Some Physics Quantities
Vector - quantity with both magnitude (size) and direction
Scalar - quantity with magnitude only
Vectors:
• Displacement
• Velocity
• Acceleration
• Momentum
• Force
Scalars:
• Distance
• Speed
• Time
• Mass
• Energy
Vectors
Vectors are represented with arrows
• The length of the
arrow represents the
magnitude (how far,
how fast, how strong,
etc, depending on the
type of vector).
5 m/s
42
°
• The arrow points in
the directions of the
force, motion,
displacement, etc. It
is often specified by
an angle.
Rectangular Coordinates
Reference is made to
x and y axes, with +
and - numbers to
indicate position in
space.
Right, up = (+,+)
Left, down = (-,-)
(x,y) = (?, ?)
Vector Components
Any vector can be broken up into two perpendicular
components that lie along the x axis and along the y axis.
-You can think of an
individual component of a
vector as the shadow it
would cast on either the x
axis or the y axis.
y component
-We call these the x and
y components of a vector.
x component
y component
also
y component
Components
x component
[Exploring Trigonometric
Functions]
Island of SOH-CAH-TOA
SOHCAHTOA Also Means:
“Let’s do Trig!!
But….What is Trigonometry!
Trigonometry, or trig are sets of useful ratios
used for finding various parts of right
triangles.
NOW…”Lets do Trig!”
SOH-CAH-TOA
[SOH]
Sine – Opposite – Hypotenuse
[CAH]
Cosine – Adjacent – Hypotenuse
[TOA]
Tangent – Opposite - Adjacent
First: A quick Geometry Review
PARTS
OF A
RIGHT
TRIANGLE
O
P
P
O
S
I
T
E
HYPOTENUSE
ADJACENT
So, Sohcahtoa!
[…trans. “Let’s do Trig.!”]
We’ll break it into syllables.
SOH-CAH-TOA
SOH: SINE-OPP-HYP
sin  = opposite side
hypotenuse
O
P
P
O
S
I
T
E
HYPOTENUSE
ADJACENT
CAH-TOA
SOH-
CAH: COSINE-ADJ-HYP
cos  = adjacent side
hypotenuse
O
P
P
O
S
I
T
E
HYPOTENUSE
ADJACENT
TOA
SOH-CAH-
TOA: TAN-OPP-ADJ
tan  = opposite side
adjacent
O
P
P
O
S
I
T
E
HYPOTENUSE
ADJACENT
A QUICK REVIEW
SOH
Sin Opposite Hypotenuse
CAH
Cosine Adjacent Hypotenuse
TOA
Tangent Opposite Adjacent
APPLICATIONS:
Let’s solve a simple problem.
Sohcahtoa!
The natives launch a coconut at 25 m/s at an angle of 30
with the horizontal. What are the horizontal and vertical
components of the velocity?
Vertical component
Y- component
30
Horizontal component
X- component
The solution!
30
Vertical component
Y- component
opposite= sin* hypotenuse
= sin 30 (25 m/s)
= 0.5 (25 m/s) = 12.5 m/s
Horizontal component
X- component
adjacent = cos * hypotenuse
= cos 30 (25 m/s)
= 0.866 (25 m/s) = 21.7 m/s
APPLICATIONS:
Let’s try a WORD problem!
Sohcahtoa!
Find the Height of Mt.
Sohcahtoa
The volcano is rumbling.
The Sohcahtoans need to
sacrifice a Physics
Student. They know the
base of the mountain is 6
Km wide. The angle
formed from the base to
the top is 60°.
How tall is the mountain?
[Use your calculator!!!]
Find the Height of Mt.
Sohcahtoa
What do we know?
=
60°
Base = 6 Km = 3 Km
2
H
e
i
g
h
t
6 Km
What else do know?
SOH - sin 
= Opposite side
Hypotenuse
CAH - cos 
= Adjacent side
Hypotenuse
TOA - tan 
H
e
i
g
h
t
= Opposite side
Adjacent side
Which one should we use?
6 Km
WHY??
tan  = Opposite side
Adjacent side
tan 60° =
h
3 Km
H
e
i
g
h
t
3 Km
h
WHY??
tan 
= Opposite side
Adjacent side
tan 60° (3km)
=
(tan 60°)(3 Km) =
(0.866)(3)
h
h . (3km)
3 km
H
e
i
g
h
t
h
= h
= 5.2 Km
3 Km
h
WHY??
tan 
= Opposite side
Adjacent side
tan 60° (3km)
(3km)
=
h .
H
e
i
g
h
t
3 km
(0.866 )(3 Km) =
answer
h
h
= 5.2 Km
3 Km
h= 5.2Km
What if I want to find an angle?
Here we know the opposite
side and the hypotenuse.
So we will use the sin function
20 cm
Sin-1(opp/hyp) = 

 = 36.87 degrees
- this is called the
inverse sin
function
Back to the Island of SOHCAHTOA
• The crafty physics student wants to escape
death by volcano and land behind the angry
SOHCAHTOANS. He builds a slide from the
top of the Volcano (5.2 Km high) to land 7 Km
from the base of the volcano. What are the
angles the slide will make with the volcano and
the ground?