VECTORS A vector has both magnitude and direction

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.

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

+ = Tail-to tip = Parallelogram

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

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

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

In 3 dimensions

A room has dimensions 3. 00 m x 3. 70 m x 4. 30 m. 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?

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

Adding Vectors by Components

Determine the magnitude and direction of

MOTION IN TWO AND THREE DIMENSIONS Position Vector Displacement

Average Velocity Instantaneous Velocity

Average Acceleration Instantaneous Acceleration

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.

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

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

Analysis of Projectile Motion The Horizontal Motion The Vertical Motion

Driving of a cliff. A movie stunt driver on a motorcycle speeds horizontally of a 50. 0 m high cliff. How fast must the motorcycle leave the cliff-top if it is to land on level ground below, 90. 0 m from the base of the cliff?

A punt. Suppose the football in the figure was a punt and left the punters foot at a height of 1. 00 m above the ground. How far did the football travel before hitting the ground?