GRAPHIC
VECTORS
MS. KNIGHT
PHYSICS I
EDITED BY S.G. 10/27/15
(DIAGRAM ERROR CORRECTED)
VECTORS AND SCALARS
Vectors are quantities that have both a direction and a
magnitude.
Scalars are Quantities that have only a magnitude.
REPRESENTING VECTORS
Vectors can be represented by words
• We traveled 45 kilometers North
• United flight 1954, fly heading 360° at 500 knots
Vectors can be represented by symbols
• Acceleration (a)
• Velocity (v)
• Displacement (d)
Vectors can be represented graphically
• Arrows are used to represent vectors graphically
• The direction of the arrow is the direction of the vector.
• The length of the arrow tells the magnitude
ADDING VECTORS
The sum of two vectors is called the resultant.
To add vectors graphically, draw each vector to scale.
Vector will be added using a tip to tail method
tail
tip
ADDING VECTORS
Vectors can be added in any order.
Remember to use tip to tail method
=
+
+
=
=
+
=
=
ADDING RIGHT ANGLE VECTORS
Remember before drawing resultant you
must check and make sure your vectors
are placed tip to tail
ADDING VECTOR PROBLEM 1
A truck driver delivering furniture travels 8 miles east, turns
around and travels 3 miles west, and then travels 12 miles east to
his destination. What is the vector sum?
+ 8 – 3 + 12 = 17 miles to the east
ADDING VECTOR PROBLEM 2
A parachutist jumps from a plane. He has not pulled is parachute
yet. His weight or force is 200 Newton south. The wind is
applying a small drag force of 50 Newton east. What is the vector
sum of the forces acting on him? So answer graphically only.
+
=
ADDING VECTOR PROBLEM 3
A guy is pulling a rope to the north at 400 Newtons. A girl is pulling
the same rope to the south at 350 Newtons. What is the vector
sum? Using arrows as vectors, draw a diagram of the forces.
+
400
=
– 350 =
50 N North
50
ADDING RIGHT ANGLE VECTORS
Vectors can be moved parallel to themselves and still be the same
vector.
Vectors only tell magnitude and direction, so a vector doesn’t care
where it starts.
• Note: For this vector addition, In order to use Tip to tail Method,
Vector B must be moved.
http://science360.gov/obj/tkn-video/0ca015f8-0d4c-4d0ba31e-257ba1445c32
ADDING PERPENDICULAR
MATHEMATICALLY
Perpendicular vectors can be easily added using the
Pythagorean theorem to find the magnitude of the
resultant.
2
A
+
2
B
=
2
C
PYTHAGOREAN
THEOREM
A2 + B 2 = C 2
(5 m)2 + (3 m)2 = C2
25 m2 + 9 m2 = C2
34 m2 = C2
𝟑𝟒 𝒎𝟐 =
5.8 m = C
𝑪𝟐
VELOCITY VECTORS
Now consider an 80-km/h airplane flying north caught in a strong
crosswind of 60 km/h blowing from west to east.
The plane’s speed relative to the ground can be found by adding
the two vectors.
The result of adding these two vectors, called the resultant, is the
diagonal of the rectangle described by the two vectors.
An airplane is flying at 80-km/h and
encounters a 60-km/h crosswind. What is
the airplane’s resultant speed?
DOES YOUR ANSWER MAKE SENSE?
think!
Suppose that an airplane normally flying at 80 km/h encounters
wind at a right angle to its forward motion—a crosswind. Will the
airplane fly faster or slower than 80 km/h?
Answer: A crosswind would increase the speed of the airplane and
blow it off course by a predictable amount.
Emily passes a soccer ball 6.0 m directly across the field to
Kara, who then kicks the ball 14.5 m down the field to Sue.
What is the balls displacement as it travels between Emily
and Sue?
A humming bird leaves her nest and flies 1.2 m parallel to
the ground. She spots a flower and drops directly downward
1.4 m. What is the humming bird’s displacement?
If a kite is being flown up in the sky and the string is 10m
long and the x component of this vector is 8 m, how high is
the kite?
EXIT TICKET
1.
Draw the Resultant Vector
2.
What is the magnitude of the resultant vector if A has a
magnitude of 4m and B has a magnitude of 6m?