# 3.5 Addition of velocities  (Page 7/12)

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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.

(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) ${H}_{\text{average}}=\text{14}\text{.}\text{9}\frac{\text{km/s}}{\text{Mly}}$

(b) 20.2 billion years

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?

A ship sailing in the Gulf Stream is heading $25.0º$ west of north at a speed of 4.00 m/s relative to the water. Its velocity relative to the Earth is $4.80 m/s$ $5.00º$ 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.)

$1\text{.}\text{72 m/s}$ , $42.3º$ north of east

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 $90.0º$ 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?

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.

Unreasonable Results A commercial airplane has an air speed of due east and flies with a strong tailwind. It travels 3000 km in a direction $5º$ 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?

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.

#### Questions & Answers

A body travelling at a velocity of 30ms^-1 in a straight line is brought to rest by application of brakes. if it covers a distance of 100m during this period, find the retardation.
what is distribution of trade
what's acceleration
The change in position of an object with respect to time
Mfizi
Acceleration is velocity all over time
Pamilerin
hi
Stephen
It's not It's the change of velocity relative to time
Laura
Velocity is the change of position relative to time
Laura
acceleration it is the rate of change in velocity with time
Stephen
acceleration is change in velocity per rate of time
Noara
what is ohm's law
Stephen
Ohm's law is related to resistance by which volatge is the multiplication of current and resistance ( U=RI)
Laura
how i don understand
how do I access the Multiple Choice Questions? the button never works and the essay one doesn't either
How do you determine the magnitude of force
mass × acceleration OR Work done ÷ distance
Seema
Which eye defect is corrected by a lens having different curvatures in two perpendicular directions?
acute astigmatism?
the difference between virtual work and virtual displacement
How do you calculate uncertainties
What is Elasticity
using a micro-screw gauge,the thickness of a piece of a A4 white paper is measured to be 0.5+or-0.05 mm. If the length of the A4 paper is 26+or-0.2 cm, determine the volume of the A4 paper in: a). Cubic centimeters b). Cubic meters
what is module
why it is possible for an object(man) to stay on air without falling down?
its impossible, what do you mean exactly?
Ryan
Exactly
Emmanuella
it's impossible
Your
Why is it not possible to stand in air?
bikko
the air molecules are very light enough to oppose the gravitational pull of the earth on the man..... hence, freefall occurs
Arzail
because of gravitational forces
Pamilerin
this mostly occur in space
Stephen
what is physics
no life without physics ....that should tell you something
Exactly
Emmanuella
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E=MC^2
study of matter and energy and an inter-relation between them.
Minahil
that's how the mass and energy are related in stationery frame
Arzail
Ketucky tepung 10m
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Tree skin and two cloud have tokside maybe
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firdaus
Kinetic energy is the energy due to montion of waves,electrons,atoms, molecule,substances an object s.
Emmanuella
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hi
Hilal
plz anyone can tell what is meteor and why meteor fall in night? can meteor fall in the day
Hilal
meteor are the glowy (i.e. heated when the enter into our atmosphere) parts of meteoroids. now, meteoroids are the debris resulting from the collision of asteroids or comets. yes, it occurs in daytime too, but due to the daylight, we cant observe it as clearly as in night
Arzail
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Hilal
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Waka
wich method we use to find the potential on a grounded sphere
Noman
with out a physics the life is nothing to see
What do you want to talk about😋😋
Emmanuella
the study of all the natural events occuring around us..... this is Physics (until those events obey the laws of physics)
Arzail
Conservation of energy😰
Emmanuella
yeah, that too
Arzail
Energy, it always remains there in a physical system. it can only take the form either in motion (kinetic energy) or in rest (potential energy)
Arzail
In nature organisms feed on one another in an orderly way.
Emmanuella
that describes the food chain, in which we humans are at the top
Arzail
The energy that came initially from the sun 🌞is converted into a form in which it can be stored in green plant.
Emmanuella
Therefore, there is conservation of energy.
Emmanuella
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