Transcript Vectors in 2 Dimensions

Adding Vectors in two
Dimensions
•Displacement Vectors
•Velocity Vectors
•Force Vectors
Ex: A boy walks 3m North and then 4m
west. What is his displacement?
4m
Resultant = 5m
3m
Resultant vector: The sum of two vectors.
Solving for a Resultant:
• Calculating the magnitude:
Use c2 = a2 + b2
• Calculating the direction:
Use SIN COS TAN
OR Draw a scaled Diagram and measure
A boy walks 8m North and 7m East. Calculate
his resultant displacement. (use 1cm = 1m)
7m
Magnitude:
C2 = a2 + b2
C2 = 82 + 72
C = 10.6m
8m
41o
10.6m
Direction:
Tan Q = opp/adj = 7/8 = .875
Q= Tan -1[.875]
Q = 41o
A car drives north 100m then west 50m then
south 30m. What is the resultant?
50m
50m
30m
30m
70m
100m
86m
86m
•Vectors can be added in any order!
current
Velocity Vector Addition
A boy can swim 2m/s in still water. He heads
across a river with a downstream current of
3 m/s. What is his resultant velocity?
3m/s
3.6m/s
2m/s
34o with the shore
Do Now:
A boat with water speed 12m/s attempts to
travel directly across a river flowing 5m/s.
What is the resultant velocity?
5
current
Q
R2 = 52+ 122 = 169
R = 13m/s
12
Q
Q = tan-1[12/5] = 67o with respect to the shore.
If he crossed the stream in 200s how wide is
the stream, and how far down stream did
he drift?
5m/s
Q
Across:
D = v t = 12 x 200 = 2400m
12m/s
Q
Down stream drift: D = v t = 5 x 200 = 1000m
What direction should he aim to avoid
drifting?
5
Q
12
Q
Q = cos-1[5/12] = 65o with respect to the shore.
A plane with air speed 200m/s flies west from
Philadelphia to Denver If a cross wind
blows 50m/s South. What direction should
the pilot head?
200
200
50
14 nw
A stream is 30. meters wide and its current flows
southward at 1.5 meters per second. A toy boat is
launched with a velocity of 2.0 meters per second
eastward from the west bank of the stream.
a) What is the magnitude of the boat’s resultant
velocity as it crosses the stream?
2.5 m/s
b) How much time is required for the boat to reach
the opposite bank of the stream?
15 s
Force Vectors
**TRICKY: Force vectors are usually drawn
tail to tail.
3N
(use parallelogram method)
4N
Equilibrium: When all forces add to zero.
Equilibrant: the force that causes equilibrium.
Draw the vectors tip to tail:
10N
15N
15N
10N
A boy is pulled 3N East and 4N
south. What is the resultant,
Equilibrant?
4N
5N
4N
5N
3N
3N
• Eqilibrant = - resultant
Two 30N forces acting concurrently on an
object. Which diagram shows the greatest
resultant.