1. Chapter 3: Projectile motion
Warm-up
Differentiate between Vector quantities and scalar quantities. Give examples of each.

2. 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

3. Adding Linier 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

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

5. Velocity vectors: Velocity can be represented by a vector.
An arrow head is used to show direction of vector, and the length of the arrow represents magnitude of the velocity.
20 km/h
60 km/h

6. Adding linier 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

7. Resultant When two or more vectors are added, we get a resultant.
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

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

9. Steps to finding resultants
Draw the first vector to scale ( D1)
Draw the second vector (D2) 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.

10. Resultant continued
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.
Resultant: use a2 + b2 = c = ___
30 km/h
South to
North
100 km/h east to west

11. Class work
Textbook
Page 40, # 1-5,
page 41 #19-21