Chapter 3: Kinematics in two Dimensions. Warm-up Differentiate between Vector quantities and scalar quantities. Give examples of each.

Vector Quantities and scalar quantities Vector quantity: are quantities that requires both magnitude and direction for a complete description Examples: velocity, acceleration, force, weight, Scalar quantities: are quantities that require magnitude only for a complete description. Examples include: distance, speed, time, mass

Adding Linear Displacement vectors Simple arithmetic is used to add vectors if they are in the same direction. Example: If a person walks 8 km east on one day, and 6 km the next day, the person will be 14 km east of his point of origin. D2 =6 km D1 =8 km DR= 14 km

Non Linear Vector addition However, is a vector equation. Because these vectors are non linear, the equation is an inequality written thus: DR < D1 + D2 Therefore; use Pythagorean theorem: Suppose a person walks 10 km east and then walks 5 km North. D2 =5 km D1 =10 km

Adding linear velocity vectors Consider an air plane moving from west to east at 60 km/h. If there is an west-east wind of 20 km/h, what will the total velocity of the airplane will be? Solution. We start by drawing vector diagrams 20 km/h speed of wind 60 km/h , speed of Airplane Combined speed will be 80 km/h

Example Find the resultant of the velocity of an airplane flying west at 120 km/h when it encounters a head wind of 20 km/h. 120 km/h airplane speed 20 km/h headwind Resultant is 100 km/h

Tail to tip Method of Adding vectors Two vectors a and b can be added as shown a+b is called resultant

Rules for graphical addition of vectors Draw the first vector to scale ( D1) Draw the second vector (D2), to scale, placing its tail at the tip of the first vector and being sure its direction is correct. Draw an arrow from the tail of the first vector, to the tip of the second vector. This is the resultant DR or the sum of the two vectors. Solve by scale drawing or by using Pythagorean Theorem.

Example Calculate the resultant of An Airplane’s velocity if it is flying E-W at 100 km/h, and encountering a 30 km/h south- north wind. 30 km/h South to North 100 km/h east to west

Parallelogram method of adding vectors. Draw the two vectors starting from a common origin. Construct a parallelogram using these two vectors as adjacent sides Draw a diagonal from the common origin. This is the resultant V1 V2 V1 +v2 =

Subtraction of vectors You can also subtract one vector from another. First you reverse the direction of the vector you want to subtract, then add them as usual:

Class/homework Textbook Page 65 Questions # 1-7, page 65: Problems #1-4