boat (from the observer on the
bank) if the boat can move 20 mph in still water and it is
crossing a river with a 5 mph downstream current ?
Example #3:
An Airplane flies directly NW with an air speed of 575 mph. If
the wind is blowing NE at 50 mph, what is the velocity of the
plane as measured from the ground?
Example #4: The Mad River is 100 m wide and flows at 2.0 m/s. A person in a canoe can row boat at 5 m/s in still water. a. What is the resultant velocity of the boat in relation to the
banks if the person is rowing downstream?
b. What is the resultant velocity of the boat in relation to the banks if the person is rowing upstream?
c. What is the resultant velocity (magnitude and direction) of the boat if the person heads directly across the river?
d. How far downstream from the launching point will the boat land on then other bank?
Components of Vectors
Vector Components
Vector Components
The perpendicular components of a vector are
independent of each other.
Often we will need to change a single vector into an equivalent
set of two component vectors at right angles to each other:
Any vector can be “resolved” into two component vectors
at right angles to each other.
Two vectors at right angles that add up to a given vector are
known as the components of the given vector.
The process of determining the components of a vector is
called resolution.
A ball’s velocity can be resolved into horizontal and vertical
components.
Components of Vectors
Vectors X and Y are the horizontal and vertical components of a
vector V.
Components of Vectors
Example #5
What are the COMPONENT vectors of an airplane flying at a
velocity of 65 km/hr at 30° north of east?
Components of Vectors
Example #6
What are the COMPONENT vectors of an airplane flying at a
velocity of 45 km/hr at 20° west of north?
Components of Vectors
Adding Vectors By Graphing
Scale Drawing and Direct Measurement
Another way to find the magnitude and direction of a resultant
vector is by using a scaled drawing and direct measurement.
1. When we deal scale diagrams, we may deal with
perpendicular vectors or vectors that may not parallel or
perpendicular. The only way to add them is by drawing a
scaled diagram.
2. Add the vectors using the parallelogram method.
3. Measure VR (resultant) and θ with a ruler and protractor.
Adding Vectors with a scaled drawing
Graphing Example #1:
Graphically find the resultant velocity (magnitude and direction)
of a plane flying 90 m/s south with a cross wind of 150 m/s East.
Graphing Example #1:
1.) We first need to state a scale. (Always state your scale!!!)
For this example we are going to use:
Scale: 1 cm = 30 m/s
2.) We next draw a “N-S-E-W compass”
N
S
W E
N
S
W E
N
S
W E
N
S
W E
90 m/s
(3 cm)
N
S
W E
90 m/s
(3 cm)
N
S
W E
90 m/s
(3 cm)
N
S
W E
90 m/s
(3 cm)
150 m/s
(5 cm)
N
S
W E
90 m/s
(3 cm)
150 m/s
(5 cm)
N
S
W E
90 m/s
(3 cm)
150 m/s
(5 cm)
N
S
W E
90 m/s
(3 cm)
150 m/s
(5 cm)
N
S
W E
150 m/s
90 m/s
(3 cm)
N
S
W E
VR = 5.8 cm
90 m/s
(3 cm)
150 m/s
(50 cm)
N
S
W E
VR = 5.8 cm x 30 m/s
VR = 174 m/s
90 m/s
(3 cm)
150 m/s
(5 cm)
N
S
W E
VR = 174 m/s
90 m/s
(3 cm)
150 m/s
(5 cm)
N
S
W E
VR = 174 m/s @ 31° S of E
90 m/s
(3 cm)
150 m/s
(5 cm)
N
S
W E
Now solve for the resultant (magnitude and
direction) mathematically to see if your
graphical method is correct.
150 m/s
(5 cm)
90 m/s
(3 cm)
