1. ADDING VECTORS

2. A vector has a magnitude (#), and direction.
I. What is a vector?
A vector has a magnitude (#), and direction.
Arrows are used to represent vectors.
Vectors we already know:
Displacement
Velocity
Acceleration

3. A. Vectors
The size of the arrow needs to represent the magnitude of the vector.
Ex:
15 m N
5 m N
10 m N

4. B. Directions
N, S, E, and West are used to indicate direction………along with degrees:
Ex:
5 m N
5 m S
5 m W

5. C. Directions with angles.
Sometimes a degree can make things more specific.
You use an angle, then direction of direction.
Ex:
15º
30º
45º
5 m 30º N of W
5 m 45º N of E
5 m 15º E of S

6. II. Adding and Subtracting vectors.
Adding Steps:
Draw the 1st vector
From the “tip” of that vector, put the “tail” of that other vector.
Repeat same process for multiple vectors.
The resulting vector is from start to finish.

7. B. Example
7 m/s E + 5 m/s S
7 m/s
5 m/s
Resulting vector
Now find the magnitude and direction of the resulting vector.

8. C. HOW? Use Pythagorean theorem. Use trig functions, sin, cos, tan.
Make sure calculator is in degrees.

9. D. Subtraction A negative vector reverses the direction.
So, -7 m/s E = 7 m/s W
Ex. 7 m/s E – 5 m/s S
7 m/s E + (-5 m/s S)
7 m/s E + 5 m/s N
SAME THING!

10. III. Why do we need to do this?
Motion in two dimensions.
Example:
A swimmer can swim 2 m/s E across a river. The river has a current of 8 m/s N. What is the resulting velocity of the swimmer?