<< Chapter < Page Chapter >> Page >

The great astronomer Edwin Hubble discovered that all distant galaxies are receding from our Milky Way Galaxy with velocities proportional to their distances. It appears to an observer on the Earth that we are at the center of an expanding universe. [link] illustrates this for five galaxies lying along a straight line, with the Milky Way Galaxy at the center. Using the data from the figure, calculate the velocities: (a) relative to galaxy 2 and (b) relative to galaxy 5. The results mean that observers on all galaxies will see themselves at the center of the expanding universe, and they would likely be aware of relative velocities, concluding that it is not possible to locate the center of expansion with the given information.

Five galaxies on a horizontal straight line are shown. The left most galaxy one has distance of three hundred millions of light years and it is moving towards left. The second and third galaxies in the figure have shown no velocities. The velocities of fourth and fifth galaxies are towards right.
Five galaxies on a straight line, showing their distances and velocities relative to the Milky Way (MW) Galaxy. The distances are in millions of light years (Mly), where a light year is the distance light travels in one year. The velocities are nearly proportional to the distances. The sizes of the galaxies are greatly exaggerated; an average galaxy is about 0.1 Mly across.

Got questions? Get instant answers now!

(a) Use the distance and velocity data in [link] to find the rate of expansion as a function of distance.

(b) If you extrapolate back in time, how long ago would all of the galaxies have been at approximately the same position? The two parts of this problem give you some idea of how the Hubble constant for universal expansion and the time back to the Big Bang are determined, respectively.

(a) H average = 14 . 9 km/s Mly alignl { stack { size 12{H rSub { size 8{"average"} } ={}} {} #"14" "." "9 " { {"km/s"} over {"Mly"} } {} } } {}

(b) 20.2 billion years

Got questions? Get instant answers now!

An athlete crosses a 25-m-wide river by swimming perpendicular to the water current at a speed of 0.5 m/s relative to the water. He reaches the opposite side at a distance 40 m downstream from his starting point. How fast is the water in the river flowing with respect to the ground? What is the speed of the swimmer with respect to a friend at rest on the ground?

Got questions? Get instant answers now!

A ship sailing in the Gulf Stream is heading 25.0º size 12{"25.0"º} {} west of north at a speed of 4.00 m/s relative to the water. Its velocity relative to the Earth is 4.80 m/s size 12{4 "." "80 m/s"} {} 5.00º size 12{5°} {} west of north. What is the velocity of the Gulf Stream? (The velocity obtained is typical for the Gulf Stream a few hundred kilometers off the east coast of the United States.)

1 . 72 m/s size 12{1 "." "72"" m/s"} {} , 42.3º size 12{"42" "." 3°} {} north of east

Got questions? Get instant answers now!

An ice hockey player is moving at 8.00 m/s when he hits the puck toward the goal. The speed of the puck relative to the player is 29.0 m/s. The line between the center of the goal and the player makes a 90.0º size 12{"90.0º"} {} angle relative to his path as shown in [link] . What angle must the puck’s velocity make relative to the player (in his frame of reference) to hit the center of the goal?

An ice hockey player is moving across the rink with velocity v player towards north direction. The goal post is in east direction. To hit the goal the hockey player must hit with velocity of puck v puck making an angle theta with the horizontal axis so that its direction is towards south east.
An ice hockey player moving across the rink must shoot backward to give the puck a velocity toward the goal.

Got questions? Get instant answers now!

Unreasonable Results Suppose you wish to shoot supplies straight up to astronauts in an orbit 36,000 km above the surface of the Earth. (a) At what velocity must the supplies be launched? (b) What is unreasonable about this velocity? (c) Is there a problem with the relative velocity between the supplies and the astronauts when the supplies reach their maximum height? (d) Is the premise unreasonable or is the available equation inapplicable? Explain your answer.

Got questions? Get instant answers now!

Unreasonable Results A commercial airplane has an air speed of 280 m/s size 12{"280 m/s"} {} due east and flies with a strong tailwind. It travels 3000 km in a direction size 12{5°} {} south of east in 1.50 h. (a) What was the velocity of the plane relative to the ground? (b) Calculate the magnitude and direction of the tailwind’s velocity. (c) What is unreasonable about both of these velocities? (d) Which premise is unreasonable?

Got questions? Get instant answers now!

Construct Your Own Problem Consider an airplane headed for a runway in a cross wind. Construct a problem in which you calculate the angle the airplane must fly relative to the air mass in order to have a velocity parallel to the runway. Among the things to consider are the direction of the runway, the wind speed and direction (its velocity) and the speed of the plane relative to the air mass. Also calculate the speed of the airplane relative to the ground. Discuss any last minute maneuvers the pilot might have to perform in order for the plane to land with its wheels pointing straight down the runway.

Got questions? Get instant answers now!

Questions & Answers

Hello want to study physics but it seems so difficult
Joshua Reply
Yes
Aifuwa
I read it but when I try to solve questions it seems difficult
Aifuwa
Jerry where are you from
Joshua
can i study some problem on motion and projection motion
Weamie
hello pls am new here so i want someone to highlight me on this "application of expansion/contraction
Awoke
want 2 do is just dat u rest for some minute,then u go back to the simple one nd one u understand and then go back to d difficult one,u will now understand it better.
rebecca
yess
rebecca
what of mine
Awoke
yess
rebecca
ok
Awoke
iam new here
Mohamed
u are welcome
Awoke
hello am new. am I welcome
Miracle
yes you are😁
clifford
we can all learn and help each other
Osei
yeah you are right
Neyaz
so we can all share our ideas on a certain topic
Osei
sure
clifford
in beginning all subjects are difficult need to work hard
Mohammed
hi guyz
Lamin
explanations on harmonic motion
Tumwiine Reply
example ofchange of state of the body in the effectof heat
Abiodun Reply
what is normal force?
Neyaz Reply
the force that pushes upward on us. the force that opposes gravity
clifford
upthrust of air
Abdikadir
Newton's 3rd law. the force of the ground (earth) that pushes back on gravity, keeping us on the ground instead of sinking into it.
clifford
I really need lots of questions on frictional force
Ogboru Reply
Questions or answers?
Shii
I can help answering what I can
Shii
does friction also need some force to perform?
Mohit
no friction is a force just like the gravitational force
clifford
yeah but u can't apply friction anywhere else like other forces
Mohit
I don't understand that question. friction does work alongside other forces based on the situation.
clifford
eg. when walking there are two forces acting on us gravitational and frictional force. friction helps us move forward and gravity keeps us on the ground
clifford
friction is a contact force. Two surfaces are necessary for the force to work.
clifford
hope this helped
clifford
the friction force which oppose while it contact with surrounding. there are two kind of friction. slidding and rolling friction.
Neyaz
Two unequal masses M1 and M2 are connected by a string of tension T on a plane,find the acceleration and tension in the string
Ogboru
derive the equation
Ogboru
Hi
Olamide
What is physics?
Jeuloriz Reply
physics is a branch of science in which we are dealing with the knowledge of our physical things. macroscopic as well as microscopic. we are going look inside the univers with the help of physics. you can learn nature with the help of physics. so many branches of physics you have to learn physics.
vijay
What are quarks?
Breanna Reply
6 type of quarks
Neyaz
what is candela
Akani Reply
Candela is the unit for the measurement of light intensity.
Osei
any one can prove that 1hrpower= 746 watt
Neyaz Reply
Newton second is the unit of ...............?
Neyaz
Impulse and momentum
Fauzia
force×time and mass× velocity
vijay
Good
Neyaz
What is the simple harmonic motion?
Fauzia Reply
oscillatory motion under a retarding force proportional to the amount of displacement from an equilibrium position
Yuri
Straight out of google, you could do that to, I suppose.
Yuri
*too
Yuri
ok
Fauzia
Oscillatory motion under a regarding force proportional to the amount of displacement from an equilibrium position
Neyaz
examples of work done by load of gravity
Maureen Reply
What is ehrenfest theorem?
Fauzia Reply
You can look it up, faster and more reliable answer.
Yuri
That isn't a question to ask on a forum and I also have no idea what that is.
Yuri
what is the work done by gravity on the load 87kj,11.684m,mass xkg[g=19m/s
Maureen
What is law of mass action?
Fauzia Reply
rate of chemical reactions is proportional to concentration of reactants ...
muhammad
ok thanks
Fauzia
what is lenses
Ndobe Reply
lenses are two types
Fauzia
concave and convex
muhammad
right
Fauzia
speed of light in space
Vikash Reply
in vacuum speed of light is 3×10^8 m/s
vijay
ok
Vikash
2.99×10^8m/s
Umair
2.8820^8m/s
Muhammed
which is correct answer
Vikash
he is correct but we can round up in simple terms
vijay
3×10^8m/s
vijay
is it correct
Fauzia
I mean 3*10^8 m/s ok
vijay
299792458 meter per second
babar
3*10^8m/s
Neyaz
how many Maxwell relations in thermodynamics
vijay
how we can do prove them?
vijay
What is second law of thermodynamics?
Neyaz
Practice Key Terms 5

Get the best College physics course in your pocket!





Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics' conversation and receive update notifications?

Ask