Download finding components of Vectors using SOHCAHTOA from this power

PHYSICS: Vectors
Day 1
Today’s Goals
Students will:
1. Be able to describe the difference
between a vector and a scalar.
2. Be able to draw and add vector’s
graphically and use Pythagorean theorem
when applicable.
Today’s Objective
By the end of today…
1.You must be able to find the magnitude
and direction of a resultant
mathematically.
A couple of quick definitions!
This should be review, but just in case…..
• Scalars
• Vectors
Remember: Force, Velocity,
Displacement, Acceleration are ALL
VECTORS!!!
Representing Vectors
• Because of direction, vectors do not add
the same way scalars do.
2 + 2 does not always equal 4!!!!
We will discuss 2 Ways to Add Vectors
1. Graphically
2. Component Addition
Adding Vectors
• When two vectors are added together, the
results are a vector called a RESULTANT.
• In order to find the resultant, you must draw
the two vectors “head to tail.”
Example:
http://www.stmary.ws/highschool/physics/home/note
s/forces/animations/AngleResultants.html
Another Reason why vectors are important:
http://www.stmary.ws/highschool/physics/home/notes/kine
matics/MotionTerms/animations/boatsRiver.swf
Find the Following Resultants
1.
5N
+
5N
= ?
3N
= ?
2.
+
6N
Components
• These two vectors are
known as components.
X - component
• In physics, we often
break vectors down into
horizontal (x) and vertical
(y) components.
Y - component
• Every vector can be
separated into two
equivalent vectors.
Calculating Components
• Use the Pythagorean Theorem to
calculate the missing component for each
velocity below.
a2 + b2 = c2
5 m/s
?
8 m/s
4 m/s
? 8.9 m/s
?
6.24 m/s
3 m/s
- 8 m/s
5 m/s
4 m/s
a2 + b2 = c2
(-8)2 + 42 = c2
64 + 16 = c2
80 = c2 c = 8.9 m/s
?
- 8 m/s
4 m/s
Right Triangle Trig.
Q: WHAT ARE TRIG FUNCTIONS?
A: Sin
Cos
Tan
• Three functions that are useful when
dealing with right triangles.
• These functions are used to determine
missing sides of right triangles when other
information is known.
Sine (sin)
• The Sin of any angle is equal to the ratio of the
length of the “opposite side” and the length of
the “hypotenuse.”
O
Sin (ø) =
H
H
O
ø
Cosine (cos)
• The Cosine of any angle is equal to the
ratio of the length of the “adjacent side”
and the length of the “hypotenuse.”
A
Cos (ø) =
H
H
A
ø
Tangent (tan)
• The Tangent of any angle is equal to the
ratio of the length of the “opposite side”
and the length of the “adjacent side.”
O
Tan (ø) =
A
O
A
ø
An easy way to remember…
• What should you do when you have dirty
feet?
»SOHCAHTOA
(pronounced: Soak A Toe.. Uhhh….)
SOH
Sine
Opposite
Hypotenuse
CAH
Cosine
Adjacent
Hypotenuse
TOA
Tangent
Opposite
Adjacent
What is a Function?
• 2x = Y
• What do I get for Y as I plug in numbers
for x?
Sin (x) Cos (x) and
Tan (x)
do the same thing!!!!
x
y
Plug in a number for the angle:
0
0
(x degrees)
1
2
and you get back a different number
(usually a decimal).
2
4
Next, following SOHCAHTOA, the
number you get back from the
function, is equal to O/H, A/H, or O/A!

Trig. Practice
Problems
#1
a. Find x.
b. Find y.
c. Find q.
d. Find r.
q
9
25o
r
sin (30) = x/20
cos (30) = y/20
sin (25) = 9/q
tan (25) = 9/r
.5 = x/20
.866 = y/20
.423 = 9/q
.466 = 9/r
(.5)20 = x
(.866)20 = y
.423q = 9
.466r = 9
x = 10
y = 17.32
q = 21.3
r = 19.3
Trig.
Problems
#1
From a point on the ground 25
meters from the foot of a
tree, the angle of elevation of
the top of the tree is
32º. (Meaning you have to
look up 32o to be looking at
the top of the tree.) Find to
the nearest meter, the height
of the tree.
HINT:
Draw a diagram showing the
information.
m
Trig.
Practice
#2
A ladder leans against a
building. The foot of
the ladder is 6 feet
from the building. The
ladder reaches height of
14 feet on the building.
a. Find the length of the
ladder to the nearest
foot.
Trig.
Practice
#2
b. What is the
angle between the
top of the ladder
and the wall it leans
on?
Trig. Practice Problem #3
3. A plane travels 25 km at an angle 35
degrees to the ground and then
changes direction and travels 12.5 km
at an angle of 22 degrees to the
ground. What is the magnitude and
direction of the total displacement?
Quiz!
• The Vectors listed below represent the velocity of an
airplane and the velocity of wind. Each Plane is trying to
Go North. Draw a Vector Diagram and Calculate the
magnitude and direction of the resulting velocity.
1. Wind: 50 m/s East
Plane Engines: 200 m/s North
2. Wind 30 m/s East
Plane Engines: 100 m/s North
3. Wind 120 m/s West
Plane Engines: 175 m/s North