Vectors

1
Vectors

• How do vectors combine into a resultant

2
Vector Diagrams

• Vector diagrams are diagrams which depict the
  direction and relative magnitude of a vector
  quantity by a vector arrow

3
Vectors Motion

• the size of the velocity vector is increasing, so
  the diagram is depicting a motion with increasing
  velocity

4
Scalars and Vectors

• Scalars are quantities which are fully described
  by a magnitude alone.
• Vectors are quantities which are fully described
  by both a magnitude and a direction

5
Distance and Displacement

• Distance is a scalar quantity which refers to
  "how much ground an object has covered" during
  its motion.
• Displacement is a vector quantity which refers to
  "how far out of place an object is" it is the
  object's change in position

6
Graphical (Scale method) and Analytical
(Pythagorean)

• C 2 a 2 b 2
• C 2 (11 km) 2 (11 km) 2
• C 2 242 km 2
• C 15.6 km

7
Example Vector Problem

• A motorboat heads due east at 16 m/s across a
  river that flows due north at 9.0 m/s.
• What is the resultant velocity of the boat?
• If the river is 136 m wide, how long does it take
  the motorboat to reach the other side?

8
Solution Graphical Method

• What is the resultant velocity of the boat?

9
Solution Calculation of time

• If the river is 136 m wide, how long does it
  take the motorboat to reach the other side?
• V d/t
• 18 m/s 136 m
• t
• t 7.56 s

10
Trigonometric Method

• Using the relationship of angles and
  Trigonometric functions to determine the
  magnitude of the vectors

11
Example Problem Trigonometry

• Determine the components of a 20 m displacement
  300 northwest.
• a west component and
• b north component.

12
Solution Trigonometry

• By choosing the proper component,
• a opposite
• b adjacent
• c resultant
• Solve for each component

13
Summary

• Vector addition problems may be solved by 2
  methods
• Graphical
• Analytical (Pythagorean)
• Graphical method depends on a scale and use of
  angular
• measurements
• Analytical method will
• use the formulas
• c2 a2 b2
• Trigonometry