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We already know so much about Vectors like…. What is a Vector? What is a Scalar? What are the parts of a Vector? And wait…there’s more. Vector Components. Any vector can be broken up into two perpendicular components that lie along the x axis and along the y axis.

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Presentation Transcript
slide1

We already know so much about Vectors like…

  • What is a Vector?
  • What is a Scalar?
  • What are the parts of a Vector?
  • And wait…there’s more
slide2

Vector Components

  • Any vector can be broken up into two perpendicular components that lie along the x axis and along the y axis.
  • We call these the x and y components of a vector.
  • 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

x component

slide3

Components

y component also

y component

x component

island of soh cah toa

Island of SOH-CAH-TOA

[Exploring Trigonometric Functions]

sohcahtoa also means let s do trig
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
NOW…”Lets do Trig!”SOH-CAH-TOA

[SOH] Sine – Opposite – Hypotenuse

[CAH] Cosine – Adjacent – Hypotenuse

[TOA] Tangent – Opposite - Adjacent

first a quick geometry review
First: A quick Geometry Review

PARTS

OF A

RIGHT

TRIANGLE

OPPOSITE

HYPOTENUSE

ADJACENT

soh sine opp hyp
SOH: SINE-OPP-HYP

sin  = opposite side

hypotenuse

OPPOSITE

HYPOTENUSE

ADJACENT

cah cosine adj hyp
CAH: COSINE-ADJ-HYP

cos  = adjacent side

hypotenuse

OPPOSITE

HYPOTENUSE

ADJACENT

toa tan opp adj
TOA: TAN-OPP-ADJ

tan  = opposite side

adjacent

OPPOSITE

HYPOTENUSE

ADJACENT

a quick review
A QUICK REVIEW

SOH

Sin Opposite Hypotenuse

CAH

Cosine Adjacent Hypotenuse

TOA

Tangent Opposite Adjacent

applications
APPLICATIONS:

Let’s solve a simple problem.

Sohcahtoa!

slide18

25 m/s

Vertical component

Y- component

30

Horizontal component

X- component

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?

the solution

Vertical component

Y- component

opposite= sin* hypotenuse

= sin 30 (25 m/s)

= 0.5 (25 m/s) = 12.5 m/s

25 m/s

30

Horizontal component

X- component

adjacent = cos * hypotenuse

= cos 30 (25 m/s)

= 0.866 (25 m/s) = 21.7 m/s

The solution!
applications20
APPLICATIONS:

Let’s try a WORD problem!

Sohcahtoa!

find the height of mt 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 sohcahtoa22
Find the Height of Mt. Sohcahtoa

What do we know?

  • = 60°

Base = 6 Km = 3 Km

2

Height

6 Km

what else do know
What else do know?

SOH - sin  = Opposite side

Hypotenuse

CAH - cos  = Adjacent side

Hypotenuse

TOA - tan  = Opposite side

Adjacent side

Which one should we use?

Height

6 Km

which one
Which one?

SOH - sin  = Opposite side

Hypotenuse

CAH - cos  = Adjacent side

Hypotenuse

TOA - tan  = Opposite side

Adjacent side

Height

6 Km

slide25
WHY??

tan  = Opposite side

Adjacent side

tan 60° = h

3 Km

Height

h

3 Km

slide26
WHY??

tan  = Opposite side

Adjacent side

tan 60°(3km) = h .(3km)

3 km

(tan 60°)(3 Km) = h

(0.866)(3) = h

h = 2.598 Km

Height

h

3 Km

slide27
WHY??

tan  = Opposite side

Adjacent side

tan 60°(3km) = h .(3km)

3 km

(0.866 )(3 Km) = h

answer h = 2.598 Km

Height

h= 2.598

3 Km

excellent
EXCELLENT!!!

You deserve a HAND!

Now, Let’s Work!!!

SOHCAHTOA!!!

what if i want to find an angle
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

12 cm

Sin-1(opp/hyp) = 

- this is called the inverse sin function

 = 36.87 degrees

back to the island of sohcahtoa
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 (2.6 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?