7. A 50 kg athlete runs and grabs a 10.0 m rope and swings to a maximum height of 1.8 m above
the ground. A second athlete, who has a mass of 100. kg runs at the same speed, v, and grabs a
5.0 m rope. What maximum height will the 100. kg athlete swing to? Assume the mass of the
ropes and air resistance are negligible. Support your answer with calculations and/or a proof.
(3 marks)
50 kg
10 m
100 kg
T
5m

A large water tank with cross sectional area A and height of h is filled to the top with water (density= rho). There is a hole of cross sectional area a located at the bottom of the tank. The velocity of the water exiting the small hole will raise to a height and then stop.

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The mass of soccer player will be 120kg.  Writing down 1/2 m1 will help us remember that KE = 1/2 mv2 (v1i) 2 + 1/2 m2(vi) (vi) 2 = 1/2 m1(v1f) (v1f) 2 + 1/2 m2 (v2f) (v2f) 2.

According to Newton's third law,

Given that a soccer player runs at 10m/s and plows into a 80kg referee standing on the field causing the referee to fly forward at 56m/s. Let

mass of the player = ?

initial velocity of the player = 10m/s

Final velocity of the player

mass of the referee = 80 kg

Initial velocity of the referee = 0 ( since he is at rest )

Final velocity of the referee = 6 m/s

Since it is a perfectly elastic collision,

U1 =V2 - V1 ........ (1)

M1U1 = M2V2 + M1V1........ (2)

Substitute all the necessary parameters into the equation (1)

10 = 6 - V1

V1 = 10 - 6

V1 = 4 m/s

Now, Substitute all the necessary parameters into the equation (2)

10M1 = (80 x 6) + (4M1)

10 M1- 4 M1 = 480

4M1 = 480

M1 = 480/4

M1 = 120kg

Therefore, the mass of soccer player will be 120kg

When kinetic energy (KE) and momentum (p) are conserved during a collision, the collision is said to be elastic. To put it another way, it denotes that KE0 = KEf and po = pf. Writing down 1/2 m1 will help us remember that KE = 1/2 mv2 (v1i) 2 + 1/2 m2(vi) (vi) 2 = 1/2 m1(v1f) (v1f) 2 + 1/2 m2 (v2f) (v2f) 2.

By dividing the entire distance traveled by the time it took the object to go a certain distance, you may calculate the object's initial velocity. V, d, and t are the three variables that make up the equation V = d/t.

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Step 1: Calculate the ratio of the final and beginning temperatures using the ideal gas law solved for temperature.

Step 2: Calculate the ratio after eliminating any constant values.

Step 3:Solve for the final temperature after substituting the beginning temperature into the ratio.

PV= nRT

However, for this method to work properly, the temperature must be stated in Kelvin. This is true because Kelvin's zero point is absolute zero. Theoretically, molecules are entirely immobile at 0 Kelvin.

T = PV/nR

The ideal gas law equivalency is used to compute the final temperature in the next two issues.

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Whenever the gases are heated at a fixed volume, no outside work is done as well as the heat energy given is simply used to make the gas more energetic internally.

The specific heat under constant pressure for an ideal gas, Cp, is higher than Cv.This is due to the fact that when the gas' temperature rises while the pressure stays constant, the gas must perform some finite work on its surroundings.

When the goal value and the specification's average are equal, Cpk equals Cp.Never can Cpk go above Cp.With the creation of descriptive statistic displays and histograms, Cp and Cpk can both be determined.

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When a magnetic field continually changes magnitude and direction, a voltage is continually induced in the coil. This voltage is called induced voltage.

Induced voltage is the type of voltage that is a product of electromagnetic induction. It is generally defined as the rate of change of magnetic flux with respect to time via a closed circuit.

A wire that is carrying a current will experience an induced voltage along its length if the current changes. The changes in current change the magnetic field flux perpendicular to the wire.

Induced voltage is calculated using the Faradays equation:

e = N(dΦ/dt)

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Important Formula:

[tex]s=\dfrac{d}{t}[/tex]

__________________________________________________________

[tex]d=85m[/tex] (measured in meters)

[tex]t=13s[/tex] (measured in seconds)

[tex]s=?[/tex] (measured in meters per second; m/s)

__________________________________________________________

[tex]s=\dfrac{d}{t}[/tex]

[tex]s=\dfrac{85}{13}[/tex]

__________________________________________________________

[tex]\fbox{6.54 m/s},\fbox{Option C}[/tex]

Since light is faster in space, it takes less time for light to travel a distance of 1000m, a time difference of 0.977ns.

Light travels more slowly in a transparent medium than in the vacuum of empty space. The speed of light in any medium (air, water, glass) is determined by the refractive index of the medium. However, this exponent itself may be wavelength dependent (ie different colored rays travel at different speeds). In fact, this is why a prism splits white light into the colors of the rainbow.

The main reason that a light beam slows down in a medium has to do with the fact that the photons, or 'raw light beams', are excited by an electromagnetic field. When the field is in the ground state (vacuum), these excitations actually propagate at the vacuum speed of light. However, when there are positively charged atoms and negatively charged electrons, the electromagnetic field does not go to the ground state. There are many virtual photons. Yes, some of the photons of the passing light beam can be absorbed. After all, no material is completely transparent. But even those who aren't are moving in an environment so different from the vacuum that their paths will be different. It also depends on the structure that the molecule forms.

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The length of the y component shown is C. 2.0.

We are given the angle of the vector, and the length of one of the components of the vetor. Given the angle we have, the available component is the hypotenuse. The y component that we are to find, will then be the opposite or perpendicular component.

To solve for the length of the y - component therefore, the useful operation would be the Sin function.

The length of the y - component would be:
Sin 42 ° = Opposite / Hypotenuse

Sin 42 ° = y component / Hypotenuse

y - component = Sin 42 ° x Hypotenuse

y - component = Sin 42 ° x 3

y - component = 0. 6691 x 3

y - component = 2. 0

In conclusion, the y - component is 2.0.

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Full question is:

What is the length of the y-component of the vector shown below?

The force of gravity acting on the 23 Kg object in the diagram is 225.4 N

The force of gravity is defined as follow:

Force of gravity (F) = mass (m) × acceleration due to gravity (g)

Using the above formula, we can easily obtain the force gravity acting on the 23 Kg object. This is shown below:

Force of gravity (F) = mass (m) × acceleration due to gravity (g)

Force of gravity = 23 Kg × 9.8 m/s²

Force of gravity = 225.4 N

Thus, from the calculation made above, we can conclude that the gravitaional force is 225.4 N

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Schedules of reinforcement farm workers are paid x amount of dollars for every basket of fruit that they pick is based on the concept of fixed ratio.

A strengthening timetable, during which an answer or reaction is only strengthened after yet another given reaction can be determined, could be determined as a fixed ratio schedule. The particular topic gives a variety of questionnaires/solutions and therefore is subsequently rewarded by the educator or coach.

The man is under a fixed interval schedule of reinforcement, while the woman is under a fixed ratio schedule of reinforcement. Fixed interval reinforcement is a type of reinforcement that gives reward only after a specific period of time has passed. A fixed ratio reinforcement is a type of reinforcement that is based on production rate.

The other type is variable ratio. Variable Ratio schedule of reinforcement will give a person rewards after he/she fulfil a specific amount of works.

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Main Answer:

The distance of L is [tex]v^{2} /2g(sin\alpha +ucos\alpha )[/tex]

Explanation:

if the block will slide a distance 'L' then syoped;

The initial velocity given to the block is V m/s

So, Total K.E given will goes to gain in potential energy and work done by friction .

K.E=1/2mv^2

P.E at hight (Lsin[tex]\alpha[/tex]) will be = mgh

And work done by the Friction Force is given as = w.r = force*displacement= - uNL= -uMgGcos[tex]\alpha[/tex]L

so,

KE+WD by friction = gain in P.E

[tex]1/2mv^{2} +(-uMgGcos\alpha L)=MgLsin\alpha \\1/2V^{2} =glsin\alpha +uglcso\alpha \\v^{2} /2= Gl(sin\alpha +ucos\alpha )[/tex]

Hence by solving we get :

[tex]v^{2} /2g(sin\alpha +ucos\alpha )[/tex]=L

So the distance = L

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If an object producing sound is moving away from us, the wavelength of the sound heard is longer than the actual wavelength. The conclusion is from the concept of Doppler effect.

The Doppler's effect is a phenomenon when the source of a wave and an observer move relative to each other, the frequency heard is not the same with the actual frequency.

The equation of the Doppler effect is

f₀ = [(v ± v₀)/(v ± vs)] × fs

Where

Note:

When an object producing sound is moving away from us, the frequency of the sound we heard changed.

Let's say we are at rest, it means v₀ = 0. The sound source is moving away makes vs (+).

With the Doppler's effect, we get

f₀ = [(v+0) / (v+vs)] × fs

f₀/fs = v/(v+vs)

v < v+vs

f₀ < fs

The frequency of sound we heard is lower that the actual frequency.

The wavelength is inversely proportional to the frequency. It is described in the equation:

λ = c/f

It means that the lower the frequency, the longer the wavelength.

Hence, the phenomenon which the wavelength of the sound we heard is longer than the actual wavelength when the sound source is moving away from us is called the Doppler's effect.

Here is the group of answer choices:

(a) Band width

(b) Doppler's effect

(c) Sound refraction

(d) Vibrations

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The length of the pendulum is 8.258 cm .

Given,

Frequency f= 3.1 Hz

Acceleration due to gravity

We have to find out the length of pendulum

L=g / ( 4 x (π)^2 x (f)^2  )    --------------(1)

Where,

L  is length

g is acceleration due to gravity

f is frequency

Put the given value in equation (1) becomes

L= (31.3)m/s^2 / (4x (3.14)^2 x (3.1)^2)Hz

L= 31.3 / 379

L = (0.08258) m

L= (8.258)cm

The length of pendulum is

L= (8.258)cm.

The rate by which velocity changes concerning time is known as acceleration. According to Newton's second law, the eventual effect of all forces applied to a body is its acceleration.

The pace at which a body's velocity varies is represented by acceleration, which is a vector quantity.

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The length of the pendulum is 8.258 cm .

What is pendulum?

A weight suspended from a pivot such that it can freely swing is called a pendulum. Gravity's restoring force will cause a pendulum to accelerate back toward its equilibrium position if it is sideways moved from its resting, equilibrium position.

Given,

Frequency f= 3.1 Hz

Acceleration due to gravity

We have to find out the length of pendulum

L=g / ( 4 x (π)^2 x (f)^2  )    --------------(1)

Where,

L  is length

g is acceleration due to gravity

f is frequency

Put the given value in equation (1) becomes

L= (31.3)m/s^2 / (4x (3.14)^2 x (3.1)^2)Hz

L= 31.3 / 379

L = (0.08258) m

L= (8.258)cm

The length of pendulum is

L= (8.258)cm.

The rate by which velocity changes concerning time is known as acceleration. According to Newton's second law, the eventual effect of all forces applied to a body is its acceleration.

The pace at which a body's velocity varies is represented by acceleration, which is a vector quantity.

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The two level portions in the graph represented phase changes.

What are phase changes?

The transition of matter from one state (solid, liquid, gas, or plasma) to another is referred to as a phase change.  These changes also take place when the pressure on the system varies, as well as when the system receives enough energy or loses enough energy.

The slope of the line dividing two phases is determined by the relative densities of the two phases. The solid-liquid line, for instance, slopes up and to the right if the liquid is less dense than the solid, whereas up and to the left if the liquid is denser than the solid.

Therefore the two level portions in the graph represented phase changes.

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D) The Sun's evolution from youngest to the oldest stage is protostar, main-sequence, red giant, a white dwarf.

A protostar is the very beginning stage of a star's life. It is a cloud of gas and dust that starts to collapse due to its own gravitational pull. As it collapses, the gas and dust heat up, and eventually, nuclear fusion begins, creating a star.

The main-sequence stage is the longest and most stable period of a star's life. During this stage, the star is converting hydrogen into helium in its core, producing energy and light. This stage can last for billions of years.

Once a star has used up its hydrogen fuel, it enters the red giant phase. This is when the star expands, becoming much larger and much brighter. The star is now converting helium into other elements in its core, such as carbon and oxygen.

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The forces the truck and car exert on each other must be internal to the truck-car system because the momentum of the center of mass of the truck-car system stays the same. Option D

We know that it is possible for an object to be able to bump into another object when this occurs, we would have to apply the law of the conservation of linear momentum. Recall that from the law of the conservation of linear momentum, momentum before collision is equal to the momentum after collision.

We would also have to consider the fact that the weight of the truck is much lager than the weight of the car. The forces that the two vehicles would exert on each other can not be the same. It is clear that the truck is going to exert more force than the car.

With that said, we must have in mind that the total momentum of the system does not change because we are going to approximate the system to function as a closed system.

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If wire loop is being pulled to the right with a constant velocity of 3 meters per second , then the potential difference induced between points X and Y is 3V .

it is given that a 5Ω resistor is connected between points X and Y ;

the magnetic field (B) = 0.5 ;

length of wire (l) [tex]=[/tex] 2 ;

velocity of the wire loop (v) = 3 m/s ;

the potential difference will be induced because charge separation on the vertical hand wire of wire loop.

Points X and Y are the same as the top and bottom of left wire.

The EMF(potential difference) induced in wire is given by

EMF = B*l*v

substituting the values ,

we get  

= (0.5)(2)(3) = 3V

Therefore , the induced potential difference between points X and Y is 3V .

The given question is incomplete , the complete question is

A wire loop, 2 meters by 4 meters, of negligible resistance is in the plane of the page with its left end in a uniform 0.5-tesla magnetic field directed into the page. A 5-ohm resistor is connected between points X and Y. The field is zero outside the region enclosed by the dashed lines. The loop is being pulled to the right with a constant velocity of 3 meters per second. Make all determinations for the time that the left end of the loop is still in the field, and points X and Y are not in the field.

Determine the potential difference induced between points X and Y.

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The mass-to-light ratio for a globular cluster is equal to 137.7 kg/lsun

To measure the mass-to-light ratio of a globular cluster, we first determine the total mass of the cluster. Since the cluster has 105 stars, and the average mass of a star in the cluster is 1 m-sun, therefore, the total mass of the cluster is 10^5 * 1 msun = 10^5 msun.

Now, we convert the luminosity of the cluster from solar units to kilograms. The luminosity of the cluster is given as 10^6 lsun, which is equal to 10^6 * 3.828 x 10^26 W.

Using the equation, [tex]E = mc^2[/tex], we can convert this energy to mass:

[tex]mass = (luminosity * time) / (c^2)[/tex]

where, c is the speed of light (3 x 10^8 m/s) and time is the amount of time over which the luminosity is measured (here, time is equal to 1 second).

Substituting the values in above equation, we find that the mass of the cluster in kilograms is approximately 1.45 x 10^31 kg.

To determine the mass-to-light ratio, divide the total mass of the cluster (in kilograms) by its luminosity (in solar units):

mass-to-light ratio = (total mass of cluster in kg) / (luminosity in solar units)

Substituting the values in above equation, we find that the mass-to-light ratio for this globular cluster is approximately:

1.45 x 10^31 kg / 10^6 lsun = 137.7 kg/lsun.

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A heat engine, symbolized by a circle in this illustration, uses some of the heat transfer to produce work.

The most effective heat engine that is theoretically possible—i.e., any machine that can transform thermal energy (heating) into mechanical energy—is the Carnot engine (work).The heat and cold reservoirs are the names given to the hot and cold items. Only the hot temperatures' absolute values affect efficiency. A portion of the heat QH that is extracted from the high-temperature source TH in the case of a heat engine is transformed into work. The ratio of net work completed to heat absorbed throughout one full cycle is known as a heat engine's thermal efficiency.

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0.025 N the force of the string on the toy, at the other end of the rope.

Friction is a force that resists the relative motion of two objects that are in contact with each other. It is caused by the interaction of the surfaces of the two objects and the molecules that make them up. Friction can be either static or kinetic. Static friction occurs when the two surfaces are not moving relative to each other, while kinetic friction occurs when the two surfaces are moving relative to each other. Friction is a type of force that can be both beneficial and detrimental.

Mass of the string (m)  = 10 grams or 10⁻² kg

Mass of the toy (M) = 50 g or 5 x10⁻² kg

Mass of the system = M + m

= 10⁻² + 5 x 10⁻²

= 6 x 10⁻²  kg

Force applied (F) = 3.0 x 10⁻² N

Acceleration of toy + string = (0.03/6) x 10⁻²

= 0.5m/s²

Thus force on the toy = 5 x10⁻² x 0.5

= 0.025 N

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The complete question is as follows:

A short 10g string is used to pull a 50g toy across a frictionless horizontal surface. if a 0.03N force is applied horizontally to the free end, the force of the string on the toy, at the other end, is:

The fraction of its final impact speed is 1/√2.

Impact speed is the speed of the vehicle at the time of impact or collision.

The rock has lost half of its gravitational potential energy, its kinetic energy at the halfway point is half of its kinetic energy at impact.

As we know kinetic energy is directly proportional to mass (m) and velocity square (v²),

KE ∝ v²

KE = (1/2)mv²

then K.E at halfway point is equal to 1/2 x K.E,

Then,

The K.E at impact, then the rock’s speed at the halfway point its speed at impact will be 1/√2 its impact speed.

Therefore option D is the correct answer, the fraction of its final impact speed is 1/√2.

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A. The momentum of the electron is 1.98×10⁻²⁴ Kg.m/s

B. The momentum of the Caliber bullet is 139.32 Kg.m/s

C. The momentum of the professional fullback is 1012 Kg.m/s

D. The momentum of the passenger plane is 540000 Kg.m/s

Momentum is defined as the product of mass and velocity. It is expressed mathematically as:

Momentum = mass × velocity

A. How do I determine the momentum of the electron?

Momentum = mass × velocity

Momentum of electron = 9.1×10⁻³¹ × 2.18×10⁶

Momentum of electron = 1.98×10⁻²⁴ Kg.m/s

B. How do I determine the momentum of the Caliber bullet?

Momentum = mass × velocity

Momentum of Caliber bullet = 0.162 × 860

Momentum of Caliber bullet = 139.32 Kg.m/s

C. How do I determine the momentum of the professional fullback?

Momentum = mass × velocity

Momentum of professional fullback = 110 × 9.2

Momentum of professional fullback = 1012 Kg.m/s

D. How do I determine the momentum of the passenger plane?

Momentum = mass × velocity

Momentum of passenger plane = 360000 × 1.5

Momentum of passenger plane = 540000 Kg.m/s

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The final velocity of the cannonball-cart system is less than the initial velocity of the cannonball and the system will move in the direction of the cannonball ( V < v_b ).

The law of conservation of linear momentum states that the sum of the initial momentum is equal to sum of the final momentum, provided that the system is Isolated.

Mathematically, the law of conservation of linear momentum is given as;

Pi = Pf

where;

m₁u₁ + m₂u₂ = v ( m₁ + m₂ )

where;

since the cart is initially at rest, the initial velocity of the cart = 0

m₁u₁ + 0 = v ( m₁ + m₂ )

m₁u₁ = v ( m₁ + m₂ )

v = ( m₁u₁ ) / ( m₁ + m₂ )

given initial velocity of the cannon ball = v_b

The final velocity of the cannonball-cart system is calculated as follows;

V = ( m₁v_b ) / ( m₁ + m₂ )

Hence, V < v_b

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The centripetal acceleration of the mass m when it is at the lowest position is 10 m/s². The correct option is A.

Centripetal acceleration is a characteristic of an object's motion along a circular path. Centripetal acceleration applies to any object moving in a circle with an acceleration vector pointing in the direction of the circle's center.

A projectile is an object that is launched into the air and then moves only in response to the acceleration of gravity. The trajectory of the object is referred to as the projectile's trajectory.

The equation of projectile motion is:

[tex]V = \sqrt{2gh}\\\\\\V = \sqrt{2 \times 10 \times \dfrac{1}{2} } \\\\V = \sqrt{20}[/tex]

a² = v² / l  = 20 / 2 = 10 m/s²

Therefore, the correct option is A, 10 m/s².

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The question is incomplete. Your most probably complete question is given below:

The centripetal acceleration of the mass m when it is at the lowest position is:

10 m/s²

5 m/s²

20 m/s²

25 m/s²

Answer: 16 Pounds.

To figure out how much YOU would weigh on the moon, take your weight and divide it by 6. So, if you weighed 100 pounds on Earth, you would weigh only about 16 pounds on the moon.

Planets exert gravitational tugs on their stars that cause stars to orbit around the center of mass of their planetary systems. is true

The complete questio is Which one makes it possible to learn of the existence of extrasolar planets without seeing the planets themselves?

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Through Schrodinger equation probability, we can prove that the probability density for the ground state solution of the one dimensional coulomb potential energy in the Schrodinger equation has its maximum at x=a₀.

Given wave function is Ψ(1s) = 1/√π{1/a₀}^(3/2) e ^(x/a₀)

Probability refers to potential.  The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means.

The Schrödinger equation is a linear partial differential equation that describes the wave function or state function of a quantum-mechanical system.

To find the most probable distance, differentiate the equation |Ψ(1s)|²x² with respect to x and equating to zero, we get

d / dr | 1/√π e(1/a₀)^3 / 2e^(-x/a₀) |² x² = 0

1 / π(1 / a₀)³ d / dr (e^-2x / e₀) (x²) = 0

[2e^(-2Zx / a₀) x + e^(-2Zx / a₀) {-2 / a₀} x²] = 0

2 + (-2 / a₀) x = 0

This gives x = a₀

Therefore, through Schrodinger equation probability, we can prove that the probability density for the ground state solution of the one dimensional coulomb potential energy in the Schrodinger equation has its maximum at x=a₀.

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The coefficient of static friction between feet and ground is 0.2522.

Static friction is defined as when there is no motion between the two surfaces, the force that one surface applies to another. The friction that exists between two or more objects when they are not moving relative to one another is referred to as static friction.

The coefficient of static friction between his feet and the ground, denoted by the symbol s, determines how to express the frictional force as

fs =μsFN1

The μs can be calculated as

μs = a / √L² - a² x d / L

μs = 0.945 / √(1.95)² - (0.945)² x 0.89 / 1.95

μs = 0.945 / √2.91225 x 0.89 / 1.95

μs = 0.2522

Thus, the coefficient of static friction between feet and ground is 0.2522.

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