2Motion in Which Direction_Vectors & Scalars

8/13/2019 2Motion in Which Direction_Vectors & Scalars

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Topic 2

Motion in which

direction?


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Motionin which direction?

Motion in which direction?

Representing vector quantities

Graphical addition of vectors Subtracting vectors

Relative velocities: Some applications

Components of vectorAlgebraic addition of vectors


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Vectors and Scalars


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Vectors and Scalar

Scalar quantityis described by a single realnumber, or magnitude, it can be positive, zero ornegative

Vector quantityhas both a magnitude and adirection in space.

Vectors are represented by a bold face type(e.g.,A).

Alternatively, we can also write it as A


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Vectors: geometric representation

Direction of the arrow gives the direction of the vector

Length of the arrow gives the magnitude of the vector

Head

Tail

A vector is geometrically represented as a line segment

with an arrow indicating direction


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Displacement

Displacementis the change of position of a

point

P2

P1

A

The displacement formpoint P1 to P2is vector

A


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Displacement

Displacement is always a

straight-line segment

directed from the starting

point to the end point If the path ends at the

same place where it

started, the displacement

is zero

P2

P1 Displacement is not relateddirectlyto the distance traveled


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Vector Addition

A

B

C =A+B


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A B

C

D

R

R = ( A+B ) + C

= D + C


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Addition of vectors


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Components of Vectors

Definition of Vector Components

In two dimensions, the vector components of avectorAare two perpendicular vectorsAxandAythat are parallel to the xandyaxes, respectively,

and add together vectorially so that

A = Ax+ Ay


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Components of Vectors

Ax

Ay Acos

sin

tan

x y

x

y

y

x

A A A

A

AA

A

A

A


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Resolving a Vector into components

xA

yA

x

yA

x yA A cos , A A sin

2 2

x yA A A


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R

A

B

Ax Bx

Rx

By

Ay

Ry

2 2

x x x

y x y

x y

R A B

R A B

A A A


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A unit vector ris a vector having length 1 and no units.

It is used to specify the direction of a vector:

So we can writeA= Ar

The unit vectors i, j, k point in the x,yand z axesrespectively.

x

y

zi

j

k

A

r^

In terms of unit vectors, we can express a 2-D

vector as follows:

x yA A A i j

UNIT VECTORS


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Summary

Scalar quantities are numbers, and combine with the usual rulesof arithmetic.

Vector quantities have direction as well as magnitude, andcombine according to rules of vector addition.

Graphically, two vectorsAand Bare added by placing the tail ofBat the head, or tip, ofA.

The vector sumA+ Bthen extends from the tail ofAto thehead of B.


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An airplane flies with a velocity of 750

kilometers per hour, 30.0south of east. What is

the magnitude of Vx and Vy ?


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End

2Motion in Which Direction_Vectors & Scalars

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