Vectors and Scalars Addition

scalars and vectors

Objectives

• differentiate scalar quantity from vector quantity

• list examples of vectors

• perform addition of vectors

Poll

It is a physical quantity that has magnitude.

• scalar

• velocity

• distance

• vector

Poll

It is a physical quantity that has a magnitude and direction.

• scalar

• velocity

• distance

• vector

Poll

Siri walks in a forest 10m east and and goes back 4 m west. What is the total distance traveled by Siri?

• 4 m

• 6 m

• 10 m

• 14 m

Poll

Which of the following is NOT an example of vector quantity?

• 30 m/s, North

• 4 N, west

• 4 meters at 35⁰

• 35 minutes

Poll

What is the resultant vector of displacement 100 m, east and 25 m, west?

• 75 m, west

• 75 m, east

• 125 m, west

• 125 m, east

Open Ended

What is scalar quantity?

Open Ended

what is vector quantity?

Poll

Determine what physical quantity is this.

• scalar

• vector

Poll

Determine what physical quantity is this.

• scalar

• vector

Poll

Determine what physical quantity is this.scalar

• scalar

• vector

Poll

Determine what physical quantity is this.

• scalar

• vector

Poll

Determine what physical quantity is this.

• scalar

• vector

Open Ended

Will you give some examples of scalar and vector quantities aside from what we have earlier.

How to add vector quantities?

• graphical method

• mathematical method

graphical method

• head-to-tail method

• parallelogram method

head-to-tail method

• The head-to-tail method of adding vectors involves drawing the first vector on a graph and then placing the tail of each subsequent vector at the head of the previous vector.

• The resultant vector is then drawn from the tail of the first vector to the head of the final vector.

parallelogram method

• link vectors tai-to-tail

• draw the resulting parallelogram

• the resultant vector A + B, bisects the parallelogram as shown.

algebraic or mathematical method

• use Pythagorean theorem in solving resultant vector

•  $R\ =\ \sqrt{a^2\ +\ b^2}$  
  
  
  

• in determining the direction of the vector use equation  $\theta\ =\ \tan^{-1}\ \frac{b}{a}$  

Open Ended

Solve for the resultant vector of the following.
a = 60 m at $$30\degree$$  
b = 30 m at  $$55\degree$$  
Find

$$\Sigma x$$   $$\Sigma y$$   $$R\$$   $$\theta$$