Vector Addition

Vector Addition
CP Physics

Vectors

• Quantity that has magnitude and direction

• Direction is indicated by (North, South, East, West, Left, Right, Up, Down, + or -)

• Represented by arrows

  • length of arrow ---> magnitude of vector

  • direction of arrow ---> direction of vector

• The vectors being added are called "components" and in math these are called triangle legs

• The vector that you end up with is called the "resultant" and in math this is called the "hypotenuse"

​ID Motion Vector Addition

• In our first unit, we were able to add and subtract vectors easily due to being on the same axis, like either the X or Y axis.

• For example: Rubi walks 5m North, 6m South, 4m further South, and then 9m North.

  • By using + for north and - for south, we are able to find out that Rubi's displacement is (+5-6-4+9) = +4m, North.

• What would we do if Rubi decided that she wanted to walk 7m to the East?

  • This is vector addition for 2D motion and requires the pythagorean theorem

2D Motion Vector Addition

• Pythagorean Theorem ONLY works with right triangles.

• The Hypotenuse (resultant in physics) is always opposite the RIGHT (90⁰) angle.

• The Legs of the triangle are the VECTOR COMPONENTS (north, south, east, west, left, right, up, down, +, -)

​Rubi headed to casa de abuela

So, for Rubi to get to her Abuela's house from her house, she has to go 4m to the east and then 3m north. We want to find out what her displacement or resultant would be from her house to Abuela's. Since this is on two different axes (x axis first and then the y axis).
Let's see a picture!

​Gersen is headed to Josue's house to pick him up to go to the movies. Gersen's GPS shows that he is 10m, southwest of Josue's house. He also knows that 10m, southwest is a displacement, but he has to take streets to get there so he will have to drive 6m south and he has to go west, but is unsure of how far west. Use the diagram below to help Gersen know how far west he has to drive.

​Example #2

​Gersen & Josue

Open Ended

A ship sails 60km west then 80km north. What is the displacement?

$$a^2+b^2=c^2$$

Open Ended

A boat is rowed 5m/s North across the river that flows 12m/s East, what is the resultant speed?

$$a^2+b^2=c^2$$

Open Ended

A football is kicked with a horizontal velocity of 12 m/s and a vertical velocity of 35m/s, calculate the total velocity.

$$a^{2\ }+b^2=c^2$$

Poll

What is your comfort level with Right Angle Math and solving for resultants?

• Very Cold...I need alot of help

• Coldish, I think I can do it with some time in class.

• Warm, I can do this easily

• HOT, I can do this and teach others. Where is CAH, SOH & TOA?