1. General Physics I Vectors & 2D Motion

2. Vectors In 1 dimension, we could specify direction with a + or - sign.
In 2 (or 3) dimensions, we need more than a sign to specify the direction of something.

3. Vectors... The components of any vector are its (x,y) coordinates
We will consider this in 2-D for our r vector: y x  r
Consider our right-triangle trigonometry: -
So…..
rx = the x-component =
ry = the y-component =

4. Vectors...
The magnitude (length) of r is found using the Pythagorean theorem (assuming we know rx & ry)
The direction (angle) of r is found using the inverse tangent function (again, assuming we know rx & ry)

5. Vector addition:
Cannot directly combine vectors that point in directions other than parallel and anti-parallel (opposite direction). 4m + 1m = 4m + 1m =
Must use vector components if they are in different directions 4m + 1m =

6. Vector addition using components:
Consider C = A + B.
Comparing components of (a) and (b):
Cx = Ax + Bx
Cy = Ay + By C Bx A By B Ax Ay 

7. θ = tan-1 (Cy / Cx) For Triangle A: & Therefore:
We would find a similar solution for Triangle B.
Therefore:
Cx = Ax + Bx = A cos θA + B cos θB
Cy = Ay + By = A sin θA + B sin θB
θ = tan-1 (Cy / Cx)
&

8. For Example...

9. Solution...

10. “x” and “y” components of motion are independent.
2D Kinematics
We will deal with 2-D problems when acceleration is constant:
Choose y axis to be along direction of the acceleration due to gravity
Choose x axis to be along the “other” direction of motion (no acceleration or deceleration in the horizontal direction)
Example: Throwing a baseball (neglecting air resistance)
Acceleration is constant (gravity)
Choose y axis up: ay = -g
Choose x axis along the ground in the direction of the throw
“x” and “y” components of motion are independent.

11. Velocity Components

12. (ax = 0…no acceleration/deceleration in the x-direction)
Using Vector Components with the Horizontal & Vertical Equations of Motion!!
(ax = 0…no acceleration/deceleration in the x-direction)
Total Flight Time:

13. The “x” & “y” Velocity Vectors

14. Problem: Fall Time Which set of binoculars hits the water first?
Which set is moving fastest when it hits the water?

15. Problem: Frustrated With It All
A disgruntled physics student, frustrated with finals, releases his tensions by bombarding the adjacent building, 18.4 m away, with water balloons. He fires one at 39o from the horizontal with an initial speed of 24 m/s.
For how long is the balloon in the air?
How far above the initial launch height does the balloon hit the opposing building?

16. Solution...

17. End of Vectors & 2D Motion Lecture