water stands at a depth H in a large, open tank whose sidewalls are vertical. a hole is made in one of the walls at adepth h below the water surface.
a)at what distance R from the foot of the wall does theemerging stream strike the floor?
b)how far above the bottom of the tank could a second hole becut so that the stream emerging from it could have the same rangeas for the first hole?
Answers
2hcosθsinθ is the distance R from the foot of the wall the emerging steam strike the floor.
the second hole should be cut at a height of (H - h/4) above the bottom of the tank in order to get the same range as the first hole.
Let's derive an expression for the velocity of water coming out of the hole. The water coming out of the hole is a free fall under gravity .
So we can use Bernoulli's equation to find the velocity of the water coming out of the hole as:
P + (1/2)ρv² + ρgh = constant ….(1)
where P is the pressure of the water inside the tank,
ρ is the density of water,
v is the velocity of the water coming out of the hole,
h is the height of the water level inside the tank, and g is the acceleration due to gravity.
Since the hole is below the water's surface, the pressure at the hole is the pressure due to water at the second hole should be cut at a height of (H - h/4) above the bottom of the tank in order to get the same range as for the first hole.
depth h. So, the pressure due to water is ρgh.
At the hole, the velocity of water is v, and the height of the water surface above the hole is (H - h). Therefore, the pressure at the surface of the water is ρg(H - h). Putting these values in equation (1), we get:
P + (1/2)ρv² + ρgh = ρg(H - h) + P₀
Where P₀ is atmospheric pressure, which can be considered constant. This is the Bernoulli's equation.
Let's apply the law of conservation of mechanical energy.
Let the velocity of the water coming out of the hole be v.
The kinetic energy of the water at the hole is (1/2)ρv².
The gravitational potential energy of the water at the hole is ρgh.
The gravitational potential energy of the water at the point where it hits the floor is zero.
Hence, by the law of conservation of mechanical energy, we can write:
(1/2)ρv² + ρgh = 0
Solving for v, we get:
v = √(2gh)
Part a) of the question:
We know the velocity of the water coming out of the hole. Let's assume that the stream coming out of the hole makes an angle of θ with the horizontal, as shown in the figure.
We need to find the horizontal distance R from the foot of the wall at which the stream hits the floor. This is given by:
R = (v²/g)sin2θ
sin2θ can be written as 2sinθcosθ. Therefore, we get:
R = (v²/g)sinθcosθ
Using the value of v from above, we get:
R = (2gh/g)sinθcosθ = 2hcosθsinθ
Part b) of the question:
Let's assume that the second hole is cut at a depth x above the bottom of the tank. We need to find the value of x such that the stream emerging from it could have the same range as for the first hole.
This means that the horizontal distance R must be the same for both holes. Using the expression for R from above, we get:
2hcosθsinθ = (2gh/g)sinθcosθ
Simplifying, we get:
x = H - h/4
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Related Questions
Describe how government helps business provide the goods and services that people need and want
Answers
Governments assist in enhancing the infrastructure necessary for companies to flourish and helps business provide the goods and services that people need and want.
What is economics?
Economics is the study of how limited resources are used to create outputs, such as commodities and services, that are then distributed among individuals. Resources serve as the resources for creating outputs. Products and services are created by combining resources. The necessary raw ingredients are provided by land and natural resources. Raw materials are turned into finished products and services by labor.
Businesses perform better when they can effectively transport raw materials to factories and deliver finished goods to plants and markets. Governments assist in enhancing the infrastructure necessary for companies to flourish. Roads, bridges, rail lines, airports, seaports, energy transmission lines, and telecommunications networks are all included in this.
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The gravitational pull between two objects depends on their mass and distance. What is meant by distance?
A. The length of the object, meaning if the object is longer it will exhibit more gravitational pull than if it is short.
B. How close the two objects are located, meaning that closer objects have a stronger gravitational pull.
C. The distance that an object has to fall before reaching ground, meaning that an object will fall faster as the distance increases between it and the surface of the object is falling toward.
D. How far apart the two objects are located, meaning that objects far apart have a stronger gravitational pull than closer objects.
Answers
Answer: b
Explanation:
The gravitational pull between two objects depends on their mass and distance. Distance meant by :
B. How close the two objects are located, meaning that closer objects have a stronger gravitational pull.
How is distance related to gravitational force?
Gravitational force depends directly on the mass of two objects and inversely on the square of the distance between them. This means that gravity increases when mass increases, but decreases when the distance between objects increases. g = GM/r2, where M is the mass of the Earth, r is the radius of the Earth (or the distance between the centre of the Earth ). and you are standing on its surface), and G is the gravitational constant. G (without subscript) is the gravitational constant and c is the speed of light.
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A cylindrical iceberg of height H floats in sea water. The top of the iceberg is at height h above
the surface of the water.
The density of ice is Pi and the density of sea water is Pw.
What is the height h of the iceberg above the sea water?
A.[1-(Pi/Pw)]×H B.[(Pi/Pw)-1]×H C.(Pw/Pi)×H D.(Pi/Pw)×H
Answers
Answer:
dang
Explanation:
If someone were to be researching and studying similarities between our sun and a neighboring star, what kind of scientific investigation would they be conducting
Answers
Answer:
a
Explanation:
because there both in the solar system
There are billions of galaxies in the universe and each contains trillions of stars which are different in size, distance from the earth, brightness etc.When we scientifically investigate about this we can obtain the stars of similarity to sun in brightness and size.
What is galaxies?Galaxies are a group of stars, dust and dark matter joined together by the force of gravitation. Three trillions of stars in each galaxies. Some stars forms a group of certain size and shape and number also they are called constellations.
Sun is the closest star to earth. Thus sunlight is the major source of energy in earth. Sunlight reaches the earth surface within a time of 8 minute and 6 seconds.
The star which nearest to sun is named proximacentory which far from the earth and we can see it as spot of light in the sky. There are many more stars which are giants are more brighter than sun.
The brightness and luminosity is determined based on the distance from the earth. Which can be calculated in terms of light years. Each star has an age and length of life. After that the star may die still their light energy can be seen in sky because their light takes more years to reach here.
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what is the frequency of a wave that travels 20 m/s with a wavelength of 200 meters?
Answers
What type of force is magnetic force? *
Strong Nuclear force
Non-contact force
Contact force. Weak Nuclear force
Answers
Answer:
non contant force
Explanation:
bcoz they push or pull on object without touching them
Answer:
energy
Explanation:
5. An object travels with constant speed through 1km for one minutes and 20 seconds and accelerates with 0.125m/s² for 20 seconds, what is the total displacement? A) 1250 m B) 275 m C) 1275 m D) 1225m
Answers
Answer:
C) Total displacement = 1275 m or 1.275 km
Explanation:
We'll break this into two parts:
1) Displacement during constant speed, and
2) Displacement during the acceleration phase.
Constant Speed
The displacement for this segment is already stated: 1 km. But the information includes the time, which will allow us to calculate the speed of travel. We'll need this for the next phase of acceleration.
Distance = Speed x Time
Speed = Distance/Time
Time = 1 minute + 20 sec, or 80 sec.
Speed = 1 km/80 sec
Speed = 0.0125 km/sec
Since we'll be using meters (not km) in the next step, convert 0.0125 km/sec to m/sec with a conversion factor:
(0.0125 km/sec)*(1000m/1 km) = 12.5 m/sec
Acceleration Phase
The obect is moving at a speed of 12.5 m/sec (from above) and then accelerates at a rate of 0.125 m/sec^2 for 20 seconds.
The distance (s) an object travels during this acceleration (a) is gven by:
s = vi*t + (1/2)a*t^2,
where vi is the initial velocity (12.5 m/sec in this case), a is the acceleration (0.125 m/sec^2), and t is the time (20 seconds).
s = (12.5 m/sec)(20 sec) + (1/2)(0.125 m/sec^2)*(20 sec)^2
s = 275 meters
Now add the two distances:
1) Constant Speed Phase = 1000 m
2) Acceleration Phase = 275 m
Total displacement = 1275 m or 1.275 km
PLEASE ANSWER THE QUESTION AS SOON AS POSSIBLE
Answers
Answer: the answer is (1) B only
Explanation: In A the ball is being acted upon by the ground. In B in order for the ball to move upwards the ball had to have force acted upon at R. In C from U to V the ball has been acted upon by the ground
As the alternating current through a conductor increases, an expanding and collapsing electromagnetic field through the conductor produces a voltage within the conductor. this is known as:_____
Answers
As the alternating current through a conductor increases, an expanding and collapsing electromagnetic field through the conductor produces a voltage within the conductor. this is known as electromagnetic induction.
As the alternating current through a conductor increases, an expanding and collapsing electromagnetic field through the conductor produces a voltage within the conductor. This process is known as electromagnetic induction, which is a fundamental principle in physics and electrical engineering. It describes the generation of an electric current in a conductor when it is exposed to a changing magnetic field. This phenomenon is the basis for various applications, including generators, transformers, and induction coils. Electromagnetic induction plays a crucial role in the functioning of many electrical devices and is a fundamental concept in the study of electromagnetism.
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A 25 newton force applied on an object moves it 50 meters. The angle between the force and displacement is 40.0 degrees. What is the value of work being done on the object
Answers
the unusually bright centers found in some galaxies are called ______.
Answers
The unusually bright centers found in some galaxies are called "active galactic nuclei" (AGN).
These centers are characterized by their extreme brightness, which is due to the intense emission of energy across the electromagnetic spectrum, from radio waves to X-rays. The source of this energy is believed to be the accretion of mass onto supermassive black holes at the heart of these galaxies. When the matter surrounding the black hole is drawn towards it, it forms an accretion disk, which heats up due to friction and emits radiation. The emitted radiation can be so powerful that it outshines the entire galaxy, making the AGN easily observable from great distances. Examples of galaxies with active galactic nuclei include quasars, blazars, and Seyfert galaxies.
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Which phenomenon is shown in this diagram?
Earth's _________
Answers
Answer:
outer layer
Explanation:
- The gravitational force on a 352 kg satellite is -2100 N. Find its
distance from Earth's center.
Answers
Answer:
8173.8 km
Explanation:
Fg=G(M*m/r^2)
r=sqrt(G*M*m/Fg)
G=6.6743*10^-11
M(earth)=5.972*10^24kg
M(object)=352kg
Fg=-2100N
r=sqrt((6.6743*10^-11)*(5.972*10^24kg)*(352)/-2100)
r=8173808m
r=8173.8km
According to Newton's calculations, gravity reduces to a fourth of what it was at the surface of the Earth if the distance from the planet's centre is doubled. At the Earth's surface, a satellite with a mass of 1,000 kg exerts a weight force of 9,800 N.
What gravitational force act on satellite?Satellites are pulled toward Earth by its gravity, even when they are hundreds of kilometres distant. The satellite doesn't fall back to Earth; instead, it travels into orbit above it due to gravity and the velocity it acquired during launch into space.
A satellite that is in a steady circular orbit around the Earth is always falling. It encounters a gravitational pull toward the centre of Earth as it orbits, which forces it to shift course and “fall” towards Earth.
Therefore, Since gravity is the only force acting on a satellite in circular orbit, the centripetal force and gravity must be equal: Fc = Fg.
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which moving object would have the least amount of kinetic energy if they were traveling at the same speed?
Answers
The object with least mass would have the least amount of kinetic-energy if they were traveling at the same speed.
Equation of kinetic energy is \(KE = (1/2) mv^2\)
m is the mass of the object and v is velocity.
From the equation of kinetic energy we can see two factors which kinetic energy is depends upon. First one is mass of the moving object. Second one is the velocity of the object.
Kinetic energy is directly depending on the mass of the object. That means if mass is higher, then kinetic energy also higher.
Likewise kinetic energy directly depends upon the square of the velocity of the object. So if velocity of A is twice than B, then the kinetic energy of A will be 4 times than of B.
In the question it is stated that objects are traveling at the same speed. If the speed is same that is if velocity is same, then the only factor that affects the kinetic energy will be mass of the moving objects.
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1. A car has a total mass of 1200 kg and is traveling at 100 km per hour when the driver experience is a brake failure and collides with the barrels. Calculate the change in momentum it will experience whilst coming to a standstill.2. According to GSU's HyperPhysics Project this crash would have been fatal for an average 80 kg person. The safety zone in terms of momentum, ranges from 0 to 1,000 kg per metre per second. Determine the minimum velocity the car can slow down to during a collision with the barrels without the crash being fatal.
Answers
Question 1.
Given:
Mass = 1200 kg
Velocity = 100 km per hour.
Let's find the change in momentum it will expperience.
To find the change in momentum, apply the formula:
\(\Delta p=mv_f-mv_i\)Where:
Δp is the change in momentum
m is the mass of the car = 1200 kg
vf is the final velocity
vi is the initial velocity.
Here, the final velocity is = 0 m/s
The initial velocity is = 100 km/h
Let's convert the initial velocity to m/s.
Where:
1 m/s = 3.6 km/h
100 km/h = 100/3.6 = 27.78 m/s
Input the values into the formula and solve for Δp.
We have:
\(\begin{gathered} \Delta p=(1200\times0)-(1200\times27.78) \\ \\ \Delta p=0-3333.33 \\ \\ \Delta p=-33333.33kg.m\text{ /s} \end{gathered}\)Therefore, the change in momentum is 33333.33 kg.m/s
Question 2.
Since the safety zone for momentum is 0 to 1000 kg.m/s, to find the minimum velocity of the car, substitute 1000 kg.m/s for Δp and solve for the final velocity vf
We have:
\(\begin{gathered} \Delta p=m_{}v_f-mv_i \\ \\ 1000=(1200v_f)-(1200\times27.78) \\ \\ 1000=1200v_f-33333.33_{} \\ \\ v_f=\frac{1000-33333.33}{1200} \\ \\ v_f=-26.94\text{ m/s} \end{gathered}\)Therefore, the minimum velocity the car can slow down to a velocity is 26.94 m/s.
ANSWER:
(a). 33333.33 kg/m.s
(b). 26.94 m/s
Find the maximum energy stored in the spring bumpers
Answers
The maximum energy stored in the spring bumpers is given as ¹/₂kx².
Maximum energy stored in a springThe maximum energy stored in a spring is given by the following equations;
E = ¹/₂kx²
where;
E is the energy stored in the springk is spring constantx is extension of the springThus, the maximum energy stored in the spring bumpers is given as ¹/₂kx².
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A substance has life of 40 years. In how many years will the substance disintegrate to 1/8 of its initial size
Answers
Answer:
5 years
Explanation:
\(\frac{1}{8}(40)\\\\= 5\)
A family drives 881 miles from Houston Texas to Santa Fe New Mexico for vacation how long will it take the family to reach their destination if they travel at a velocity of 55.0 miles per hour northwest?
Answers
Answer:
about 16 hours
Explanation:
if driving 55mph for 16 hrs you will travel about 880 miles
a 280 nm thin film with index of refraction 1.6 floats on waterwhat is the largest wavelength of reflected light for which constructive interference occur? answer in units of m.
Answers
Answer:
Inside the film the wavelength will be λ/n
For constructive interference to occur the film must be λf/4 thick where λf is the wavelength of the light in the film - there will be a 180 degree phase shift at the water/film interface since the index of refraction of the film is greater than that of water - and the light has to travel λ/2 inside the film for constructive interference to occur
280 nm / 1.6 * 4 = 700 nm is the greatest wavelength allowed
Note that 700 nm is also the upper wavelength of the visible spectrum
Define mixture, heterogeneous, homogeneous, solution, colloid, suspension, solvent, solute, saturation.( please don't answer the question if you don't know the answer )
20 points
Answers
Answer:
1) a substance made by mixing other substances together.
2) diverse in character or content.
3) of the same kind; alike.
4) a means of solving a problem or dealing with a difficult situation.
5) a homogeneous noncrystalline substance consisting of large molecules or ultramicroscopic particles of one substance dispersed through a second substance. Colloids include gels, sols, and emulsions; the particles do not settle, and cannot be separated out by ordinary filtering or centrifuging like those in a suspension.
6) the temporary prevention of something from continuing or being in force or effect.
7) having assets in excess of liabilities; able to pay one's debts.
8) the minor component in a solution, dissolved in the solvent.
9) the state or process that occurs when no more of something can be absorbed, combined with, or added.
REFER TO IMAGE ...
Explain why someone might say that a ball dropped in New Zealand will not travel in the same direction as a ball dropped in Scotland.
Answers
Since the Earth is a sphere, the direction in which a ball falls when dropped will be affected by the Earth's curvature. At the equator, the Earth is more curved than at the poles, so a ball dropped at the equator will fall in a direction that is affected by this curvature.
In Scotland, which is located at a higher latitude than New Zealand, the Earth is less curved. As a result, a ball dropped in Scotland will fall in a direction that is less affected by the Earth's curvature than a ball dropped in New Zealand.
Therefore, someone might say that a ball dropped in New Zealand will not travel in the same direction as a ball dropped in Scotland because the Earth's curvature affects the direction in which the ball falls at these two locations.
I have a science quiz Please answer the question
Answers
The statements true about the model are:
A. If the orientation of the right magnet in Position 3 were reversed, the magnets would become less attractive to one another.C. A force must have been applied to decrease the magnetic potential energy for Position 5.D. An outside force must have been applied to achieve Position 4, decreasing the magnetic potential energy.What happens in each position?In Position 3, the magnets are attracted to each other. If the orientation of the right magnet were reversed, the magnets would repel each other. This is because like poles repel and unlike poles attract.
In Position 5, the magnets are repelling each other. This means that the magnetic potential energy is higher than in Position 1, where the magnets are attracted to each other. In order to get the magnets into Position 5, a force must have been applied to overcome the magnetic force of attraction.
In Position 4, the magnets are attracted to each other, but they are not in contact. This means that the magnetic potential energy is lower than in Position 1, where the magnets are in contact. In order to get the magnets into Position 4, an outside force must have been applied to overcome the magnetic force of attraction.
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if v⃗ 1 and v⃗ 2 are parallel, express your answer in terms of v1 and v2.
Answers
If the vectors v⃗ 1 and v⃗ 2 are parallel, the v⃗ 1* v⃗ 2 is v1v2.
A vector refers to a quantity or phenomenon that is characterized by two independent properties: magnitude and direction. The dot product of two vectors gives a scaler value and is equal to the magnitude of first vector multiplied by magnitude of second vector multiplied by the cosine angle between the two vectors. It is given by:
v⃗ 1* v⃗ 2 = │v⃗ 1│*│v⃗ 2 │cos Ɵ
If the two vectors are parallel, the Ɵ = 0, hence
v⃗ 1* v⃗ 2 = │v⃗ 1│*│v⃗ 2 │cos 0 = v1*v2*1 = v1v2
Note: The question is incomplete. The complete question probably is: If v⃗ 1 and v⃗ 2 are parallel, find v⃗ 1* v⃗ 2, express your answer in terms of v1 and v2.
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Which properties are characteristics of non metals
Answers
Non - Metals:
Non- metals are bad conductor of electricity ( except Graphite ).Non- metals are also bad conductor of heats. ( except diamond )Non - metal are neither malleable nor ductile. They are brittle. Non-metal are not strong. Non-metal are not sonorous.Some terms:
★ Malleable: This means that metals can be beaten into thin sheets with hammer.
★ Ductile: This means that metals can be drawn into thin wires.
★ Brittle: This means that non-metal break into pieces on hammering.
★ Sonorous: This means capable of producing a ringing sound.
An inductor is connected across an oscillating emf with a peak current of 2.00 A. If the peak emf ℰ0 is doubled, what is the peak current?
2.00 A
4.00 A
1.00 A
1.41 A
Answers
An inductor is made up of two terminals and an insulated wire coil that either loops around air or around a core substance that boosts the magnetic field.
The relationship between peak current and peak emf in an inductor is given by:
I0 = ℰ0 / XL
where I0 is the peak current, ℰ0 is the peak emf, and XL is the inductive reactance.
Since the inductor is connected across an oscillating emf, we can assume that the frequency is constant. Therefore, the inductive reactance remains constant.
If the peak emf is doubled, then the peak current is given by:
I0' = (2ℰ0) / XL
I0' = 2(I0)
I0' = 2(2.00 A) = 4.00 A
The peak value of a sine wave is given by the root-mean-square (rms) value divided by the square root of 2:
I0peak = Irms / √2
For a sine wave with a peak current of 2.00 A, the rms current is:
Irms = 2.00 A / √2 = 1.41 A
Therefore, if the peak emf is doubled, the peak current will be:
I0peak' = Irms / √2
I0peak' = 1.41 A / √2 = 1.41 A
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Make a graph of the relationship between the amplitude (x-axis) and decibel level (v-axis) of sound. Describe this relationship.
Answers
The graph of the relationship between amplitude and decibel level of sound is not a linear graph but a logarithmic graph.
It is known as the Sound Intensity Level graph, where the amplitude of the sound is plotted on the x-axis, and the decibel level of sound is plotted on the y-axis.
As the amplitude of the sound increases, the decibel level increases as well. The relationship is not directly proportional, as a small change in amplitude can result in a significant change in decibel level. For example, a sound with an amplitude of 1 Pa has a decibel level of 0 dB, whereas a sound with an amplitude of 10 Pa has a decibel level of 20 dB. This indicates that the decibel level is increasing exponentially with the increase in amplitude.
Moreover, the graph shows that the human ear has a limited range of hearing, which is between 0 dB and 140 dB. Beyond this range, sounds become too loud to hear or can cause damage to the ear. Therefore, it is important to monitor the decibel level of sound to protect our hearing.
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Make the following prefix conversions.
0.001s =ms
Answers
Answer:
To convert a millisecond measurement to a second measurement, divide the time by the conversion ratio. The time in seconds is equal to the milliseconds divided by 1,000.
Explanation:
hope it helps
The N-type and P-type doping levels of a silicon
P–N junction are ND = NA = 5 × 1016 cm−3.
Calculate the built-in voltage Vbi
(a) at room temperature
(b) at 700◦C (ni = 1.10 × 10^18 cm−3). Does a
negative value for Vbi mean anything?
Answers
The built-in voltage Vbi at 700◦C is -0.28 V, which means that the P-N junction is reverse-biased.
The built-in voltage Vbi of a P-N junction is given by:
\(Vbi = (kT/q) * ln(ND*NA/ni^2)\)
where k is Boltzmann's constant, T is the temperature in Kelvin, q is the electron charge, ND and NA are the N-type and P-type doping levels, and ni is the intrinsic carrier concentration.
(a) At room temperature (T = 300 K) and with ni = \(1.5 * 10^1^0 cm^3\) (for silicon), we have:
\(Vbi = (kT/q) * ln(ND*NA/ni^2)\)
\(= (1,38* 10^-^2^3 * 300 / 1.6 * 10^-^1^9) * ln (5 * 10^1^6 * 5 * 10^1^6 / (1.5 * 10^1^0)^2)\\= 0.71 V\)
Therefore, the built-in voltage Vbi at room temperature is 0.71 V.
(b) At 700◦C (T = 973 K) and with \(ni = 1.10 * 10^1^8 cm^3\), we have:
\(Vbi = (kT/q) * ln(ND*NA/ni^2)\)
\(= (1.38 * 10^-^2^3 * 973 / 1.6 * 10^-^1^9) * ln(5 * 10^1^6 * 5 * 10^1^6 / (1.10 * 10^1^8)^2)\\= -0.28 V\)
Therefore, the built-in voltage Vbi at 700◦C is -0.28 V, which means that the P-N junction is reverse-biased. A negative value for Vbi means that the majority carriers (electrons in the N-type and holes in the P-type) are attracted to the junction and will tend to flow away from it when an external voltage is applied in the forward direction.
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What is the difference between a meteor shower and just the occasional meteor?
Answers
Answer:
Meteors enter our atmosphere on a regular basis. On a normal night you can typically see a few sporadic meteors per hour. However, at certain times the rate of observable meteors is much higher. These periods are called meteor showers.
Explanation:
A ray of sunlight forms a 24°-angle with the ground. what is the length of the shadow cast by a person 1.82 m tall?
Answers
The length of the shadow cast by a person who is 1.82 m tall when a ray of sunlight forms a 24° angle with the ground is approximately 4.09 meters.
To solve this problem, we'll use trigonometry with the given angle and the height of the person to find the length of the shadow. We know that the angle between the sunlight and the ground is 24°, and the person is 1.82 m tall.
We can model this situation using a right triangle, where the person's height represents the opposite side, the length of the shadow represents the adjacent side, and the angle of elevation is 24°. To find the length of the shadow, we can use the tangent function, which is defined as the ratio of the opposite side to the adjacent side in a right triangle.
So, we have:
tan(24°) = opposite side (height of the person) / adjacent side (length of the shadow)
Now, we can plug in the height of the person:
tan(24°) = 1.82 m / length of the shadow
To find the length of the shadow, we can rearrange the equation and solve for it:
Length of the shadow = 1.82 m / tan(24°)
Using a calculator, we find that:
Length of the shadow ≈ 1.82 m / 0.4452 ≈ 4.09 m
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