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Algebraic addition and subtraction of vectors

Vectors in a straight line

Whenever you are faced with adding vectors acting in a straight line (i.e. some directed left and some right, or some acting up and others down) you can use a very simple algebraic technique:

Method: Addition/Subtraction of Vectors in a Straight Line

  1. Choose a positive direction. As an example, for situations involving displacements in the directions west and east, youmight choose west as your positive direction. In that case, displacements east are negative.
  2. Next simply add (or subtract) the magnitude of the vectors using the appropriate signs.
  3. As a final step the direction of the resultant should be included in words (positive answers are in the positive direction, while negativeresultants are in the negative direction).

Let us consider a few examples.

A tennis ball is rolled towards a wall which is 10 m away from the ball. If after striking the wall the ball rolls a further 2,5 m along the ground away from the wall, calculate algebraically the ball's resultant displacement.

  1. We know that the resultant displacement of the ball ( x R ) is equal to the sum of the ball's separate displacements ( x 1 and x 2 ):

    x R = x 1 + x 2

    Since the motion of the ball is in a straight line (i.e. the ball moves towards and away from the wall), we can use the method of algebraic additionjust explained.

  2. Let's choose the positive direction to be towards the wall. This means that the negative direction is away from the wall.

  3. With right positive:

    x 1 = + 10 , 0 m · s - 1 x 2 = - 2 , 5 m · s - 1
  4. Next we simply add the two displacements to give the resultant:

    x R = ( + 10 m · s - 1 ) + ( - 2 , 5 m · s - 1 ) = ( + 7 , 5 ) m · s - 1
  5. Finally, in this case towards the wall is the positive direction , so: x R = 7,5 m towards the wall.

Suppose that a tennis ball is thrown horizontally towards a wall at an initial velocity of 3 m · s - 1 to the right. After striking the wall, the ball returns to the thrower at 2 m · s - 1 . Determine the change in velocity of the ball.

  1. A quick sketch will help us understand the problem.

  2. Remember that velocity is a vector. The change in the velocity of the ball is equal to the difference between the ball's initial and finalvelocities:

    Δ v = v f - v i

    Since the ball moves along a straight line (i.e. left and right), we can use the algebraic technique of vector subtraction just discussed.

  3. Choose the positive direction to be towards the wall. This means that the negative direction is away from the wall.

  4. v i = + 3 m · s - 1 v f = - 2 m · s - 1
  5. Thus, the change in velocity of the ball is:

    Δ v = ( - 2 m · s - 1 ) - ( + 3 m · s - 1 ) = ( - 5 ) m · s - 1
  6. Remember that in this case towards the wall means a positive velocity , so away from the wall means a negative velocity : Δ v = 5 m · s - 1 away from the wall.

Questions & Answers

what is the stm
Brian Reply
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Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
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it is a goid question and i want to know the answer as well
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characteristics of micro business
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for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
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how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
how did you get the value of 2000N.What calculations are needed to arrive at it
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Properties of longitudinal waves
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Source:  OpenStax, Siyavula textbooks: grade 10 physical science [caps]. OpenStax CNX. Sep 30, 2011 Download for free at http://cnx.org/content/col11305/1.7
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