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Vector Sum and Resolving a Vector
Adding Vectors
• The process of adding or combining two or more
vectors to give a single vector is called composition of vectors or simply vector addition.
• The single vector represents the sum is called the Resultant.
Graphical Method of Adding Vector
Tail-head Method Example 1: Justine walks 300 m East, stops to rest and then
continues 400 m East. Solution: (Use scale) 1cm:100 m
A= 300 m, East B=400 m, East
R = 700 m, east
Graphical Method of Adding Vector
Tail-head Method Example 2: Bryan walks home from school 300 m East and
remembers that he has to bring home his Science book which a classmate borrowed. He walks back 500 m West to his classmate’s house. What is his total displacement?
Solution: (Use scale) 1cm:100 m
A= 300 m, East
B=500 m, West
R = 200 m, West
Graphical Method of Adding Vector
Tail-head Method Example 3: Hanz walks 500 m East and then turns North and
walks 300 m.
N
R = 580 m, 31o N of E
B=300 m, North
W E
Ɵ = 31o
A= 500 m, East
S
Graphical Method of Adding Vector
Parallelogram Method Example 3: Hanz walks 500 m East and then turns North and
walks 300 m. Solution: N
R = 580 m,
B=300 m, North
W Ɵ = 31o E
A= 500 m, East
S
Graphical Method of Adding Vector
Polygon Method for more than two vectors Example 4: Gino walks 600 m East, then turns 400 m North and
finally walks 300 m West. Find the resultant vector. Solution: C=300m, West (Use scale 1cm:100 m) N
R = 500 m, 54o N of E
B=400 m, North
W Ɵ = 54 E
A= 600 m, East
S
Vectors that form right triangle
Can be solve by Pythagorean Theorem
N
Example
F1 =6 N, East
F2 =5N, North
Find FR W E
(FR )2 = (F1)2 + F2)
2
Direction: S
tan Ɵ = opp/adj
5 newtons
6 newtons
Component Method
Example:
an ant crawls on table top. It moves 2
cm east, turns 3 cm 40o North of East
and finally moves 2.5 cm North. What
is the ants total displacement?
Given:
d1 = 2 cm E
d2 = 2 cm 40o N of E
d3 = 2.5 cm North
2 cm
3 cm
2 .5cm
40o Vector dx dy
2 cm E 2 cm 0
3 cm 40o N of E 2.31 cm 1.92 cm
2.5 cm 0 2.50 cm
Σx = Σy =
Vector Addition by Components
R
Ry =Ay +By
x Rx = Ax+Bx
B
By
Bx
A
Ax
y
Ay
Component Method
Example:
an ant crawls on table top. It moves 2
cm east, turns 3 cm 40o North of East
and finally moves 2.5 cm North. What
is the ants total displacement?
Solution:
Use Pythagorean Theorem
4.31 cm
4.42 cm
Ɵ
Problem Set 1. If the force the boy exerts on the wagon is 60 N and Ɵ=24o, find Fx and
Fy.
2. A woman on the ground sees an airplane climbing at an angle of 35o
above the horizontal. She gets into her car and by driving at 120 km/hr
is able to stay directly below the airplane. What is the airplane’s speed?
3. A car weighing 12.0kN (2700lb) is parked on a driveway that is at 15o
angle with the horizontal. Find the components of the car’s weight
parallel and perpendicular to the driveway.
4. The Sailboat Ardent Spirit is headed due north at a forward speed of 6.0
knots (kn). The pressure of the wind on its sails causes the boat to
move sideways to the east at 0.5 kn. A tidal current is flowing to the
southwest at 3.0 kn. What is the velocity of the Ardent Spirit relative to
the earth’s surface? (A knot is a unit of speed equal to 1 nautical mile
per hour. The nautical mile is widely used in air and water navigation
because it is the same in length as one minute [1’] of latitude, where 60’
= 1o . Since 1 nautical mile = 1.852 km=6076ft= 1 kn=1.852 km/h=1.151
mi/h)
Problem Set
A man exerts a force of 60 N along a
handle of a lawn mower push it
across the lawn. If the handle is held
at an angle of 30o with he lawn, what
are the horizontal and vertical
components of the force exerted by
the man?
