PHYSICS
Vectors and Scalars
Useful Vector Math
SOHCAHTOA
•
Trigonometry
– sine:
sin q = opp/hyp
– cosine:
cos q = adj/hyp
– tangent:
tan q = opp/adj
hypotenuse
q
adjacent
side
opposite
side
Useful Vector Math
Pythagorean Theorum
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
Vector Basics
• Vectors
– displacement vectors
d = d (displacement),
q (direction)
• length proportional to
amount
• direction measured by
angle
Co-linear Vectors
• Combining Vectors
– Collinear vectors:
–
v1
v2
v1
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?
Non Co-linear Vectors
• Perpendicular vectors:
resultant’s magnitude:
vx
vy
v
q
2
2
vx  vy
resultant’s direction:
v
1 vy 
q  tan 

 vx 
Graphical Method
•
Tail to tip method
1.
2.
3.
4.
5.
+y
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
-x
vector is called the
resultant.
The order that you add
vectors doesn’t matter
(commutative property)
+x
-y
Component Method