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8/11/2019 3-Vectorsdsfg

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AP Physics Vectors 101

Good Stuff on Vectors: Weve briefly mentioned vectors and scalars. The time has now cometo undertake a thorough study of the things.

Of the two, scalars are the easiest to understand and deal with. See, when you deal with scalars, its all

very simple, theyre just like everyday numbers just use the regular arithmetic stuff that you

have laboriously mastered during the past !" # !$ years. %ike adding apples with apples.

&ealing with vectors is a whole 'nuther thang. (ts more like adding apples and pork bellies together

or something.

When you add scalars you simply do this) $ kg * + kg - kg.

ut with vectors, $ * + might e/ual 01 %ord, how can this be1

Well, your basic vectors have both magnitude and direction. (f you add two velocities, one that is

north at !" m2s and the other is south at !" m2s, you end up with 3ero m2s. 4an you see why this is so5The classic way to add vectors is to represent them with arrows, draw them to scale, and then measure

out things with a ruler and protractor to see what the answer would be.

6 vector is represented as an arrow. The arrowhead points in the

vectors direction and the length represents the vectors

magnitude. To represent the magnitude, you have to use a scale to

figure out how long to draw the thing. 7ach vector has a head and atail.

The graphical vector addition method is sometimes called the 8headtotail9 method. :ou draw onevector, then draw the second vector with its tail on the head of the first. The ne;t vector would be

drawn with its tail on the head of the second and so on. The final answer, known as the resultantvector, is found by drawing a vector form the tail of the first vector to the head of the last.

(t makes no difference in what order you add the vectors as you can see by the drawing above.

++

R = A + B

A

B

t a i l

h e a d

a

b


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:ou will not be re/uired to add vectors graphically # its a lot of trouble and not very accurate and

there are better ways to do it.


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@or our original triangle)

sin a

c= cos

b

c= tan

a

b=

6 plane travels east -+- km, then flies north, then flies back to its takeoff point a distance of A!Bkm. =a> What is the angle 5

=a> 6 simple way to find the distance the plane traveled north would be to use the Cythagorean

theorem.$ $ $c a b= + solve for a)

( ) ( )$ $$ $ A!B -+- 0ADa c b km km km= = =

=b> To find the angle we can use the tangent function =opposite side over adjacent side>)

o0ADtan 0!.B

-+-

a km

b km = = =

This is actually a vector problem # it may be your very first vector problem. Wow1 &ont you feel all

warm and fu33y inside5

Vector Components:6ny vector can be drawn as the resultant of two perpendicular vectors,one along thex a;is and the other along they a;is. The two vectors are perpendicular to each

other and are called component vectors. Turning a single vector into two component vectorsis called 8resolving the vector into its ; and y component vectors9. This is done using

trigonometry.


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Eector 6 is the one we start with. (t is made up of two vectors that lie in the ; and y plane. We call theone along the ; a;is 86;9 and the one along the y a;is is 86y9. Fsing trig we see that)

cosxA A = sinyA A =

The angle can also be easily found)

!tan

Y

X

A

A

=

6 ball is thrown with a velocity of $$.- m2s at an angle of $+."to the hori3on. What are itsvertical and hori3ontal velocity components5

The components look like this)

Fsing trig to solve the thing we get)

cos $$.- cos $+." $".Ax xm m

v v vs s

= = =

sin $$.- sin $+." B.ADy ym m

v v vs s

= = =

+G

A

A

A

x

y

v2 3 . 0

o

v

v x

v y


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More Vector Problems:

6 velocity vector has the following components) vy is !$.0 m2s and vxis !-.0 m2s, find the angle.

!tan Y

X

vv

=

!

!$.0

tan +B.B

!-.0

o

m

sm

s

= =

6 boat is traveling north directly across a river that is -." km across. The current is to the east at+." km2h. The boat travels at -." km2h. =a> What is the boats resultant velocity5 =b> @ind the time to cross) the velocity component that is in the direction to cross the river determines

how /uickly the boat crosses, so use bv .

xvt

= xtv

= ! !-""." ".!""!"""

-."

kmt m hkm m

h

= =

=c> @ind distance in hori3ontal direction)

xv

t= x vt= ( )+." ".!" ".+"

kmx h km

h= =

+A

v b

vc

v r


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Hourmet rownie Iecipe

! bo; brownie mi; and bake as directed11OJ7 Ao3 jar marshmallow crKme

Spread crKme onto baked brownies appro;imately !" # !- minutes after they come out of the oven.6s it melts it is easier to spread.

@rosting)$ cups powdered sugar,

L cup butter at room temperature,

!2+ cup cocoa,!2+ cup evaporated milk

Mi; all the ingredients on high using a mi;er and spread on top of marshmallow creme

+B

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