1. PHYSICS
Vectors and Scalars

2. Useful Vector Math SOHCAHTOA sine: sin q = opp/hyp
Trigonometry
sine: sin q = opp/hyp
cosine: cos q = adj/hyp
tangent: tan q = opp/adj

3. Useful Vector Math
Pythagorean Theorum

4. Vectors vs. Scalars
scalars: only magnitude (size) ex. distance, time, speed, mass, temperature
vectors: magnitude and a direction
Examples of vectors
displacement, s or x : distance and direction
velocity, v : speed and direction
acceleration, a: change in speed and direction

5. Vector Basics
Vectors
displacement vectors d = d (displacement), q (direction)
length proportional to amount
direction measured by angle

6. Co-linear Vectors Combining Vectors resultant: vnet= v1+ v2
Collinear vectors:
v v v v2
resultant: vnet= v1+ v2
ex: A plane flies 40 m/s E into a 10 m/s W headwind. What is the net velocity?
ex: A plane flies 40 m/s W with a 10 m/s W tailwind. What is the net velocity?

7. Non Co-linear Vectors Perpendicular vectors: resultant’s magnitude:
resultant’s direction:

8. Graphical Method Tail to tip method+y
Tail to tip method
Place first vector on graph with tail starting at the origin
Place the second vector with the tail at the tip of the first vector
Repeat step two for multiple vectors
Draw a line from the tail of the first vector to the tip of the final vector. This final vector is called the resultant.
The order that you add vectors doesn’t matter (commutative property) +x -x -y

9. Component Method