[tex]\frac{mv^{2} }{2}[/tex]their common speed after the collision is 2.1 m/s and
height the package of mass m rebound is 22cm using conservation of energy and conservation of momentum.
conservation of energy:
Energy cannot be created or destroyed, according to the rule of conservation of energy. However, it is capable of change from one form to another. An isolated system's total energy is constant regardless of the types of energy present. The law of energy conservation is adhered to by all energy forms.
conservation of momentum:
The product of an object's mass and velocity is that object's momentum. A vector quantity, that is. A fundamental tenet of physics is the conservation of momentum, which asserts that in the absence of an external force, the overall momentum of an isolated system remains constant. In other words, if no outside force influences the system, its total momentum is constant throughout every interaction. The vector sum of the individual momenta represents the total momentum.
Here, we first have to apply conservation of energy:
P.E = K.E
mgh = [tex]\frac{mv^{2} }{2}[/tex] (i)
mass cancels out
v = √2gh = √2×9.8×2 = 6.26099m/s
now applying the conservation of momentum. Since the package sticks after collision, we have for final momentum m = m1 + m2 and initially u2=0
m1u1 + m2u2 = (m1+m2)v
m*6.26099 = 3m*v
v = 2.1 m/s
now using eq (i) we have,
mgh = [tex]\frac{mv^{2} }{2}[/tex]
masses cancels out
h=22cm
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a converging lens with a focal length of 20 cm and a diverging lens with a focal length of -38 cm are 78.0 cm apart. a 2.7-cm-tall object is 40 cm in front of the converging lens.
The image height for a converging lens with a 20 cm focal length and a diverging lens with a 38 cm focal length that are 78.0 cm apart is 1.35 cm. 40 cm are in front of the converging lens
And a 2.7 cm tall object is there. An optical lens that converges all light rays travelling through it is known as a converging lens. A converging lens main function is to concentrate and converge the incoming light rays from an object to create an image. Depending on how close an object is to the lens, the image may be enlarged or unchanged.
h = (-di/do)(-di2/do2)*height
h = (-38/38)(-(-15))/30 (2.7)
h = -1.35 cm
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The complete question is-
a converging lens with a focal length of 20 cm and a diverging lens with a focal length of -38 cm are 78.0 cm apart. a 2.7-cm-tall object is 40 cm in front of the converging lens. Calculate the image height. Express your answer to two significant figures and include the appropriate units.
An electromagnetic wave travelling in the x-direction has frequency of 2×10 14 Hz and electric field amplitude of 27 Vm −1. From the options given below, which one describes the magnetic field for this wave?
The magnetic field for this wave is
[tex]B(x, t)=(9*10^{-8}T )i sin[2\pi (1.5*10^{-8}x-2*10^{14}t )][/tex].
Electromagnetic Wave:
The oscillations between an electric field and a magnetic field produce waves known as electromagnetic waves or EM waves. In other words, magnetic and electric fields oscillate to form electromagnetic (EM) waves.
Given,
Frequency of the wave; [tex]f=[/tex] [tex]2*10^{14} Hz[/tex]
The amplitude of the Electric Field; [tex]E_{0} = 27 N/C[/tex]
We know that Maxwell's equation is given by,
[tex]\frac{E_{0} }{B_0} =c[/tex] .....................(1)
Where,
[tex]E_{0} =[/tex] The amplitude of the electric field
[tex]B_{0}=[/tex] The amplitude of the magnetic field
[tex]c=[/tex] The velocity of light = [tex]3*10^{8} N/m^{2}[/tex]
By solving equation (1), we get
[tex]B_{0} =\frac{27}{3*10^{8} }[/tex]
[tex]B_{0}=9*10^{-8}[/tex]
We know that,
Angular frequency; ω [tex]= 2\pi f[/tex]
The equation of the magnetic field can be given by
[tex]B_{0}sin(kx-\omega t) =B_{0}sin(2\pi (\frac{x}{\lambda}-ft ))[/tex]
[tex]B_{0}sin(kx-\omega t)=9*10^{-8} sin(2\pi (\frac{x}{\lambda}-2*10^{14} t))[/tex].
Hence,
The magnetic field for this wave is
[tex]B(x, t)=(9*10^{-8}T )i sin[2\pi (1.5*10^{-8}x-2*10^{14}t )][/tex].
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Question From what activity can you be sure that athletes find great utility?
Composing music
Raising children
Playing sports
Reading books
Playing sport is the activity in which you can be sure that athletes find great utility and is therefore denoted as option C.
Who is an Athlete?This is referred to a person who competes in one or more sports such as soccer, basketball etc that involve physical strength, speed, or endurance etc.
Therefore playing sports by an athlete will lead to an increase in utility as a result of them developing various skills and composure from it in the form of endurance, strength etc and various positions on the field which isn't applicable in reading books or composing music and is therefore the reason why it was chosen as the correct choice in this scenario.
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If a conductor is in electrostatic equilibrium near an electrical charge:A) The total charge on the conductor must be zero.B) The electric field inside the conductor must be zero.C) The charges on the conductor must be uniformly distributed.D) The sum of all forces between conductor and the electrical charge must be zero.
If a conductor is in electrostatic equilibrium near an electrical charge i.e. the correct option is, B) The electric field inside the conductor must be zero.
Because charge carriers can freely move within a conductor, when a charged or uncharged conductor is exposed to an external electric field, charge will flow until a steady state is reached, at which point the net flow of charge will cease. This state is known as electrostatic equilibrium. If the conductor is charged, the charges within it are rearranged, resulting in a zero net electric field inside the conductor. The net field inside the conductor again becomes zero if the conductor is polarized after being neutral.A neutral or charged conductor will typically achieve electrostatic equilibrium with a net zero electric field inside of it when it is kept close to an electric charge.The conductor in electrostatic equilibrium has characteristics such as a zero electric field inside and excess charges that are located on the surface. Therefore, the conductor's internal electric field must be zero.
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Which of the following is/are accurate? (select any that apply)
a muscle cell has many nuclei
the muscle cell membrane is called the sarcolemma
muscle cells have multiple mitochondria
a muscle cells has one myofibril
The accurate statements about muscle cells are:
the muscle cell membrane is called the sarcolemmamuscle cells have multiple mitochondriaWhat are the features of a muscle cell?A muscle cell also known as a myocyte is a cell that has differentiated with contractility ability.
The muscles differ according to the type of muscle.
There are two types of muscles; smooth muscles and skeletal muscles.
The features of skeletal muscle cells include:
they are long, cylindrical, multi-nucleated, and striatedThe features of smooth muscle cells include:
they contain thick and thin filaments and are non-striated.Muscles cells contain many mitochondria and myofibrils.
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An alien spaceship traveling at 0.550c toward the Earth launches a landing craft. The landing craft travels in the same direction with a speed of 0.790c relative to the mother ship (as measured by aliens on the mother ship). As measured on the Earth, the spaceship is 0.160 ly from the Earth when the landing craft is launched.
(a) What speed do the Earth-based observers measure for the approaching landing craft?
c
(b) What is the distance to the Earth at the moment of the landing craft's launch as measured by the aliens (mother ship)?
ly
(c) What travel time is required for the landing craft to reach the Earth as measured by the aliens on the mother ship?
yr
(d*) What travel time is required for the landing craft to reach the Earth as measured by Earth-based observers?
yr
(e*) What travel time is required for the landing craft to reach the Earth as measured by those on the landing craft?
yr
(a)The velocity (Xv) of the craft as measured from the earth is given as follows:
Vx = v¹x+v/1+( v¹x+v/c²) = 0.79∝ + 0.550c/1+(0.79c)(0.550c)
= Vx = 0.434c
Hence Vx is the velocity of the craft with respect to the mother ship and the velocity of the mother ship with respect to earth.
(b) distance between craft and earth, as measured by the mother ship as follows.
[tex]L0 = \sqrt[L]{\frac{1-V^{2} }{C^{2} } } = (0.160ly)\sqrt{1-(\frac{0.550}{c})^{2} }[/tex]
L0 = 0.1336ly.
(c)The velocity of craft with respect to earth as measured from the mother ship is as follows:
VCO = Vcmt + Vme
= 0.790 + 0.550 = 1.34c
Time taken by craft to land on earth as measured by the mother ship is as follows:
t = 0.1336ly/1.34 = 0.0997yr
(d) Time taken by craft to reach earth as measured from the earth is as follows:
t = 0.60ly/0.934c
t = 0.171yr
(e) Time taken by the craft to reach earth with respect to its rest frame is as follows:
to =[tex]\sqrt[t]{1-\frac{v^{2} }{c^{2} } }[/tex]
= 0.171 yr [tex]\sqrt{1-\frac{(0.934c)^{2} }{c^{2} } }[/tex]
to = 0.0610yr
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a person holds a book at rest a few feet above a table. the person then lowers the book at a slow constant speed and places it on the table. which of the following accurately describes the change in the total mechanical energy of the earth-book system?
The person exerts negative work on the book by applying a force in the direction opposite to its displacement, causing the total mechanical energy to decrease. Hence, option (D) is correct.
The given problem is based on the concept of mechanical energy. The mechanical energy is the energy of any object by virtue of its position or motion. And mathematically, it is expressed as the sum of kinetic energy and potential energy.
And the work completed is described as,
W = F * d
here,
W is the work done
F is the applied force
d is the displacement
The individual lowers the book in the provided situation at a slow manner. This means some work has been done by applying force in downward direction. This work will be negative, because it is opposite to the displacement. So, work done is negative.
And according to work energy concept,
Work done = Change in kinetic energy
Negative work accounts for negative value of kinetic energy. Which means kinetic energy is decreasing continuously. Additionally, if kinetic energy declines, mechanical energy will eventually follow.
The question is incomplete. The complete question is ' A. the total mechanical energy is unchanged, because there is no change in the book's kinetic energy as it is lowered to the table.
B. the total mechanical energy is unchanged, because no work is done on the earth-book system while the book is lowered.
C. the total mechanical energy decreases, because the person does positive work on the book by exerting a force that opposes the gravitational force.
D. The total mechanical energy decreases, because the person does negative work on the book by exerting a force on the book in the direction opposite to its displacement.'
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What is the weight of an 11 kg crate?
When completely filled with apples, the crate weighs 15 kg; when only 2/3 full, it weighs 11 kg; and when only 1/3 full (with only 1/3 of the crate's apples), it weighs 15-11=4 kg.
What does it mean to weigh?Definition of WEIGH in the Britannica Dictionary. She measures herself every morning in order to determine how heavy she is. 1. a [+ object]: to determine (someone or something's) weight. The bananas were weighed using a scale.
what are they Weight scales?To quantify weight or mass, one uses a scale or balance. These are also referred to as weight balances, mass balances, and scales of both mass and weight.
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in 1.8 hours a sailboat sailed 81 kilometers east across the sea at a constant velocity. what was the sailboats velocity?
The velocity of the sailboats at sailed a distance of 81 km is 12.5 m/s.
What is velocity?
Velocity is the rate of change of displacement.
To calculate the velocity of the sailboats, we use the formula below.
Formula:
v = d/t................. Equation 1Where:
v = Velocity of the sailboatsd = Distancet = TimeFrom the question,
Given:
d = 81 km = 81000 mt = 1.8 hours = 1.8×60×60 = 6480 sSubstitute these values into equation 1
v = 81000/6480v = 12.5 m/sHence, the velocity is 12.5 m/s.
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Consider a circuit where the input voltage source is connected in series with a capacitor, inductor and resistor. Which of the following statements are true: a. Voltage across the inductor must be continuous c. Voltage across the resistor in this circuit must be continuous c. Current through the capacitor must be continuous d. None of the above
Consider a circuit where the input voltage source is connected in series with a capacitor, inductor and resistor. Which of the following statements are true (A) Voltage across the inductor must be continuous.
Due to the physical property of electric charge, charged material experiences a force when it is exposed to an electromagnetic field. You could be electrically positive or negative. While like charges repel one another, opposite charges attract.
Because the charge (Q) is constant and equal, the capacitor's value alone
V = Q /C
determines the voltage drop across the capacitor. Lower capacitance values will produce higher voltages, but bigger capacitance values will provide smaller voltage drops.
The voltage drop across a capacitor is correlated with its charge and is uncharged, as opposed to a resistor where the voltage drop is proportional to the initial current and there is an initial current.
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One end of an object has a definite positive charge, which is an instance of _____ or a positive or negative state that reacts to an electric field.
One end of an object has a definite positive charge, which is an instance of inverse-square or a positive or negative state that reacts to an electric field.
A positive or negative energy is what?
A fundamental characteristic of some of the constituent particles, of which all matter is made, is electric charge.
Electric charges come in two different flavours.
(+) positive charges
adverse charge (-)
A negative charge is present when there are more electrons than protons in an item.
When an atom has more protons than electrons, it has a positive charge.
Protons have a positive charge, whereas electrons have a negative charge.
The coulomb is the unit of charge (C).
Similar charges repel one another.
Similar charges are drawn to one another.
The positive charge produces an electric flux.
The negative charge is the point where electric flux ends.
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On a _________ periapical image, the nasal fossa appears as a large ______________ area located above the roots of the maxillary incisors.
a. maxillary; radiopaque
b. maxillary; radiolucent
c. mandibular; radiopaque
d. mandibular; radiolucent
On a maxillary periapical image, the nasal fossa appears as a large radiolucent area located above the roots of the maxillary incisors. there is option b is correct.
It appears as a tiny, ovoid or circular radiolucent region between the roots of the maxillary central incisors on an anterior maxillary periapical imaging. Periapical radiographs allow for the visualization of the maxillary tuberosity. Periapical radiographs do not show the mastoid process. The term "internal oblique ridge" or "mylohyoid line" refers to this anatomical characteristic. The submandibular fossa often manifests as an oval-shaped radiolucent region beneath the dentition's roots in the mandible's posterior body. refers to objects that are less dense and can be penetrated by the x-ray radiation. In the radiographic picture, radiolucent structures appear dark or black. Structures that are thick and impede the passage of x-rays are said to be radiopaque.
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Explain how magnetic stripes on the ocean floor are evidence for sea-floor spreading
Answer:
When the Earth's magnetic field reverses, a new stripe, with the new polarity, begins. Such magnetic patterns led to recognition of the occurrence of sea-floor spreading, and they remain some of the strongest evidence for the theory of plate tectonics.
Explanation:
The elevator descends with an acceleration of 0.9 m/s². Find how much a 95 kg person weighs in it at the moment of descent.
Scientists are now targeting Europa, one of Jupiter's moon, as a likely site for searching elementary life-forms because
Jupiter's moon Europa is regarded as one of the solar system's most promising locations to look for indications of modern life.
The geophysical characteristics of Europa, particularly the potential existence of an ocean of subglacial water, raise the prospect that human life could exist on or below the surface. The solar system's frozen moon Europa of Jupiter may provide the greatest promise for discovering modern settings conducive to life outside of Earth. Scientists have made progress in their quest to determine whether extraterrestrial life actually does exist. The best contender for alien habitability in our solar system is Jupiter's moon Europa. The hypothesis that life could exist in the inner ocean of Jupiter's moon Europa is supported by a new model created by NASA scientists.
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which of the following observations indicates that conditions on mars may have been suitable for life in the past?
Answer:
Liquid water one flowed on mars,the existence of nutrients,and the previous discovery of a past magnetic field that protected the planet from cosmic and solar radiation.
the bitewing tab is a heavy paperboard tab or loop fitted around a periapical film or sensor and used to stabilize the receptor during exposure. (2) the periapical receptor is oriented in the bite loop so that the tab portion extends from the white side (tube side) of the film or sensor.
the bitewing tab is a heavy paperboard tab or loop fitted around a periapical film or sensor and used to stabilize the receptor during exposure. true
What is stabilize?
to stop changing and fix something, especially to prevent it from getting worse, or to induce something to stop changing and fix it: These drugs reduce blood pressure and calm your heart rate.
the periapical receptor is oriented in the bite loop so that the tab portion extends from the white side (tube side) of the film or sensor.True
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A 4kg blob of putty moving at 8 m/s slams into a 12 kg blob of putty at rest. What is the velocity of the two stuck- together blobs immediately after colliding?
The speed of the to stick together blobs immediately after colliding will be 2m/s.
How to solve?Given that:
Mass of first blob = 4kg = m1
Velocity of blob = 8m/s = v1
Mass of second blob = 12kg = m2
Velocity of blob = 0m/s = v2
To find:
Final velocity = Vf
Formula to be use:
(m1*v1) + (m2*V2) = Vf(m1 + m2)
(4*8) + (12*0) = Vf(4+12)
32 + 0 = Vf(16)
32 = Vf(16)
Vf = 2m/s
So the speed of two blobs immediately after colliding = 2m/s
How do we arrive at the V1 and V2 equations for elastic collisions?V1: (m1-m2/m1+m2)
u1 + (2m2/m1+m2)
u2 V2: ( 2m1/m1+m2) u1 + (m2-m1/m1+m2) u2 Assume that mass 1 has an initial velocity of u1, a final velocity of v1, a mass 2 beginning velocity of u2, and a mass 2 final velocity of v2.
What in physics does m1v1 m2v2 mean?V1 stands for the volume of stock solution required to create the new solution. M1 = Stock solution concentration. The total volume of the solution is V2.
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Approximately, ___ municipal solid waste landfills in the United States combust landfill gas to generate heat and electricity
400
Approximately, 400 tons of municipal solid waste landfills in the United States combust landfill gas to generate heat and electricity
What is municipal waste?We know that municipal waste has to do with the waste products that can be obtained from the activities that go on in the city. the magnitude of the municipal waste that is generated in a place would have a lot to do with the population of the area as well as the industrial saturation of the area.
This is the reason why the areas that have less population and the industries that are there are not so much do not expirience a lot of pollution and do not have a large amount of waste water that goes out as sewage.
The solid wastes that are generated in the United States is just as large as the sewage that is generated in the united states and calls for a very urgent attention.
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an automobile of mass m is proceeding around a highway curve of 40 meter radius. The surface of the roadway is horizontal, and the coefficient of friction between the tires and roadway is 0.50. The max speed with which the car can round the curve without slipping isa. 6.3 m/sb. 4.9 m/sc. 9.8 m/sd. 14.0 m/se. 19.6 m/s
The max speed with which the car can round the curve without slipping is 14 m/s
What is friction?
Friction is a force that develops when objects rub against one another. The ability of the tyre to "push" off the road and propel the vehicle is due to the frictional force between the road and tyre.
The radius of the curve,r = 40m
The coefficient of friction μ = 0.5
From the Newton's law, we have, μmg = mv^2/r
in terms of speed we get, v = √μrg
v = √(0.5)(40m)(9.8m/s^2)
= 14 m/s
Therefore the max speed with which the car can round the curve without slipping is 14 m/s
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Match the astronomical distance measuring techniques with their approximate ranges: Triangulation. distances up to about 1000 light years.
Spectroscopy. distances up to about 10,000 light years.
What is astronomical distance?Astronomical distance is the measurement of space between objects in the universe. It is usually measured in light years, which is the distance light travels in a year. Astronomical distance is incredibly vast and hard to comprehend, as it is measured in trillions of miles. Astronomical distance is used to measure distances between objects in the universe such as stars, galaxies, and planets. Astronomical distances are also used to measure the size of the universe, as well as the age of galaxies and stars. Astronomical distances can be measured using advanced instruments such as telescopes and spectroscopes. Astronomical distances are essential for understanding the structure of the universe and the evolution of galaxies and stars.
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Two blocks on a surface of negligible friction are attached together by a spring, as shown in the figure above. The mass of block 1 is MM, and the mass of block 2 is 2M. Block 1 is initially moving toward block 2, which is at rest. The spring compresses and decompresses in a repeated motion as the two blocks slide to the right. Which of the following statements best describes the speed of the center of mass of the two-block system?
In the absence of an external force, the total linear momentum of the system maintains conservation, indicating that the speed of the system's center of mass is constant.
This is because the spring force between the masses acts as an internal force between the two masses.
The product of an object's mass, m, and velocity, v, is known as linear momentum, and it is a vector quantity. In order to express it and refer to momentum informally, the letter "p" is utilized. You should be aware that a body's momentum always points in the same direction as its velocity vector. Because it is a conserved quantity, the overall momentum of a system is always constant. Linear momentum is measured in kg/s.
The total linear momentum prior to an object's interaction and the total linear momentum following that interaction is identical. Any system of objects that is subject to no net external force has a constant total linear momentum.
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dr. bronfman has administered her new 100-item test of abstract reasoning to a large sample of students. she is presently comparing their scores on the odd-numbered questions with those on the even-numbered questions in an effort to
Determine the test's reliability. Test-retest reliability is a metric of dependability that is acquired by giving the same test to a set of people twice over time.
How long should reliability tests be repeated?Although the ideal testing interval will vary depending on the construct being assessed, its stability over time, and the target population, several research have demonstrated that the target time of 2 weeks is the most frequently advised interval [15].
Interrater reliability between tests is it?The degree to which various raters and observers provide consistent estimates of the same occurrence is measured by inter-rater or inter-observer reliability. Test-Retest Reliability: Used to evaluate a measure's consistency across time.
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this is a record of climate from 1880 and on with measures of land and ocean temperatures around the world increasing over time.
From the 1880s to the 1910s, the yearly average worldwide temperature was roughly 13.7 °C (56.7 °F). The temperature increased by around 0.1 °C (0.18 °F) per decade from the 1920s through the 1940s.
The average worldwide temperature then remained stable until the 1980s at about 14.0°C (57.2°F). The total land and ocean temperature has risen at an average pace of 0.14 degrees Fahrenheit (0.08 degrees Celsius) every decade since 1880, according to NOAA's 2021 Annual Climate Report; however, the average growth rate since 1981 (0.18°C / 0.32°F) has been more than double that rate. NASA utilizes the years 1951–1980 as a baseline to track changes in the earth's temperature. Since the start of modern recordkeeping in 1880, the last eight years have collectively been the warmest on record. The worldwide temperature record is comprised of these annual temperature measurements.
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human activities, such as agriculture, can require altering the land. i. identify an environmental problem associated with large-scale intensive agriculture on soil.
Intensive agriculture leads to ecosystem loss and contributes to global warming.
Intensive agriculture is a farming method that uses large amounts of labor and investment to increase the yield of the land.
Human beings form an integral part of the environment and have the largest ecological footprint.The environment has suffered for thousands of years due to human activity.Intensive agriculture is generally aimed at feeding a large population of people, however, this method has contributed as one of the biggest threats to the global environment as it leads to ecosystem loss and global warming.It is responsible for 80 percent of tropical deforestation and the emergence of new parasites and the reappearance of parasites that were once under control.It reduces beneficial plants and insects and depletes and degrades the soil on which they depend.Thus intensive agriculture results in soil erosion followed by the genetic erosion of livestock and crop species worldwide.
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a concentration of 400 ppm is the safe soil lead concentration threshold. the scientist used method a and found the soil sample had a lead concentration of 1358 ppm. write a conclusion about the lead concentrations in this sample of soil. in your conclusion include one recommendation from the table.
The lead pollution can be remediated by the appllication of the approppiate reagents.
What is the recommendation?We know that we need to always consider the threshold concentration of pollution as we are looking at the safety of the environment
Now we are told that the safe concentration of the lead must not be more than 400 ppm. Above that concentration, the effects may be quiet fatal.
There should be spirited attempts to remediate the soil by the use different methods so that the soil can become good again for the growing of crops.
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The __________ field of the earth is produced in part by the flow of hot liquid iron near the earth's core.
The magnetic field of the earth is produced in part by the flow of hot liquid iron near the earth's core.
What is a magnetic field?A magnetic field is defined as the field that is being created or produced by a magnetic material which permits the action of magnetic force.
The innermost part of the earth is made up of the earth core which is surrounded by an outer part.
The outer core of the earth is mostly made up of liquid iron and nickel.
Therefore, the magnetic field of the earth is produced in part by the flow of hot liquid iron near the earth's core.
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landings at the top and bottom of stairs should be at least equal in length to the of the stairway.
In cases when the stairway is straight, the width of the landing in the direction of travel must at least match the stair's width and cannot be greater than 1219mm.
The four main axes are north, south, east, and west. A map is a representation or drawing of the entire or a portion of the surface of the earth done to scale and on a flat surface. A spherical shape, however, cannot be totally flattened. Distance, direction, and symbol are the three elements that make up a map.
Most maps have an arrow with the letter "N" on them in the upper right-hand corner. North is indicated by this arrow's orientation. It is referred to as the north line. You can determine which direction is east, west, or south once you know which way is north. The four main axes are North, South, East, and West.
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If a cable originates inside one building and leaves the building, the landlord loses control of that cable. T or F?
It is true to say that If a cable originates inside one building and leaves the building, the landlord loses control of that cable.
Cable originating from one building to another building will have total control by the landlord from which the cable have passed. Since cable passes from one building to another building in that case some part of cable is not inside the building due to that control over the cable is distributed between more than one type of landlords .Worms can be spread through means other than direct network .Now, when it passed between the two building, in that case if one landlord did some changes in some part of cable then that change will not be controlled by the landlord who live in other building.
Hence, given statement is true.
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one of the strongest emission lines observed from distant galaxies comes from hydrogen and has a wavelength of 122 nm (in the ultraviolet region).
(a) The galaxy moves with a velocity of 0.8 c away from us.
(b) When the galaxy moves towards us we observed that the wavelength of the line is 40.67 nm.
We know that,
The relativistic Doppler effect when the galaxy is moving away from us
In this case, when the source moves away from the observer its frequency ([tex]f[/tex]) is lower than the emitted frequency ([tex]f_{0}[/tex]) and the preceding wavelength ([tex]\lambda[/tex]) is higher than the emitted wavelength ([tex]\lambda_{0}[/tex]).
[tex]f=f_{0} \sqrt{\frac{1-\frac{u}{c} }{1+\frac{u}{c} } }[/tex]
[tex](\frac{\lambda_{0} }{\lambda})^{2} = \sqrt{\frac{c-u}{c+u} }[/tex]
Given that
[tex]\lambda_{0} =122 nm\lambda=366nm[/tex]
So
[tex](\frac{122}{366} )^{2} =\frac{c-u}{c+u} \frac{1}{9} = 8cu=0.8c[/tex]
Where c is the velocity of light it is equal to [tex]3*10^{8} m/s[/tex].
So when the galaxy moves towards us we observed that the wavelength of the line is 40.67nm.
(b) When the galaxy moves towards us its wavelength is shorter than the emitted wavelength.
The expression of the wavelength in this case is given by
[tex]\frac{\lambda _{0} }{\lambda } =\sqrt{\frac{c-u}{c+u} }[/tex]
= 40.67 nm
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