Vector Basics

1
Vector Basics
2
OBJECTIVES

• CONTENT OBJECTIVE TSWBAT read and discuss in
  groups the meanings and differences between
  Vectors and Scalars
• LANGUAGE OBJECTIVE TSW read and discuss the key
  vocabulary words Vectors and Scalars and
  Resultants.

3
Scalar

• Scalar quantities only have magnitude (size
  represented by a number unit) ex. Include mass,
  volume, time, speed, distance

4
Vectors

• Vector quantities have magnitude and direction.
  Ex. Include force, velocity, acceleration,
  displacement

5
Vector Representation

• Vectors are represented as arrows
• The length of the vector represents the
  magnitude

start
end
head or tip
tail
6
Vectors are always drawn to a scale comparing the
magnitude of your vector to the metric scale

• Ex.
• 1.0 cm 1.0 m/s
• Draw a 3.0 m/s East vector
• Vector will be 3.0 cm long

• Ex.
• 1.0 cm 1.5 m/s
• Draw a 3.0 m/s East vector
• Vector will be 2.0 cm long

7
Direction of Vectors

• Direction of vectors is represented by the way
  the arrow is pointed
• Vector components are based on coordinate plane
  so vectors can point in negative or positive
  directions

N
Positive X, Positive Y
Negative X, Positive Y
E
W
Negative X, Negative Y
Positive X, Negative Y
S
8
Resultant Vectors

• A resultant vector is produced when two or more
  vectors combine
• If vectors are at an angle, vectors are always
  drawn tip to tail

9
Adding and subtracting vectors Same Direction

• If the vectors are equal in direction, add the
  quantities to each other.
• Example

the resulting vector is
10
Adding and subtracting vectors Opposite
Directions

• If the vectors are exactly opposite in direction,
  subtract the quantities from each other.
• Example

the resulting vector is
11
Vectors at Right Angles to each other

• If vectors act at right angles to each other, the
  resultant vector will be the hypotenuse of a
  right triangle.
• Use Pythagorean theorem to find the resultant

12
Pythagorean Theorema2 b2 c2 where c is the
resultant
Hypotenuse resultant vector
c
a
b
13
Example

• A hiker leaves camp and hikes 11 km, north and
  then hikes 11 km east. Determine the resulting
  displacement of the hiker.

14
112 112 R2
121 121 R2
242 R2
R 15.56 km, northeast
15
Calculating a resultant vector

• If two vectors have known magnitudes and you also
  know the measurement of the angle (?) between
  them, we use the following equation to find the
  resultant vector.
• R2 A2 B2 2ABcos?

Use this for angles other than 90º
Make sure your calculator is set to DEGREES! (go
to MODE)
16
Example 1
R
4.0 N, SW

• ? 110
• R2 5.02 4.02 2(5.0)(4.0)(cos 110)
• R2 54.68
• R 7.39 N, Southwest

5.0 N, W
?
17
Example 2
? 35º

• R2 4.32 5.12 (2)(4.3)(5.1)(cos 35)
• R2 8.57
• R 2.93 m, northwest

18
Vector Equations

• Pythagorean Theorema2 b2 c2 where c is the
  resultant
• Law of Cosines
  R2 A2 B2 2ABcos?