<< Chapter < Page Chapter >> Page >

Solution

Because v tot size 12{v rSub { size 8{ bold "tot"} } } {} is the vector sum of the v w and v p , its x - and y -components are the sums of the x - and y -components of the wind and plane velocities. Note that the plane only has vertical component of velocity so v p x = 0 and v p y = v p . That is,

v tot x = v w x size 12{v rSub { size 8{"tot"x} } =v rSub { size 8{wx} } } {}

and

v tot y = v w y + v p . size 12{v rSub { size 8{"tot"y} } =v rSub { size 8{wx} } +v rSub { size 8{p} } "."} {}

We can use the first of these two equations to find v w x size 12{v rSub { size 8{ ital "wx"} } } {} :

v w y = v tot x = v tot cos 110º . size 12{v rSub { size 8{wx} } =v rSub { size 8{"tot"x} } =v rSub { size 8{"tot"} } "cos110" rSup { size 8{o} } "."} {}

Because v tot = 38 . 0 m / s size 12{v rSub { size 8{ ital "tot"} } ="38" "." 0m/s} {} and cos 110º = 0.342 size 12{"cos""110º""=""-""0.342"} {} we have

v w y = ( 38.0 m/s ) ( –0.342 ) = –13 m/s.

The minus sign indicates motion west which is consistent with the diagram.

Now, to find v w y size 12{v rSub { size 8{ ital "wy"} } } {} we note that

v tot y = v w y + v p size 12{v rSub { size 8{"tot"y} } =v rSub { size 8{wx} } +v rSub { size 8{p} } } {}

Here v tot y = v tot sin 110º size 12{v rSub { size 8{"tot"y} } =v rSub { size 8{"tot"} }  = v rSub { size 8{"tot"} }  "sin 110º"} {} ; thus,

v w y = ( 38 . 0 m/s ) ( 0 . 940 ) 45 . 0 m/s = 9 . 29 m/s. size 12{v rSub { size 8{wy} } = \( "38" "." 0" m/s" \) \( 0 "." "940" \) - "45" "." 0" m/s"= - 9 "." "29"" m/s."} {}

This minus sign indicates motion south which is consistent with the diagram.

Now that the perpendicular components of the wind velocity v w x size 12{v rSub { size 8{wx} } } {} and v w y size 12{v rSub { size 8{wy} } } {} are known, we can find the magnitude and direction of v w size 12{v rSub { size 8{w} } } {} . First, the magnitude is

v w = v w x 2 + v w y 2 = ( 13 . 0 m/s ) 2 + ( 9 . 29 m/s ) 2

so that

v w = 16 . 0 m/s . size 12{v rSub { size 8{w} } ="16" "." 0" m/s."} {}

The direction is:

θ = tan 1 ( v w y / v w x ) = tan 1 ( 9 . 29 / 13 . 0 ) size 12{θ="tan" rSup { size 8{ - 1} } \( v rSub { size 8{wy} } /v rSub { size 8{wx} } \) ="tan" rSup { size 8{ - 1} } \( - 9 "." "29"/ - "13" "." 0 \) } {}

giving

θ = 35 . . size 12{θ="35" "." 6º"."} {}

Discussion

The wind’s speed and direction are consistent with the significant effect the wind has on the total velocity of the plane, as seen in [link] . Because the plane is fighting a strong combination of crosswind and head-wind, it ends up with a total velocity significantly less than its velocity relative to the air mass as well as heading in a different direction.

Note that in both of the last two examples, we were able to make the mathematics easier by choosing a coordinate system with one axis parallel to one of the velocities. We will repeatedly find that choosing an appropriate coordinate system makes problem solving easier. For example, in projectile motion we always use a coordinate system with one axis parallel to gravity.

Relative velocities and classical relativity

When adding velocities, we have been careful to specify that the velocity is relative to some reference frame . These velocities are called relative velocities . For example, the velocity of an airplane relative to an air mass is different from its velocity relative to the ground. Both are quite different from the velocity of an airplane relative to its passengers (which should be close to zero). Relative velocities are one aspect of relativity    , which is defined to be the study of how different observers moving relative to each other measure the same phenomenon.

Nearly everyone has heard of relativity and immediately associates it with Albert Einstein (1879–1955), the greatest physicist of the 20th century. Einstein revolutionized our view of nature with his modern theory of relativity, which we shall study in later chapters. The relative velocities in this section are actually aspects of classical relativity, first discussed correctly by Galileo and Isaac Newton. Classical relativity is limited to situations where speeds are less than about 1% of the speed of light—that is, less than 3,000 km/s size 12{"3,000 km/s"} {} . Most things we encounter in daily life move slower than this speed.

Let us consider an example of what two different observers see in a situation analyzed long ago by Galileo. Suppose a sailor at the top of a mast on a moving ship drops his binoculars. Where will it hit the deck? Will it hit at the base of the mast, or will it hit behind the mast because the ship is moving forward? The answer is that if air resistance is negligible, the binoculars will hit at the base of the mast at a point directly below its point of release. Now let us consider what two different observers see when the binoculars drop. One observer is on the ship and the other on shore. The binoculars have no horizontal velocity relative to the observer on the ship, and so he sees them fall straight down the mast. (See [link] .) To the observer on shore, the binoculars and the ship have the same horizontal velocity, so both move the same distance forward while the binoculars are falling. This observer sees the curved path shown in [link] . Although the paths look different to the different observers, each sees the same result—the binoculars hit at the base of the mast and not behind it. To get the correct description, it is crucial to correctly specify the velocities relative to the observer.

Questions & Answers

what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
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
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
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
NANO
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
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
Berger describes sociologists as concerned with
Mueller Reply
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
Practice Key Terms 5

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Selected chapters of college physics for secondary 5. OpenStax CNX. Jun 19, 2013 Download for free at http://legacy.cnx.org/content/col11535/1.1
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Selected chapters of college physics for secondary 5' conversation and receive update notifications?

Ask