1. VECTORS A vector has both magnitude and direction.
A quantity that can be represented by a vector is called vector quantity.
Not all quantities involve direction
Scalars
Temperature, Pressure, Energy, Mass, Time
If a particle changes its position from A to B, an arrow pointing A to B is displacement vector.

2. A vector can be shifted without change in its value if its magnitude (length) and direction are not changed.
ADDING VECTORS GEOMETRICALLY

4. + =
Tail-to tip =
Parallelogram

5. “ + “ has different meaning in vector algebra.
involves both magnitude and direction.
Important properties
Cumulative law
Associative Law

6. How about subtraction?
-b has the same magnitude but opposite direction.

8. Components of a Vector
A component of a vector is the projection of the vector on an axis

9. In 3 dimensions

10. A room has dimensions 3. 00m x 3. 70m x 4. 30m
A room has dimensions 3.00m x 3.70m x 4.30m. A fly starting at one corner, flies around, ending up at diagonally opposite corner. (a) what is the magnitude of its displacement? (b) Could the length of its path be less then this magnitude?

11. Unit Vectors
A unit vector is a vector that has a magnitude exactly 1 and points a particular direction.
Vector components

12. Adding Vectors by Components

13. Determine the magnitude and direction of

14. MOTION IN TWO AND THREE DIMENSIONS
Position Vector
Displacement

15. Average Velocity
Instantaneous Velocity

17. Average Acceleration
Instantaneous Acceleration

19. PROJECTILE MOTION
It is a special case of two dimensional motion: A particle moves in a vertical plane with some initial velocity but its acceleration is always the free-fall acceleration g, which is downward.

20. In projectile motion, the horizontal motion and the vertical motion are independent from each other and neither affect the other.

21. Thus, we can break up the problem into two separate and easy one-dimensional problems

22. Analysis of Projectile Motion
The Horizontal Motion
The Vertical Motion

24. Driving of a cliff. A movie stunt driver on a motorcycle speeds horizontally of a 50.0m high cliff. How fast must the motorcycle leave the cliff-top if it is to land on level ground below, 90.0m from the base of the cliff?

25. A punt. Suppose the football in the figure was a punt and left the punters foot at a height of 1.00m above the ground. How far did the football travel before hitting the ground?