1. Vector Operations
Chapter 2.4 A

2. Coordinate Systems in 2 D
Two methods can be used to describe motion: one axis {x-axis} two axis {x-axis; y-axis}

3. Coordinate Systems in 2 D
1 dimension y v = 300 m/s Northeast

4. Coordinate Systems in 2 D
The problem with this method is that the axis must be turned again if the direction of the object changes.

5. Coordinate Systems in 2 D
It will also become difficult to describe the direction of another object if it is not traveling exactly Northeast.

6. Coordinate Systems in 2 D
The addition of another axis not only helps describe motion in two dimensions but also simplifies analysis of motion in one dimension.

7. Coordinate Systems in 2 D
y x v = 300 m/s Northeast

8. Coordinate Systems in 2 D
When analyzing motion of objects thrown into the air orienting the y-axis perpendicular to the ground and therefore parallel to the direction of the free fall acceleration simplifies things.

9. Coordinate Systems in 2 D
There are no firm rules for applying to the coordinate system. As long as you are consistent, your final answer should be correct. This is why picking a frame of reference is extremely important.

10. Resultant Magnitude & Direction
In order to determine the resultant magnitude and direction, we can use two different methods: 1) Pythagorean Theorem 2) Tangent Function

11. Resultant Magnitude & Direction
The Pythagorean theorem states that for any right angle, the square of the hypotenuse (side opposite to the right angle) equals the square of the other 2 sides.
c2 = a2 + b2

12. Resultant Magnitude & Direction
Use the tangent function to find the direction of the resultant.
Opposite hypotenuse
adjacent
tanѲ = opposite = ∆ y
adjacent ∆ x