Activity on the Sun, such as solar flares and coronal mass ejections, hurl large numbers of charged particles into space. When the particles reach Earth, they can interfere with communications and the power grid by causing electromagnetic induction. In one example, a current of millions of amps (known as the auroral electrojet) that runs about 100 km above Earth's surface can be perturbed. The change in the current causes a change in the magnetic field it produces at Earth's surface, which induces a potential difference along Earth's surface and in the power grid (which is grounded). Induced electric fields as high as 6.0 V/km have been measured. We can model the circuit at Earth's surface as a rectangular loop made up of the power lines and completed by a path through the ground beneath, and we can treat the magnetic field as being uniform (but not constant). The height of the power lines is 5.0 m,they are 1 km long, and the potential induced in the loop is 6.0 V.


Required:

At what rate must the magnetic field be changing to induce that emf?

Answer:

33.33Watts

Explanation:

Given parameters:

Work done  = 1000J

Time taken  = 30s

Unknown:

Power  = ?

Solution:

To solve this problem, we must understand that power is the rate at which work is done.

So;

       Power  = \(\frac{Work done }{time}\)  

Now insert the parameters:

 Power = \(\frac{1000}{30}\)     = 33.33Watts

Answer:

i) 20-30 kg

Explanation:

The child with the smallest mass range of 20-30 kg will require the smallest force to move his skate board because he/she has a smaller inertia force to overcome. The mass of a body is the measure of the inertia forces of the body. The inertia force makes it difficult for a body at rest to start moving, and a body already in motion to stop moving.

When the children try to move the skateboard, they exert a force that is proportional to the product of their mass and the acceleration with which they start moving. This force must exceed their body's inertia force before they would start moving.

from

F = ma

where F is the force required

m is the mass

a is the acceleration

We can see that for the given mass ranges, the children with the larger mass range will require more force in order to move their skateboard. Consequently, the child with the smallest mass range will require the smallest pushing force to move his skate board.

Answer:

75 volt

Explanation:

Current (I) = 5 A

Resistance (R) = 15 Ω

Voltage (V) = ?

We know

R = V/I

15 = v / 5

v = 75 Volt

Answer:

In general, the concept of output work being less than input work does not align with the laws of physics, specifically the principle of conservation of energy. According to this principle, energy cannot be created or destroyed, but it can be transformed from one form to another. Therefore, the total amount of energy in a closed system remains constant.

When considering work, which is the transfer of energy through the application of force over a distance, the input work and output work should theoretically be equal if no energy is lost to other forms, such as heat or friction. However, in real-world scenarios, various factors can result in a decrease in output work compared to input work. Some possible reasons for this disparity include:

Inefficiencies: Real systems are not perfectly efficient, and energy losses can occur due to factors like friction, heat dissipation, electrical resistance, or mechanical limitations. These losses reduce the amount of useful work obtained from the input energy.

Energy conversion: If the input work is in one form of energy (such as electrical or chemical), and the output work is in a different form (such as mechanical), energy losses can occur during the conversion process. The efficiency of the conversion process determines the amount of output work obtained.

External forces: External factors, such as resistance or opposing forces, can require additional work to overcome, resulting in a decrease in net output work compared to the input work.

It's important to note that while output work can be less than input work in certain situations due to these factors, the total amount of energy remains conserved. Energy that is not converted into useful work is typically dissipated as waste heat or other forms of energy loss.

Answer:

The output work is always less than the input work because of friction.

Explanation:

Friction is a force that opposes the relative motion of two surfaces in contact. When a machine is used, frictional forces are created between the moving parts of the machine and the surfaces they rub against.

These frictional forces require some of the input work to be used to overcome them, which reduces the amount of work that is available to do the desired task.

The term that is defined as the entire set of surrounding parts of the world with which the user interacts is the user interface (UI).

The user interface encompasses all the elements and components that enable users to interact with a system, device, or application. It includes the visual, auditory, and tactile elements that facilitate communication and interaction between the user and the technology. The UI serves as the bridge between the user and the underlying system, allowing users to input commands, receive feedback, and access the functionality of the system.

The user interface can take various forms, including graphical user interfaces (GUIs), command-line interfaces (CLIs), voice-activated interfaces, touchscreens, and more. It involves the design and arrangement of buttons, menus, icons, text fields, and other interactive elements that enable users to navigate, input data, and perform tasks within the system.

The main purpose of a user interface is to create a user-friendly and intuitive environment that facilitates efficient and effective interaction. It should present information in a clear and organized manner, provide appropriate feedback to user actions, and ensure that users can easily access the desired features and functions of the system.

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Answer: 180 m south

Explanation:

The displacement of the horse in this time is 180 m south. The correct option is A.

The displacement is the shortest distance travelled by the particle. It is the vector quantity which re[presents both the magnitude and direction.

Velocity is the time rate of change of displacement with time.

Given is a horse runs for 15 seconds to the south at a speed of 12 m/s. So, the displacement is

Displacement = Speed x Time

Put the values, we get

Displacement = 12 m/s x 15s

                      = 180 m

Thus, the displacement of the horse in this time is 180 m south.

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The statement that the terminal voltage of a DC generator decreases due to armature reaction effect and armature resistance voltage drop is true.

A shunt generator will build up its voltage when its field resistance is less than the critical value. When the field resistance is lower, it allows more field current to flow, resulting in a stronger magnetic field and increased generator voltage output.

A DC motor has a linear mechanical characteristic when it is shunt connected. In a shunt connection, the field winding is connected in parallel with the armature winding. This configuration allows for independent control of the field current, resulting in a more stable and linear mechanical response of the motor to varying loads.

The terminal voltage of a DC generator decreases due to the combined effects of armature reaction and armature resistance voltage drop. Armature reaction refers to the distortion of the magnetic field caused by the current flowing through the armature windings, which leads to a reduction in the generated voltage. Additionally, the resistance of the armature windings causes a voltage drop, further decreasing the terminal voltage of the generator.

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Answer:

1-a

2-d

3-c

4-b

Explanation:

i tookt he words and put it in the sentance and these made most sence to me

Opacity adjusts the transparency or translucence of a shape or a layer. It is a measure of the degree to which light is allowed to pass through an object. Option B is correct.

The opacity setting is often used in graphic design and image editing software to control the visibility of layers, allowing designers to create interesting visual effects and overlays. When the opacity is set to 100%, the object is completely opaque and does not allow any light to pass through.

When the opacity is set to 0%, the object is completely transparent and allows all light to pass through. Intermediate values of opacity create varying degrees of transparency or translucence, allowing the underlying layers or background to show through to some extent.

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The amount of metal in a closed cylindrical can that is 10 cm high and 4 cm in diameter if the metal on the top and the bottom is 0.1 cm thick and the metal on the sides is 0.05 cm thick is 8.8 cm.

The formula for calculating the volume of a cylinder is given below.

V = πr^2 h

Get the differential of the volume as shown:

dV = V/ h dh + V / r dr

V/ h = πr^2

V/ h  = 2  πr h

Now, the differential becomes

dV =  πr^2dh +  2πrh dr

Given the following parameters

dh = 0.1 + 0.1 = 0.2 cm

dr = 0.05 cm

h = 10 cm

r = 4 cm

Substituting the values in the above equation, we get

dV = 3.14(2)^2(0.2)  + 2(3.14)(2)(10)(0.05)

dV = 2.512 + 6.28

dV = 8.792 cm

dV = 8.8 cm

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Answer:

They cause heat to flow from the system to the surroundings.

The height of the bridge can be determined by gravitational acceleration the  of the problem which is derived from the of   the height of an object dropped from a certain height.

"a man drops a stone from a high bridge and hears it strike the water exactly time t later how high is the bridge" is given by the equation below;

h=0.5*g*t² Where;

h = height of the bridge.

g = gravitational acceleration (9.8 m/s²)

t = time taken for the stone to fall We are given;

The time taken for the stone to fall,

t = t The height of the bridge is h.

To determine the height of the bridge, we need to use the equation of motion;

h=0.5*g*t²

We know that gravitational acceleration (g) is constant and has a value of 9.8 m/s². Therefore, we can substitute the known values to determine the height of the bridge;

h=0.5*g*t²h=0.5 * 9.8 m/s² * t²h

= 4.9t² meters

Therefore, the height of the bridge can be calculated by substituting the value of time (t) in seconds in the equation

h = 4.9t² meters.

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To determine the work done on the basketball by air resistance, we need to calculate the change in kinetic energy of the ball. The work done by air resistance is equal to the negative change in kinetic energy.

Mass of the ball (m) = 0.610 kg

Initial height (h1) = 1.90 m

Final height (h2) = 3.04 m

Initial speed (v1) = 7.03 m/s

Final speed (v2) = 4.29 m/s

The initial kinetic energy (KE1) of the ball is given by:

KE1 = (1/2)mv1^2

The final kinetic energy (KE2) of the ball is given by:

KE2 = (1/2)mv2^2

The work done by air resistance is given by:

Work = -(KE2 - KE1)

Substituting the given values into the equations:

KE1 = (1/2)(0.610 kg)(7.03 m/s)^2

KE2 = (1/2)(0.610 kg)(4.29 m/s)^2

Work = -[(1/2)(0.610 kg)(4.29 m/s)^2 - (1/2)(0.610 kg)(7.03 m/s)^2]

Calculating the work:

Work = -[(1/2)(0.610 kg)(18.3841 m^2/s^2) - (1/2)(0.610 kg)(34.2909 m^2/s^2)]

Work = -[5.63586705 J - 10.42909715 J]

Work = -(-4.7932301 J)

Work ≈ 4.793 J

Therefore, the work done on the ball by air resistance, a nonconservative force, is approximately 4.793 Joules.

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Answer:

165 kPa

Explanation:

Absolute pressure is:

P = Patm + ρgh

where Patm is the atmospheric pressure,

ρ is the density,

g is acceleration due to gravity,

and h is the depth.

P = 101,300 Pa + (1000 kg/m³) (9.8 m/s²) (6.50 m)

P = 165,000 Pa

P = 165 kPa

Power sources that are connected in parallel should have the same voltage output. This statement is true.

What does it mean when we say two power sources are connected in parallel?  Power sources are connected in parallel to increase the current output. This means that the positive terminals of the power sources are connected to the other positive terminals, and the negative terminals of the power sources are connected to the other negative terminals. This results in the voltage output remaining the same, but the current output increasing. This is useful when more current is required for a particular application. To summarize, when power sources are connected in parallel, the voltage output should remain the same, and the current output should increase.

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Answer:

Gravity

Explanation:

Gravity is a force that acts upon every single object on Earth.

The persοn is mοving at a speed οf 55 miles per hοur in the Sοuth directiοn when the persοn is 50 miles West and 70 miles Sοuth οf the car, and the distance between them is increasing at a rate οf 55 miles per hοur.

Tο determine the speed at which the persοn is mοving, we can use the cοncept οf relative velοcity.

Let's cοnsider the hοrizοntal and vertical cοmpοnents separately:

Hοrizοntal Cοmpοnent:

The persοn is walking due East, which is perpendicular tο the Nοrth directiοn οf the car. Therefοre, the hοrizοntal cοmpοnent οf the persοn's velοcity dοes nοt affect the speed at which the persοn is mοving away frοm the car.

Vertical Cοmpοnent:

The persοn is 70 miles Sοuth οf the car, and the distance between them is increasing at a rate οf 55 miles per hοur. This indicates that the persοn's vertical pοsitiοn is changing with time. Since the persοn is mοving in the Sοuth directiοn and the distance is increasing, the persοn's speed can be determined by the rate οf change οf the vertical distance.

Given that the distance is increasing at a rate οf 55 miles per hοur, the persοn's speed in the Sοuth directiοn is 55 miles per hοur.

Therefοre, the persοn is mοving at a speed οf 55 miles per hοur in the Sοuth directiοn when the persοn is 50 miles West and 70 miles Sοuth οf the car, and the distance between them is increasing at a rate οf 55 miles per hοur.

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We will have that the picture that shows the highest average kinetic energy is image B.

When the air near the freezer compartment is cooled, the transfer of thermal energy causes the air particles to lose kinetic energy.

When the air near the freezer compartment is cooled, the transfer of thermal energy causes the air particles to lose kinetic energy. As a result, the average motion of the air particles decreases, leading to a decrease in their temperature. Cooling is typically achieved by removing heat energy from the air, which results in a decrease in the thermal motion of the particles and a decrease in their overall energy level.

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Answer:

True

Explanation:

The graphical representation of Tara is correct because of energy of the wave depends on the amplitude of the wave.

The energy of a wave due to the motion of a spring is calculated as follows;

E = ¹/₂KA²

where;

Thus, the graphical representation of Tara is correct because of energy of the wave depends on the amplitude of the wave.

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Answer:  No, it is not correct because as the amplitude of a wave increases, the energy it carries also increases. This graph shows that as the amplitude increases, the energy decreases.  

Explanation:

waves that are created as a result of vibrations between an electric field and a magnetic field.

Answer:

Electromagnetic waves or EM waves are waves that are created as a result of vibrations between an electric field and a magnetic field. In other words, EM waves are composed of oscillating magnetic and electric field. EM waves travel with a constant velocity of 3.00 x 108 ms-1 in vacuum.

Explanation:

It would take 1,452.6 Calories of work to climb Mount Everest and, with a power output of 100 W, it would take 16.88 hours to complete the climb.

To calculate the work done in climbing Mount Everest, we'll use the formula:

work = force x distance

The force involved here is your weight, which we'll assume to be 70 kg for this example. The distance is the height of Mount Everest, which is 8,848 meters.

First, let's find the force by multiplying the mass (70 kg) by the acceleration due to gravity (9.81 m/s²):
Force = mass x gravity = 70 kg x 9.81 m/s² = 686.7 N (Newtons)

Next, we'll calculate the work:
Work = force x distance = 686.7 N x 8,848 m = 6,075,465.6 J (Joules)

To convert Joules to Calories, we'll use the conversion factor of 1 Calorie = 4,184 Joules:

6,075,465.6 J ÷ 4,184 J/Calorie = 1,452.6 Calories

Now, let's find the time it would take by using the "slow" power calculation. Let's assume your power output is 100 W (Watts).

Power is defined as work divided by time, so we can rearrange the formula to find the time:

Time = work ÷ power = 6,075,465.6 J ÷ 100 W = 60,754.7 seconds

Convert seconds to hours, divide by 3,600:

60,754.7 s ÷ 3,600 s/hour = 16.88 hours

In conclusion, it would take 1,452.6 Calories of work to climb Mount Everest and, with a power output of 100 W, it would take approximately 16.88 hours to complete the climb.

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The statement “Increased levels of endorphins are released into the brain, boosting a person's mood” best explains how the regular form of exercise is beneficial to the brain.

Generally, when individuals exercise regularly, their bodies tend to release chemicals named endorphins. Some of the significant characteristics of endorphins are listed as follows:

Thus, we can conclude that regular exercise can boost a person’s mood by increasing the endorphin levels that are released into the brain. Hence, option A is the correct answer.

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Gravitational force between two masses m, and m, is represented as F = Gm₂ m₂ / r^2 where r = xi+yj + zkG, m, m₂ are nonzero constants and let's assume that I = 0

a) Calculation:For F = Gm₂ m₂ / r^2.

Using r = xi+yj + zk and let r^2 = x^2 + y^2 + z^2∴ F = Gm₂ m₂ / (x^2 + y^2 + z^2), Where G, m, m₂ are nonzero constants. Divergence of F = ∇ · F= 1/r^2(d/dx(r^2Fx) + d/dy(r^2Fy) + d/dz(r^2Fz))= 1/r^2(d/dx(r^2Gm₂ m₂ x/(x^2+y^2+z^2)^(3/2)) + d/dy(r^2Gm₂ m₂ y/(x^2+y^2+z^2)^(3/2)) + d/dz(r^2Gm₂ m₂ z/(x^2+y^2+z^2)^(3/2)))= 1/r^2(d/dx(r^2Gm₂ m₂ x/(x^2+y^2+z^2)) * (x^2+y^2+z^2)^(3/2) + d/dy(r^2Gm₂ m₂ y/(x^2+y^2+z^2)) * (x^2+y^2+z^2)^(3/2) + d/dz(r^2Gm₂ m₂ z/(x^2+y^2+z^2)) * (x^2+y^2+z^2)^(3/2))= 1/r^2(Gm₂ m₂ [2x(x^2+y^2+z^2)-3x^2]/(x^2+y^2+z^2)^(5/2) + Gm₂ m₂ [2y(x^2+y^2+z^2)-3y^2]/(x^2+y^2+z^2)^(5/2) + Gm₂ m₂ [2z(x^2+y^2+z^2)-3z^2]/(x^2+y^2+z^2)^(5/2))= 1/r^2(Gm₂ m₂ [(2x^2+2y^2+2z^2-3x^2)/(x^2+y^2+z^2)^(3/2)] + [2x^2+2y^2+2z^2-3y^2]/(x^2+y^2+z^2)^(3/2)] + [2x^2+2y^2+2z^2-3z^2]/(x^2+y^2+z^2)^(3/2)])= 1/r^2(Gm₂ m₂ [x^2+y^2+z^2]/(x^2+y^2+z^2)^(3/2))= 0.

Curl of F = ∇ × F= i(d/dy(Fz) - d/dz(Fy)) - j(d/dx(Fz) - d/dz(Fx)) + k(d/dx(Fy) - d/dy(Fx))= i(d/dy(Gm₂ m₂ z/(x^2+y^2+z^2)) - d/dz(Gm₂ m₂ y/(x^2+y^2+z^2))) - j(d/dx(Gm₂ m₂ z/(x^2+y^2+z^2)) - d/dz(Gm₂ m₂ x/(x^2+y^2+z^2))) + k(d/dx(Gm₂ m₂ y/(x^2+y^2+z^2)) - d/dy(Gm₂ m₂ x/(x^2+y^2+z^2)))= i(Gm₂ m₂ [-2xz]/(x^2+y^2+z^2)^(5/2)) - j(Gm₂ m₂ [-2yz]/(x^2+y^2+z^2)^(5/2)) + k(Gm₂ m₂ [(x^2+y^2-2z^2)]/(x^2+y^2+z^2)^(5/2))

b) Calculation:The line integral of F along a curve C can be evaluated by the following formula∫C F.dr = ∫∫ ( ∇ x F) ds, Where r is the position vector of the curve, s is the scalar parameter representing the curve, and the integral is evaluated from the initial point to the final point.

Using the curl of F obtained in part a) and for the surface with ∂S as C∫C F.dr = ∫∫ ( ∇ x F) ds= ∫∫ curl(F) ds= ∫∫ (-2xz i -2yz j + (x^2+y^2-2z^2)k) ds...[1]

Let's consider the surface S as a plane perpendicular to the z-axis of the form ax+by+c=0 and the curve C as the intersection of the plane and the cylinder x^2 + y^2 = a^2.

Let's choose the unit normal to the surface S as k (along the z-axis).

The curl of F is a vector field perpendicular to the plane and along the direction of k.

Thus the integral can be written as∫C F.dr = ∫∫ ( ∇ x F) . k ds= ∫∫ (x^2+y^2-2z^2) ds...[2]

Now let's evaluate the integral over the given plane ax+by+c=0. We can write x = t, y = (c-at)/b and z = 0, where t is the scalar parameter along the line of intersection of the plane and the cylinder (x^2 + y^2 = a^2).

Since the curve C is on the cylinder of radius a, we have x^2+y^2 = a^2 ⇒ t^2+(c-at)^2/b^2 = a^2On solving for t, we have t = (bc±ab √(a^2-b^2-c^2))/[a^2+b^2].

Substituting t in x and y, we get the curve C in the x-y plane as a function of the scalar parameter s asx = (bc±ab √(a^2-b^2-c^2))/[a^2+b^2]y = (c-at)/b= (c-(bc±ab √(a^2-b^2-c^2))/[a^2+b^2])/b.

Now we can evaluate the integral over the curve C, which is along the intersection of the plane and the cylinder.

Integral over C (x^2+y^2-2z^2) ds= ∫t₁^t₂ [(t^2 + [(c-at)^2]/b^2 - 2(0)^2)^(1/2)] dt= ∫t₁^t₂ [(a^2-b^2-c^2)t^2+2bc(c-at)+b^2c^2-a^2b^2]^(1/2) dt.

Now we can choose the value of t₁ and t₂ such that the square root in the integrand is minimized (so that the integral is path-independent).

This can be done by choosing the value of t that gives the minimum value of (a^2-b^2-c^2)t^2+2bc(c-at)+b^2c^2-a^2b^2 over the range of t from t₁ to t₂.

On differentiation with respect to t and equating to 0, we get the value of t = bc/(a^2+b^2).

Substituting this value of t in the integrand, we get the minimum value of the square root in the integrand to be |c| √(a^2+b^2)/|b|.

Thus the integral over C is given by∫C F.dr = ∫∫ (-2xz i -2yz j + (x^2+y^2-2z^2)k) ds= ∫∫ (x^2+y^2-2z^2) ds= ∫t₁^t₂ |c| √(a^2+b^2)/|b| dt= |c| √(a^2+b^2)/|b| (t₂-t₁).

Now we can see that the integral is path-independent as it depends only on the end points t₁ and t₂ and not on the path taken to reach them.

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The current through the circuit after 12.5 ms is 2.5864 A.

The characteristic time constant of a 23.2 mh inductor that has a resistance of 4.21 ω is 5.82115 ms.

If it is connected to a 12.0 v battery, the current after 12.5 ms will be 2.5864 A.

Below are the steps to get to the answer:(a) Calculate the characteristic time constant of the circuit using the formula:τ = L/RWhere τ is the time constant, L is the inductance of the inductor, and R is the resistance of the circuit.tau=23.2mH/4.21Ω=5.82115ms

Hence, the characteristic time constant of the circuit is 5.82115 ms.

(b) To calculate the current through the circuit, we need to use the formula:i = (V/R) [1 - e(-t/τ)]Where i is the current, V is the voltage of the battery, R is the resistance of the circuit, t is the time, and τ is the characteristic time constant of the circuit.i = (12/4.21) [1 - e(-12.5/5.82115)]i = 2.5864

Hence, the current through the circuit after 12.5 ms is 2.5864 A.

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If it is critical to measure the wavelengths precisely for a given lamp, the grating with the highest number of lines per centimeter (lines/cm) should be used. In this case, the grating with 800 lines/cm would be the most suitable option.

Gratings are optical devices with a periodic pattern of equally spaced lines or grooves. They are commonly used in spectroscopy to disperse light into its component wavelengths. The number of lines per centimeter on a grating determines its resolution or ability to separate closely spaced wavelengths.

Higher line densities (more lines/cm) provide finer resolution and allow for more precise measurement of wavelengths. With a grating having 800 lines/cm, it would offer a higher resolution compared to the gratings with 400 lines/cm or 100 lines/cm. This means it would enable more accurate determination of the specific wavelengths present in the lamp's emission spectrum.

By using the grating with the highest line density, finer details in the lamp's spectrum can be resolved, resulting in more precise measurements of the wavelengths.

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Answer:

infra-red

molecules

vacuum

ionizing (?)

transmission

redirected

absorbed

emission

dark

emitter

reflectors

deflect

 3,958 miles miles would you have to dig

The mile, sometimes the best of international mile or statute mile to distinguish it from the  other miles, is a British imperial unit and United States customary to know unit of to the relative distance; both are based on to the older English unit of to the length equal to 5,280 English-english feet, or 1,760 yards.

Well, it depends what you mean by “bottom.” Earth is the  ball, so if you wanted to dig in to  the center of it, it's 3,958 miles. But if you wanted to dig all the way throughs and pop out the other side, it's twice as far, or 7,916 miles.

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