The speed of light in a medium, such as plastic, is given by the equation v = c/n, where v is the speed of light in the medium, c is the speed of light in vacuum (approximately 3 x 10^8 m/s), and n is the refractive index of the medium. To determine the speed of red light in plastic, the refractive index of the specific plastic material must be known.
The wavelength of light in a medium can be determined using the equation λ = λ0/n, where λ is the wavelength of light in the medium, λ0 is the wavelength of light in vacuum, and n is the refractive index of the medium. Given that the red laser has a wavelength of 633 nm (633 x 10^-9 m) in vacuum, the wavelength of red light in plastic can be calculated using the refractive index of the plastic material.
In conclusion, to determine the speed and wavelength of red light in plastic, the specific refractive index of the plastic material needs to be known.
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list at least three differences between storms and atmospheric circulation on jupiter compared to those phenomena on earth.
Jupiter's storms and atmospheric circulation differ from those on Earth in their scale, composition, and dynamics.
Jupiter's atmospheric circulation and storms are much larger and more intense than those on Earth. For example, the Great Red Spot, a persistent storm on Jupiter, is over twice the size of Earth.
Jupiter's atmosphere is primarily composed of hydrogen and helium, while Earth's atmosphere is composed mostly of nitrogen, oxygen, and trace amounts of other gases. This difference in composition leads to different behaviors and processes in the atmosphere.
The energy source driving atmospheric circulation on Jupiter is primarily internal, from the planet's internal heat, while on Earth it is primarily driven by solar radiation. This leads to different patterns of circulation and different types of storms.
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A certain simple pendulum has a period on the earth of 1.70s . What is its period on the surface of Mars, where g=3.71m/s^2?
The period of the pendulum on the surface of Mars, where g = 3.71m/s², would be the same as the period on Earth, 1.70s. The pendulum on the surface of Mars has a period of roughly 3.31 seconds, according to our calculation of this expression.
A basic pendulum's period is determined by the equation T = 2(L/g), where T is the period, L is the pendulum's length, and g is the acceleration brought on by gravity.
L = (T/(2))2g can be solved for on Earth with a period of 1.70s by rearranging the equation.
Using the same equation and the Mars surface gravity, g = 3.71m/s2, we can now get the period on Mars' surface: T\(_{mars}\) = 2(L/g\(_{mars}\)).
The equation T\(_{mars}\) = 2(((T/(2))2g)/(g\(_{mars}\))) is obtained by substituting the expression for L and the surface gravity of Mars.
T\(_{mars}\) = T(g/g_Mars), to simplify the formula.
T\(_{mars}\) = 1.70s(9.81m/s2 / 3.71m/s) is the result of plugging in the data. The pendulum on the surface of Mars has a period of roughly 3.31 seconds, according to our calculation of this expression.
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How do you find the image size in a concave mirror?
The concave mirror is represented by a vertical line MMl. The principal axis is represented by a horizontal line drawn on the PC. 1 mm. 12 mm (focal length: 12 cm); I Image position.
Here, u = 25 cm for the object distance (To the left of the mirror)
Also, the focal length is f = 20 cm (It is a concave mirror)
What is the size of the image in a concave mirror?
The size of image formed by a concave mirror is same as the size of object.
Use the magnification of a mirror formula to obtain the size of the object. Accordingly depict its nature using the sign of the image height. Where v is the image distance u is the object distance and f is the focal length.
However, if we increase the distance between the object and the mirror then the size of the image reduces and a real and inverted image is formed. The image formed by the concave mirror can be small or large and can be real or virtual.
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The concave mirror is represented by a vertical line MMl. The principal axis is represented by a horizontal line drawn on the PC. 1 mm. 12 mm (focal length: 12 cm); I Image position.
Here, u = 25 cm for the object distance (To the left of the mirror)
Also, the focal length is f = 20 cm (It is a concave mirror)
What is the size of the image in a concave mirror?
The size of image formed by a concave mirror is same as the size of object.
Use the magnification of a mirror formula to obtain the size of the object. Accordingly depict its nature using the sign of the image height. Where v is the image distance u is the object distance and f is the focal length.
However, if we increase the distance between the object and the mirror then the size of the image reduces and a real and inverted image is formed. The image formed by the concave mirror can be small or large and can be real or virtual.
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Mercury has a radius of 2.43x10^6 m, and a mass of 3.2x10^23 kg, what is Mercury's acceleration due to gravity?
I think that you need the gravitational acceleration of mercury
so we will use Newton's gravitational law :
gravitational acceleration = \(\frac{G * m}{r^{2} }\)
G is the gravitational constant = G = 6.673×10^-11 N m^2 kg^-2
after substitution :
6.673×10^-11 * 3.2x10^23 / (2.43x10^6)^2
using calculator :
gravitational acceleration of mercury = 3.61625 m/s^2
pls give me brainliest
Unpolarized light is passed through two successive polaroid filters, each with its transmission axis at 45.0° to the preceding filter. what percentage of light energy gets through?
The amount of light that passes through the three Polaroid filters in order is 12.5%.
Does "light" imply "not heavy"?
Light is an adjective that describes something that isn't weighty, cumbersome, or depressing. A conversation topic or a music piece are both examples of things that can be considered light. The weight is light even though the trip is long, for instance.
Angle of transmission axis; θ = 45°
Formula for intensity of light from first polarizer is;
I₁ = ¹/₂I₀
Formula for intensity of light from second polarizer is;
I₂ = I₁cos²θ
Formula for intensity of light from third polarizer is;
I₃ = I₂cos²(90 - θ)
Combining the 3 equations;
Put ¹/₂I₀ for I₁ in second formula to get;
I₂ = ¹/₂I₀cos²θ
Put ¹/₂I₀cos²θ for I₂ in third formula to get;
I₃ = ¹/₂I₀cos²θ*cos²(90 - θ)
Plugging in 45° for θ gives;
I₃ = ¹/₂I₀cos²45*cos²(90 - 45)
⇒ I₃ = ¹/₂I₀cos²45*cos²45
⇒ I₃ = ¹/₂I₀cos⁴45
Now, cos 45 in surd form is 1/√2. Thus;
I₃ = ¹/₂I₀(1/√2)⁴
I₃ = ¹/₂I₀(¹/₄)
I₃ = ¹/₈I₀
I₃/I₀ = ¹/₈
I₃/I₀ = 0.125
In percentage form, we have;
I₃/I₀ = 12.5%
Therefore, the amount of light that passes through the three Polaroid filters in order is 12.5%.
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Assertion: MnO2 + 4 HCl --- MnCl2 + Cl2 + 2 H2O is redox reaction.
Reason : MnO2 oxides HCl to Cl2 and gets reduced to MnCl2
we can conclude that the assertion and reason are true and are related to each other in the given statement.
The given equation MnO2 + 4 HCl → MnCl2 + Cl2 + 2 H2O is a redox reaction. Here’s why: Assertion: MnO2 + 4 HCl → MnCl2 + Cl2 + 2 H2O is a redox reactionThis assertion is true because the given chemical equation represents a redox reaction. In a redox reaction, one reactant gets oxidized, and the other gets reduced.
In this equation, MnO2 (manganese dioxide) gets reduced, and HCl (hydrochloric acid) gets oxidized. Reason: MnO2 oxidizes HCl to Cl2 and gets reduced to MnCl2
This reason is true because, in the given equation, MnO2 reduces to MnCl2, which means it is gaining electrons and, hence, getting reduced. On the other hand, HCl oxidizes to Cl2, which means it is losing electrons and, hence, getting oxidized. The process of oxidation and reduction is a redox reaction. Hence, the reason for the assertion is correct.
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6. A person starts at rest and accelerates at a uniform rate of at 3.2 m/s2 for 3.0 seconds. What distance
does this person cover in that time?
Answer:
14.4m
Explanation:
u = 0 i.e it started from rest
acceleration (a) = 3.2m/s2
time taken (t) = 3.0s
Using the second equation of motion:
s = ut + 1/2at2
s = 0(3.0) + 1/2(3.2)(3.0)2
s = 1.6(9.0)
s = 14.4m
hence the distance covered within that time is 14.4m.
sulfur and oxygen can react to form both sulfur dioxide and sulfur trioxide in sulfur dioxide there are 32.06 grams of sulfur and 32 grams of oxygen in sulfur dioxide there are 32.06 grams of sulfur are combined with 48 grams of oxygen
a. what is the ratio of the weights of oxygen that combine with 32.06 g of sulfur ?
b. How do these data illustrate the law of multiple proportions?
Answer:
a. 2:3
b. The data illustrates the law of multiple proportions by showing that the the masses of oxygen that reacts with a fixed mass of sulfur are in a ratio of small whole numbers
Explanation:
The weight of oxygen that combines with 32.06 grams of sulfur in sulfur dioxide = 32 grams
The weight of oxygen that combines with 32.06 grams of sulfur in sulfur trioxide = 48 grams
a. The ration of the weights of oxygen that combine with 32.06 g of sulfur = 32:48 = 2:3
b. The law of multiple proportions states that when two elements are able to interact chemically to form more than one compound, then the (different) weights of one of the element that combines with a fixed weight of the other element are in small whole number ratios
The data demonstrates the law of multiple proportions by showing that the ratios of the weights of oxygen that combine with a fixed weight of sulfur to form sulfur dioxide and sulfur trioxide is in the ratio of 2 to 3 which are small whole number ratios
A dog sits on a flat surface. If the dog has a mass of 13 kg, what is the normal force acting on it?
85 N
13 N
127 N
41 N
Answer:
127
Explanation:
f(n)=mg
(13)*(9.81)
127.4N
Two blocks A and B of masses 5 kg and 1 kg are connected with the help of massless strings
The system is just at the verge of slipping. The coefficient of static friction between the block A and surface below it is
Answer:
The coefficient of friction between all contact surfaces is 0.4. The force, necessary to move the block B with constant velocity, will be (g = 10 m/s)
The coefficient of friction between all contact surfaces is 0.4. The force, necessary to move the block B with constant velocity, will be (g = 10 m/s).
In which condition block B moves?Two blocks A and B of masses 5 kg and 1 kg are connected with the help of massless strings and the system is just at the verge of slipping. The coefficient of static friction between the block A and surface below it is necessary to move the block B.
Static friction is the friction that exists between two surfaces that are not trying to move over each other and which must be overcome before one object starts moving the other.
Two blocks are static equilibrium indicates that the force acting on both blocks is equal.
The frictional force acting on block A is calculated as follows:
Frictional force = coefficient of static friction * normal reaction
Normal reaction on Block A = 30 * 9.8
The coefficient of static friction between block A and the surface = 0.55
Frictional force = 30 * 9.8 * 0.55
Force on Block B = 161.7
Mass of Block B = 161.7 / 9.8
Mass of Block = 18 kg
Therefore, The coefficient of friction between all contact surfaces is 0.4. The force, necessary to move the block B with constant velocity, will be (g = 10 m/s).
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A vector a has components a x equals -5. 00 m in a y equals 9. 00 meters find the magnitude and the direction of the vector
A vector has two components: a magnitude and a direction. Magnitude is the length of the vector, and direction is the angle that the vector makes with the x-axis. We can use the Pythagorean theorem to find the magnitude of the vector a.Magnitude of vector a :
\(a = √(a_x² + a_y²)a_x = -5.00 ma_y = 9.00 m\)
Substituting the values in the formula, we get;
\(a = √((-5.00 m)² + (9.00 m)²)a = √(25.00 m² + 81.00 m²)a = √1066 m²a = 32.7 m\) (rounded to one decimal place)
Now, to find the direction of the vector, we can use trigonometry. The direction of the vector a is given by the angle that the vector makes with the positive x-axis. We can find this angle using the tangent function.
\(tan θ = a_y / a_xtan θ = (9.00 m) / (-5.00 m)θ = -60.3°\) (rounded to one decimal place)The angle is negative because it is measured clockwise from the positive x-axis. Therefore, the magnitude of the vector a is 32.7 m, and the direction of the vector is 60.3° clockwise from the positive x-axis.
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Explain what is happening in this
induction example.
Answer:
An electrical field duh
Explanation:
None needed self explanitory
How do you find the instantaneous velocity on a position-time graph?
A. Find the slope of the overall trend line.
B. Find the slope between any two points.
C. Find the slope of the tangent at any point.
D. Find the slope of only horizontal portions.
Answer: The answer is C. Find the slope of the tangent at any point.
PLS HELP MEH!!!!
Sound travels fastest in
a) air
b) water
c) glass
d) diamond
WILL MARK BRAINLIEST IF ANSWER
Answer:
hope this helps
Explanation:
Of the three phases of matter (gas, liquid, and solid), sound waves travel the slowest through gases, faster through liquids, and fastest through solids
so your answer would be B.
Two identical cylinders at the same pressure contain the same gas. if cylinder a contains three times as much gas as cylinder b, which cylinder has the higher temperature?
By ideal gas theory, cylinder b has the higher temperature.
We need to know about the ideal gas theory to solve this problem. The ideal gas can be represented by
P . V = n . R . T
where P is the pressure, V is volume, n is the number of molecules, R is the ideal gas constant and T is temperature.
From the question above, we know that
Pa = Pb = P
na = 3nb
Find the temperature of the cylinder a
P . V = n . R . Ta
Ta = P . V /( na . R )
Substitute na
Ta = P . V /( (3nb) . R )
Ta = (1/3) x (P . V /( (nb . R ))
Find the temperature of the cylinder b
P . V = n . R . Tb
Tb = P . V /( nb . R )
The cylinder a temperature is 3 times smaller than the temperature in cylinder b.
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charged particles a and b experience a static electric force of f. if the distance between the charged particles triples, then the static electric force becomes
If the distance between charged particles A and B triples, the static electric force between them will decrease by a factor of 1/9.
The static electric force between two charged particles is inversely proportional to the square of the distance between them. Mathematically, the relationship can be expressed as: F ∝ 1/r^2
Where F is the static electric force and r is the distance between the charged particles.
When the distance triples (r' = 3r), we can calculate the ratio of the new force (F') to the original force (F) as:
F'/F = (1/r'²) / (1/r²) = (r^2) / (r'²) = (r²) / (3r)² = 1/9
Therefore, the static electric force between the charged particles A and B becomes 1/9 of its original value when the distance between them triples.
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a bead slides without friction around a loopthe-loop. the bead is released from a height of 22.2 m from the bottom of the loop-theloop which has a radius 8 m. the acceleration of gravity is 9.8 m/s 2 . what is its speed at point a ? answer in units of m/s.
The speed of a bead at point A is 11.02m/s
Take a look at the illustration bellow.
From the illustration and question, we know that:
h = 22.2m
r = 8m
g = 9.8 m/s²
h of A = 2r = 16m
Based on the Conservation of Energy, the total of mechanical energy in the system is eternal for all of the time.
Hence, the total of mechanical energy of the bead when it was just released from the top of the loop-the-loop is equal to its mechanical energy when it reaches point A.
When the bead is stil on the top of the loop-the-loop, all of its mechanical energy is in a form of potential energy. However some of its energy then change into a kinesthetic energy when it reaches point A.
Assume that the original position of the bead is the first point and point A is the second point.
We could make an equation from this concept:
Em1 = Em2
Ep1 + Ek1 = Ep2 + Ek2
Because the bead has no movement before sliding down the loop-the-loop, it has no kinesthetic energy at point 1. Hence:
Ep1 + 0 = Ep2 + Ek2
Ep1 = Ep2 + Ek2 ... (i)
We know from the energy formulas that:
Ep = m×g×h
Ek = mv²
2
The equation (i) could be rewritten as:
mgh1 = mgh2 + mv2²
2
Eliminates all of the m elements:
gh1 = gh2 + v2²
2
v2² = 2g (h1-h2)
v2² = 2 × 9.8 × (22.2 - 16)
v2² = 121.52
v2 = 11.02m/s
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What is the acceleration of a 25 kg object when a 200 N force is applied to it?
Answer: 8
Explanation: 200/25=8
Help pls I need 20 characters so yh
Please answer asap
Question 12 6 pts 3.7 kg/s of a mixture of oxygen and carbon dioxide containing 90% of oxygen by mole, undergoes a steady flow, isobaric heating process from an initial temperature of 50°C to a final temperature of 120°C. Using the ideal gas model, determine the heat transfer for this process? Express your answer in kW.
Using the ideal gas model, the heat transfer for the given process is 237.53 kW.
The formula for heat transfer is given by the first law of thermodynamics. The first law of thermodynamics is expressed mathematically as follows;
ΔU = Q - W
Where ΔU is the change in internal energy of the system, Q is the heat transfer, and W is the work done by the system.
Since the process is isobaric, then work done = PΔV = P(V2 - V1), where P is the pressure of the system, V1 is the initial volume, and V2 is the final volume.
In this case, since the mass flow rate is given, we can use the formula Q = mCp(T2 - T1)
Where m is the mass flow rate and Cp is the specific heat capacity of the mixture.
Substituting the given values into the above equation,
Q = mCp(T2 - T1) = 3.7 × Cp × (120 - 50) = 3.7 × Cp × 70
Since the mixture contains oxygen and carbon dioxide, we need to find the average specific heat capacity of the mixture. The average specific heat capacity, Cpa can be expressed as follows;
Cpa = (CpO₂ × xO₂ + CpCO₂ × xCO₂)
Where CpO₂ and CpCO₂ are the specific heat capacity of oxygen and carbon dioxide respectively, and xO₂ and xCO₂ are the mole fraction of oxygen and carbon dioxide respectively.
Since the mixture contains 90% oxygen by mole, then the mole fraction of oxygen is 0.9, and that of carbon dioxide is 0.1.
Substituting the specific heat capacity values;
CpO₂ = 0.919 kJ/kg K, and CpCO₂ = 0.846 kJ/kg K,
Cpa = (0.919 kJ/kg K × 0.9 + 0.846 kJ/kg K × 0.1) = 0.910 kJ/kg K
Substituting the value of Cp into the equation Q = 3.7 × Cp × 70, we have;
Q = 3.7 × 0.910 × 70 = 237.53 kJ/s = 237.53 kW
Therefore, the heat transfer for the process is 237.53 kW.
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Distinguish between heat and work in terms of energy
Answer:
Heat is the energy associated with the random motion of particles, while work is the energy of ordered motion in one direction. Therefore heat is "low-quality" energy and work is "high-quality" energy, and this supports the entropy statement of the Second Law.
Explanation:
Jenny and Fred both play a long note on their trombones. A stationary observer hears the sound increasing and decreasing repeatedly in loudness. Which of these must be true?
A.The sound waves from the two trombones have slightly different frequencies.
B. The sound waves from the two trombones have the same frequency.
C. The sound waves from the two trombones have slightly different amplitudes.
D. The sound waves from the two trombones have the same wavelength.
E. The sound waves from the two trombones have slightly different velocities.
Answer:
A.The sound waves from the two trombones have slightly different frequencies.
Explanation:
This is because, a difference in frequency of waves from two different sources would result in either constructive or destructive interference of the waves. Thereby, causing the observer to hear the sound increasing or decreasing.
Answer:
A.The sound waves from the two trombones have slightly different frequencies.
How are infrared waves and radio waves similar? How might you use each?
Answer:
They are both eletro-magnetic waves, they are both outside of the range humans can see with our eyes. Infrared waves can can carry enough energy to give heat to objects. There is a lot of Infrared light that is put out by a fire and we feel that as the heat. Radio waves can be used to carry other signals like when we listen to the radio.
Explanation:
Answer:
Both infrared and radio waves are longer than visible light and are not considered harmful to humans.Infrared light is how remote controls communicate with electronics like televisions and stereos, while radio waves are how cell phone signals are transmitted.
Explanation:
This is what my teacher wrote as the answer lol.
On a day that a total solar eclipse is occurring, would it be visible everywhere around earth?.
On a day that a total solar eclipse is occurring, it would not be visible everywhere around the earth.
It would only be visible to a particular region of the earth.
Total solar eclipse is an astronomical event that occurs when the Moon passes between the Sun and the Earth. It casts its shadow over the earth, creating a temporary darkness. In order for an observer to see the total solar eclipse, the observer must be within the path of the moon’s shadow, which is called the umbra. The area that the eclipse is visible is known as the path of totality.
During a solar eclipse, the area that experiences a total eclipse can be as small as a few miles wide or as wide as 100 miles. So, it’s not visible everywhere around the earth.
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Which planets are terrestrial? select three options. jupiter mars mercury uranus venus
Mars, mercury, and venus are the planets that are terrestrial planets.
What is the terrestrial planet?A terrestrial planet is one that is predominantly made up of silicate rocks or metals. The inner planets nearest to the Sun, are Mercury, Venus, Earth, and Mars, as terrestrial planets within the solar system.
Mars, mercury, and venus are the planets closest to the sun.
Hence mars, mercury, and venus are the planets that are terrestrial planets.
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a girl standing on a bridge throws a stone vertically upwards at 6 ms⁻1. it hits the water below the bridge after 2 seconds. find the speed at which the stone hits the water and the initial height of the stone
The speed at which the stone hits the water is 13.6m/s and the initial height of the stone is 7.6m.
Speed of stone as it hits the waterInitial velocity of stone = 6 ms⁻¹
At the maximum height, the final velocity, v = 0
Acceleration of the stone, g = 9.8 ms⁻²
Time taken to reach maximum height = t₁
Using, v = u + gt₁t₁ = v - u/g
since the stone is travelling upwards, g = -9.8 m/s⁻²
t₁ = 0 - 6/-9.8
t₁ = 0.61 s
Time take to fall from maximum height, t = 2 - 0.61s
Time take to fall from maximum height = 1.39s
Calculating the final velocity using the formula, v = u + gtwhere u = 0 m/s
v = 0 + 9.8 * 1.39
v = 13.6 m/s
Initial height of stoneInitial height of stone = Height of bridge, H
Time taken by the stone to fall down from height, H in water, t = 2s
Initial velocity of stone = 6 ms⁻¹
Acceleration of the stone, g = 9.8 ms⁻²
Height of the bridge, H = -ut + gt²/2Initial velocity is negative since it is against gravityH = -6 * 2 + 9.8 * 2² /2
H = 7.6m
Therefore, the speed at which the stone hits the water is 13.6m/s and the initial height of the stone is 7.6m
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Which object has unbalanced forces acting on it?
A: a dog running at 1 m/s
B: a car accelerating at 4.5 m/s 2
C: an airplane flying at 225 m/s
D: a windmill blade spinning at 50 m/s
Answer:
B: a car accelerating at 4.5 m/s 2
Explanation:
what distinguishes the orbit of pluto from that of the eight major planets of the solar system?
Pluto's orbit is much more eccentric and inclined compared to the orbits of the eight major planets in the solar system. This means that Pluto's orbit is more elliptical and tilted relative to the plane of the solar system, while the orbits of the major planets are generally more circular and on the same plane.
First, Pluto's orbit is much more eccentric (elongated) than the orbits of the other planets. This means that its distance from the Sun varies more dramatically over the course of its orbit. While the other planets have nearly circular orbits, Pluto's orbit is more oval-shaped.
Second, Pluto's orbit is also more inclined (tilted) relative to the plane of the Solar System. The eight major planets all orbit in roughly the same plane, but Pluto's orbit is tilted at an angle of about 17 degrees. This means that it sometimes travels above and below the plane of the Solar System during its orbit.
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The distance between points s and t of a cylindrical surface is equal to the length of the shortest track f in the strip m0 m1 with the following properties: f consists of curves f1,f2 ,…,fn ;f1 starts at the point S covering s, and fn ends at the point T covering t; and for each i=1,2,…,n−1,f i+1 starts at the point opposite the endpoint of its predecessor fi Theorem 2 can be interpreted by imagining that an instantaneous jet service operates between opposite points of the strip, so that arriving at a point of m0, one can instantaneously transfer to the opposite point of m1, and conversely. An inhabitant of the strip can move about the strip with unit speed, and make free use of the jet service. The distance in Σ between s and t is equal to the minimum time which is needed to travel from S to T. This is not yet the definitive answer, since we have not indicated how to find the shortest of all possible paths joining S and T; but at least we have reduced the study of geometry on Σ to a certain problem in plane geometry. Exercises 1. Prove that in the definition of distance between points of Σ given in Theorem 2, it is sufficient to consider only tracks f for which each curve f i is a line segment.
f' is a shortest track from S to T that consists of line segments only.
Theorem 2 states that the distance between points s and t on a cylindrical surface is equal to the length of the shortest track in the strip m0 m1. This track f consists of curves f1,f2 ,…,fn, where f1 starts at point S covering s, fn ends at point T covering t, and for each i=1,2,…,n−1, fi+1 starts at the point opposite the endpoint of its predecessor fi. An inhabitant of the strip can move about the strip with unit speed, and make free use of the jet service. The distance in Σ between s and t is equal to the minimum time needed to travel from S to T.
In order to prove that in the definition of distance between points of Σ given in Theorem 2, it is sufficient to consider only tracks f for which each curve fi is a line segment, we proceed as follows:
Proof:Let f be a shortest track in the strip m0 m1, consisting of curves f1,f2 ,…,fn. We need to show that there exists a track f' consisting of line segments only, such that f' is a shortest track from S to T. Consider the curves fi, i = 1, 2, ..., n - 1, which are not line segments. Each such curve can be approximated arbitrarily closely by a polygonal path consisting of line segments. Let f'i be the polygonal path that approximates fi. Then, we have:f' = (f1, f'2, f'3, ..., f'n)where f'1 = f1, f'n = fn, and f'i, i = 2, 3, ..., n - 1, is a polygonal path consisting of line segments that approximates fi.Let l(f) and l(f') be the lengths of tracks f and f', respectively. By the triangle inequality and the fact that the length of a polygonal path is the sum of the lengths of its segments, we have:l(f') ≤ l(f1) + l(f'2) + l(f'3) + ... + l(f'n) ≤ l(f)
Therefore, f' is a shortest track from S to T that consists of line segments only.
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It is diffult to measure the volume of gas.Why?
Answer:
The volume of a gas is dependent on pressure and temperature.
Explanation:
Pressure and temperature affect different gases differently giving varied conclusions to the exact volume of that gas.
:-befrank