at what speed do a bicycle and its rider, with a combined mass of 110 kg , have the same momentum as a 1300 kg car traveling at 5.4 m/s ?

The focal length of a spherical mirror is N times its radius of curvature where N is 2

Describe focal length.

A lens's focal length is established when it is focused at infinity. We can determine the magnification—how large individual elements will be—and the angle of view—how much of the picture will be captured—by knowing the focal length of the lens. The narrower the field of view and higher the magnification, the longer the focal length.

1/f = 1/u + 1/v is the general formula for the mirror. The equation changes to 1/f = (N-1)/r for a sphere with a radius of curvature of N. Using the mirror formula to equate this, we obtain N=2.

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According to the question the Average angular acceleration is 1.64 rad/s².

Acceleration is the rate of change of an object's velocity in a certain direction. It is typically measured in meters per second squared (m/s2) and is a physical vector quantity, meaning it has both magnitude (size) and direction. Acceleration is the result of an applied force, an unbalanced force, or a change in velocity. Examples of acceleration include speeding up a car, an object falling due to gravity, and a rocket taking off. Acceleration is an important part of Newton's laws of motion, which gives us an understanding of how forces interact with objects.

The average angular acceleration can be calculated by using the equation:
Average angular acceleration = (final angular velocity - initial angular velocity) / time
Therefore, the time is equal to 30π / 7.01, which is approximately 4.28 s.
Substituting these values into the equation, the average angular acceleration is:
Average angular acceleration = (0 - 7.01) / 4.28 = -1.64 rad/s²

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A laser beam passes from air into a 25% glucose solution at an incident angle of 37°.

We can use Snell's Law to solve both parts of this question.

Part 1

Snell's Law states that

n1 sinθ1 = n2 sinθ2

Where n1 and n2 are the indices of refraction of the two media, θ1 is the incident angle, and θ2 is the refracted angle.

In this case, n1 = 1 (for air) and n2 = 1.33 (for the 25% glucose solution). We are given θ1 = 37°. Solving for θ2, we get

sinθ2 = (n1/n2) sinθ1

sinθ2 = (1/1.33) sin(37°)

sinθ2 = 0.516

θ2 = 31.7°

Therefore, the direction of the light in the glucose solution is at an angle of 31.7° relative to the normal.

Part 2

In this case, we are going from ethyl alcohol to air, so n1 = 1.36 and n2 = 1. We are given θ1 = 12°. Solving for θ2, we get

sinθ2 = (n1/n2) sinθ1

sinθ2 = (1.36/1) sin(12°)

sinθ2 = 0.188

θ2 = 11.0°

Therefore, the angle of the refracted beam in air is 11.0°.

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Inductor 1 stores the same amount of energy as inductor 2, although its inductance is only half the inductance of inductor 2. What is the ratio i1/i2 of the currents in the two inductors?

To answer this question, we'll use the formula for the energy stored in an inductor, which is:

Energy (E) = (1/2) * L * I², where L is the inductance, and I is the current.

Since both inductors store the same amount of energy, we have:

(1/2) * L1 * I1² = (1/2) * L₂ * I₂²

Given that the inductance of inductor 1 (L1) is half the inductance of inductor 2 (L₂ ), we can substitute L1 with (1/2) * L₂ :

(1/2) * (1/2) * L₂  * I₁² = (1/2) * L₂ * I₂²

Now, we can simplify the equation and find the ratio, i₁/i₂,:

I₁² / I₂²= 1

Taking the square root of both sides:

i₁/ i= 1

So, the ratio of the currents in the two inductors, i₁/i₂, is 1.

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the Schwarzschild radius in kilometers of a black hole with a mass of 2.3 million solar masses is approximately 13.6 billion kilometers.

The Schwarzschild radius of a black hole is given by the formula:

r_s = (2GM) / c^2

where G is the gravitational constant, M is the mass of the black hole, and c is the speed of light.

To find the Schwarzschild radius in kilometers of a black hole with a mass of 2.3 million solar masses, we first need to convert the mass to kilograms. One solar mass is equal to approximately 1.99 × 10^30 kilograms, so 2.3 million solar masses is equal to:

M = 2.3 million × 1.99 × 10^30 kg/solar mass = 4.577 × 10^36 kg

Next, we can substitute the values into the formula for the Schwarzschild radius:

r_s = (2GM) / c^2 = (2 × 6.6743 × 10^-11 m^3 kg^-1 s^-2 × 4.577 × 10^36 kg) / (299792458 m/s)^2

Simplifying the expression gives:

r_s = 13.6 × 10^12 m = 13.6 × 10^9 km

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The rotation speed required for a projected space station with a circular tube of 1.1 km diameter to feel an effect equivalent to gravity at the surface of the Earth (1g) is approximately 1.8 revolutions per minute or 1296 revolutions per day.

To explain this, the force experienced by an object due to its rotation is known as centrifugal force. For an object to feel an effect equal to gravity (1g), the centrifugal force experienced by the object must be equal to the force of gravity. The centrifugal force is proportional to the square of the rotation speed and the radius of rotation. In this case, the radius of rotation is half the diameter of the circular tube, or 550 meters. Thus, we can use the formula Fc = mv^2/r to find the required rotation speed.

Since we are given that the effect should be equal to 1g, we can set the centrifugal force equal to the force of gravity, or Fc = Fg. Using the value of the gravitational constant (g) at the surface of the Earth and plugging in the known values, we can solve for the rotation speed (v). This gives us a speed of approximately 1.8 revolutions per minute or 1296 revolutions per day.

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Angular momentum is a vector quantity that describes the rotation of an object around a fixed axis. The direction of the angular momentum vector is determined by the direction of the object's rotation and the axis of rotation.

For the minute hand of a clock, the direction of the angular momentum vector is towards the mechanism of the clock when viewed from the back of the clock and towards the glass of the clock when viewed from the front of the clock. This is because the minute hand rotates around the axis of the clock's mechanism, which is perpendicular to the face of the clock.

For the right front tire of a car moving backwards, the direction of the angular momentum vector is to the right, away from the car when viewed from the front of the car, and to the left, towards the center of the car when viewed from the top of the car. This is because the tire rotates around its axis, which is perpendicular to the direction of motion of the car.

For an ice skater spinning clockwise, the direction of the angular momentum vector is downward when viewed from above the skater. This is because the skater rotates around an axis perpendicular to the ground, and the angular momentum vector points in the direction of the skater's thumb when the fingers of their right hand curl in the direction of rotation.

In conclusion, the direction of the angular momentum vector depends on the direction of rotation and the axis of rotation, and it can be determined using the right-hand rule.

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The diameter of the moon is 3. 47x[tex]10^{6}[/tex] m and it subtends an angle of 0. 00904 rad when viewed from the surface of the earth, the distance to the moon from the surface of the earth is approximately 3.83 × [tex]10^{8}[/tex] meters.

We can use the small angle formula to relate the angle subtended by an object, the distance to the object, and its size

Angle = size / distance

Here, we know the size of the moon (its diameter), and the angle it subtends when viewed from the surface of the earth. We can use this formula to solve for the distance to the moon

Distance = size / angle

Substituting the values given, we get

Distance = 3. 47x[tex]10^{6}[/tex] m / 0.00904 rad

Evaluating this expression, we get

Distance = 3.83 × [tex]10^{8}[/tex] m

Therefore, the distance to the moon from the surface of the earth is approximately 3.83 × [tex]10^{8}[/tex] meters.

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According to the question the temperature change on the Celsius scale is 40 C°.

Temperature is a measure of the average kinetic energy of the molecules in a system. It is a physical quantity, usually expressed as a numerical value, that indicates how hot or cold something is. Temperature is measured in degrees on a variety of scales, including Celsius, Fahrenheit, and Kelvin. The higher the temperature, the greater the average kinetic energy of the molecules in the system. Temperature is an important factor in many physical and chemical processes, and it can affect the behavior of matter in a variety of ways.

To convert from Fahrenheit to Celsius, use the formula C = (F - 32) * (5/9).  So,
the temperature change on the Celsius scale would be (75 - 35) * (5/9) = 40 C°.

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(a)Two-source interference maxima would occur at angles of ±45°, ±22.5°, ±67.5°, ±90°, (b) The slit diffraction minima would occur at angles of ±22.5°, ±67.5°, ±90°,(c)The required wavelength for -90° ≤ 0 ≤ 90° is λ ≥ 4a.

Angles are geometric shapes which are formed when two straight lines intersect. They are measured in degrees, and can range from 0° to 360°. Angles are used in mathematics to describe the direction or orientation of objects, and can be used to solve many problems.  Acute angles are those that measure less than 90°, right angles measure 90°, obtuse angles measure more than 90° but less than 180°, and straight angles measure 180°.

a) Without diffraction effects, the angles of 2-source interference maxima will occur when the path difference between the two slits is equal to an integer multiple of the wavelength (A). The path difference between two slits is d, so the angles for the 2-source interference maxima are given by: θ = ± (2π/A) * (d/2)

Since A = d/5, the angles are given by: θ = ± (2π/d) * (d/10) = ± (2π/10)

Therefore, the angles for the 2-source interference maxima are 0°, ± 18°, ± 36°, ± 54° and ± 72°.

b) When diffraction effects due to the slit width are included, the angles for the 2-source interference maxima will be slightly different. The angles of the 2-source interference maxima that are "missing" are 0°, ± 18° and ± 72°.

c) In order for there to be no minima in the single slit diffraction intensity for -90° ≤ 0 ≤ 90°, the wavelength must be greater than the slit.

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A temperature change of 20 C° corresponds to a Fahrenheit temperature change is 36 F°.

Fahrenheit is a temperature scale where water freezes at 32 degrees and boils at 212 degrees. This temperature scale was developed by the German physicist Daniel Gabriel Fahrenheit in the early 1700s. Although it is no longer used as the official temperature scale in many countries, it is still widely used in the United States. The Fahrenheit scale is also sometimes referred to as the “centigrade” scale.

The formula for converting Celsius to Fahrenheit is F = (9/5)C + 32.

Therefore, to find the Fahrenheit temperature change when the Celsius temperature changes by 20 C°, we can use the formula as follows:

F = (9/5)(20) + 32

F = 36 + 32

F = 68 F°

Since the temperature change in Fahrenheit is 68 F°, the temperature change in Fahrenheit is 36 F°.

So, the correct answer is option C.

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The length of probation after a license suspension for points varies by state and can depend on the severity of the violation. It is best to check with your local DMV or state motor vehicle agency for specific information.

Suspension refers to the temporary revocation of a privilege or right. For example, a driver's license can be suspended for a period of time due to a violation of traffic laws or regulations. Similarly, a student can be suspended from school for a period of time due to a violation of school policies. Probation, on the other hand, refers to a period of time during which an individual is closely monitored and required to follow specific rules or conditions. This can occur as part of a sentence for a criminal conviction, where the offender is released into the community under the supervision of a probation officer. It can also occur in the context of a workplace or school, where an individual is placed on probation for a period of time to monitor their behavior and ensure they are meeting certain expectations. In both cases, the individual is subject to specific terms and conditions, and failure to comply can result in further penalties or consequences.

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The image of your face in a small convex mirror would be smaller and appear upside down. This is because convex mirrors curve outward, causing light rays to diverge, and creating a virtual image that is smaller than the original object.

In explanation, when light rays reflect off a convex mirror, they spread out and do not converge at a point like they would with a concave mirror.

This causes the image to be smaller and appear upside down.

This is because convex mirrors curve outward, causing light rays to diverge, and creating a virtual image that is smaller than the original object

In summary, holding a small convex mirror in front of your face would produce a smaller, upside-down image of your face due to the outward curvature of the mirror causing light rays to diverge.

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If you were to grab the edge of the spinning wheel on a merry-go-round, it would cause the entire ride to slow down and eventually come to a stop. This is because the momentum of the spinning wheel, which is connected to the entire ride, is suddenly stopped by your hand.

The rest of the ride can't keep moving at the same speed because it's all connected and the momentum is lost.
It's important to note that stopping the spinning wheel can be dangerous, as the sudden stop can cause anyone on the ride to be thrown off or injured. It's important to follow all safety guidelines and not attempt to stop the ride on your own.
In addition, if the spinning wheel is part of the mechanism that powers the ride, stopping it could cause the entire ride to shut down or malfunction. In general, it's best to leave the operation and maintenance of amusement park rides to trained professionals.

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The magneto used in the ignition system of old automobile engines produces a spark by utilizing the principle of electromagnetic induction. As the flywheel, with the permanent magnet mounted on it, turns, it generates a changing magnetic field around the stationary coil. This changing magnetic field induces an electric current in the coil, which is then sent to the spark plug. The spark plug, in turn, produces a spark to ignite the fuel mixture in the engine's cylinders. Therefore, the magneto is responsible for providing the necessary spark for the engine to start and run.
I'm happy to help you with your question about the magneto ignition system in old automobile engines. Here's a step-by-step explanation:

1. In a magneto ignition system, a permanent magnet is mounted on the engine's flywheel.

2. As the flywheel rotates with the engine, the magnet also moves along with it.

3. The magnet passes by a stationary coil, which is connected to the spark plug. This coil is also known as the ignition coil.

4. When the magnet moves past the stationary coil, it generates a change in magnetic flux, which in turn induces an electromotive force (EMF) in the coil according to Faraday's law of electromagnetic induction.

5. The induced EMF in the ignition coil causes a current to flow through the coil. This current charges the capacitor, which is part of the ignition circuit.

6. When the current reaches a certain threshold, the contact breaker (or points) in the circuit opens, rapidly interrupting the current flow through the coil.

7. This abrupt interruption of current flow causes the magnetic field in the coil to collapse quickly, which in turn induces a high voltage across the coil terminals, as per Lenz's law.

8. The high voltage generated at the coil terminals is then sent to the spark plug through the distributor.

9. The high voltage across the spark plug creates an electric field strong enough to ionize the air-fuel mixture in the combustion chamber, resulting in a spark.

10. This spark ignites the air-fuel mixture, initiating the combustion process in the engine, and thus, powering the automobile.

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The equivalent resistance of the three resistors connected in series is 350 Ω.

In a series circuit, resistors are connected end to end, so the current flowing through each resistor is the same. The equivalent resistance of a series circuit is the sum of the individual resistances. In this case, the equivalent resistance is 50 Ω + 120 Ω + 180 Ω = 350 Ω. This means that if a voltage source were connected to the circuit, the total current flowing through the circuit would be determined by Ohm's Law, which states that current is equal to voltage divided by resistance. The greater the resistance, the less current will flow through the circuit.

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To get stud multipliers in Lego Star Wars: The Skywalker Saga, you'll need to locate and collect red bricks throughout the game. These red bricks can be found by completing various challenges, exploring levels thoroughly, or by purchasing them from the in-game store.

Once you have collected a red brick, you can activate it by going into the pause menu and selecting "extras." From there, you can toggle on the stud multiplier you have unlocked. There are several stud multipliers available in the game, ranging from 2x to 10x. Activating these multipliers will allow you to collect more studs and unlock more characters and items.

To get stud multipliers in LEGO Star Wars: The Skywalker Saga, follow these steps:

1. Progress through the game: As you complete levels, you will unlock new areas and features, which may contain stud multipliers.

2. Explore hub areas: While navigating the open-world hub areas, look for hidden collectibles, such as Red Bricks, which may unlock stud multipliers.

3. Complete side quests: Take on side quests and challenges offered by NPCs, as some may reward you with stud multipliers upon completion.

4. Purchase multipliers: Once unlocked, stud multipliers can be purchased using in-game currency (studs) from the game's store or menu.

5. Activate multipliers: After purchasing a stud multiplier, access the Extras menu and enable it to increase the number of studs you earn while playing.

Remember to explore thoroughly and complete various in-game tasks to find and unlock stud multipliers in LEGO Star Wars: The Skywalker Saga.

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If the mechanical advantage of a lever is 3 and the input distance (effort arm) is 12 meters, the output distance (load arm) would be 4 meters.

To solve this problem, we can use the formula for mechanical advantage: MA = output force / input force = input distance / output distance.

Since we know that the mechanical advantage is 3 and the input distance is 12 meters, we can plug in those values to solve for the output distance:
3 = input distance / output distance
3(output distance) = 12
output distance = 12 / 3
output distance = 4 meters
So the output distance (load arm) would be 4 meters.

It's important to remember that in a lever, the mechanical advantage depends on the ratio of the length of the effort arm to the length of the load arm. In this case, a mechanical advantage of 3 means that the effort arm is three times longer than the load arm. By knowing one of the distances, we can solve for the other.

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The Torino scale is an important tool used to evaluate the potential risks associated with comet and asteroid impacts. It is a numerical scale that ranges from 0 to 10, with each category representing a different level of hazard.

The scale has 10 categories in total, with category 0 indicating no threat and category 10 representing a collision that would cause a global catastrophe. The other categories fall in between these two extremes and take into account factors such as the size, speed, and proximity of the object to Earth.

The higher the category, the more urgent the need for action to mitigate the potential effects of a collision. In summary, the Torino scale provides a standardized way of communicating the level of risk associated with potential impacts from comets and asteroids.

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The object with a temperature of 1000 K radiates the largest amount of power at a frequency of 1.03 x 1014 Hz.

Temperature is a measure of the average kinetic energy of the particles in a substance. It is typically measured in degrees Celsius (°C), Kelvin (K), and Fahrenheit (°F). Temperature can be used to describe the thermal energy of a system, and is often used to describe the state of a system. Hot objects have more thermal energy than cold objects.

The wavelength of radiation with the highest power output from an object with a temperature of 1000 K is given by the Wien Displacement Law and is equal to: λ = (2.90 x 10-3 m . K) / (1000 K) = 2.90 x 10-6 m

The frequency of radiation corresponding to this wavelength is equal to:

f = (3.00 x 10 m/s) / (2.90 x 10-6 m) = 1.03 x 1014 Hz

The object with a temperature of 1000 K radiates the largest amount of power at a frequency of 1.03 x 1014 Hz. The Stefan-Boltzmann Law states that the total power emitted from an object is directly proportional to the fourth power of the object's temperature (P = σT4). The higher the temperature of an object, the greater the amount of power it radiates at a given frequency.

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Complete Question

In the vicinity of what frequency does an object with a temperature of 1000 K radiate the largest amount of power? (c 3.00 x10 m/s, Wien displacement law constant equals 2.90 x 10-3 m . K, σ= 5.670 × 10-8 W/m2 . K4).

False. The water cycle is a much more complex process that involves multiple steps. The sun's energy causes water to evaporate from the ocean, but it also causes evapotranspiration from plants and other sources.

This water vapor rises into the atmosphere and condenses into clouds. Eventually, the clouds release their moisture as precipitation, which can fall back into bodies of water or onto land. This water can then infiltrate the ground and become groundwater, or flow into rivers and other bodies of water, where the cycle begins again.

So, while the sun's energy is an important factor in the water cycle, it is not the only factor and the process is much more intricate than simply warming the ocean.

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The ratio of the second moment of inertia to the first is [tex]\frac{1}{12}[/tex]

Inertia is the resistance of a body to a change in its state of motion. It is a fundamental property of matter that resists changes in its motion, whether it is at rest or moving. Inertia is related to mass; the greater the mass of a body, the greater its inertia. Inertia is the reason why a moving object will keep moving at the same speed and direction, unless acted upon by an outside force.

Let the 1 m long stick have a mass m. The first moment of inertia is given by
[tex]I_1 = \frac{1}{12}m \times (1 \text{m})^2 = \frac{1}{12}m[/tex]
The second moment of inertia is given by
[tex]I_2 = \frac{1}{12}m \times (0.84 \text{m})^2 = \frac{1}{144}m[/tex]
The ratio of the second moment of inertia to the first is given by
[tex]\frac{I_2}{I_1} = \frac{\frac{1}{144}m}{\frac{1}{12}m} = \frac{1}{12}[/tex]

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Complete Question:

Consider a stick 1.00 m long and its moments of inertia about axes perpendicular to the stick's length and passing through two different points on the stick: first, a point at its center and second, a point 16 cm from one end. Calculate the ratio I/I, the ratio of the second moment of inertia to the first. 11 Record your numerical answer below, assuming three significant figures. Remember to include a "-" as necessary,

When a current flows through a metal wire, the moving charges are only electrons.

Hence, the correct option is B.

When a current flows through a metal wire, the moving charges are electrons. In a metal, electrons are delocalized and free to move through the lattice of positive metal ions. When a voltage is applied across the metal, the electric field created by the voltage causes the free electrons to move in a particular direction, creating an electric current. Protons are located within the atomic nucleus of the metal and are not free to move through the lattice, so they do not contribute to the electric current.

Hence, the correct option is B.

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Steam causes more severe burns than liquid water at 100 degrees Celsius because it has much more energy due to its increased surface area.

Energy is the ability to do work. It can take many forms, such as kinetic, potential, thermal, electrical, chemical, nuclear, and others. It is a property of matter and an important component of physical and chemical processes. Energy is often measured in joules (J), kilojoules (kJ), or calories (cal). It is an essential component of physical and chemical reactions, and it is the source of power for many activities, such as the operation of machines, the production of light, and the movement of vehicles. In addition, it is important for the growth and maintenance of living organisms, and for the transformation of matter. Energy is neither created nor destroyed, but it can be converted from one form to another, such as when heat is converted to electrical energy, or when chemical energy is converted to kinetic energy.

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The resistance of the heater is 10.3 ohms.

The power (P) dissipated by the electric space heater is given by the formula P = V²/R, where V is the voltage across the heater and R is the resistance of the heater. In this case, the power is given as 1320 W and the voltage is given as 120 V. So we can rearrange the formula to solve for the resistance: R = V²/P. Substituting the given values, we get R = (120 V)² / 1320 W = 10.3 ohms. Therefore, the resistance of the heater is 10.3 ohm

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Answer:

The cosmological  constant accounts for the effects of dark energy.

Explanation:

The cosmological constant was first introduced by Albert Einstein, in 1917.

It was defined in the general relativity and it is used to represent a repulsive force in the expansion of the universe.

Vacuum Energy causes the cosmological constant.

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Suppose a lion is in free fall.  The lion covers the same distance as the second before.

In free fall, an object falls with a constant acceleration of 9.8 meters per second squared (9.8 m/s^2) due to the force of gravity. This means that the lion's speed increases by 9.8 m/s every second it falls. However, since the lion starts from rest, its initial speed is 0 m/s. Therefore, after one second of free fall, the lion's speed is 9.8 m/s, after two seconds it's 19.6 m/s, and so on. Despite the increase in speed, the lion's displacement (i.e., the distance it covers) in each second of free fall is the same, as the acceleration due to gravity is constant. Hence, the lion covers the same distance as the second before.

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The answer  is that the fraction of a piece of copper that will be submerged when it floats in mercury is equal to the ratio of the densities of copper and mercury.

When an object floats in a fluid, it displaces an amount of fluid equal to its own weight. If the weight of the object is less than the weight of the fluid it displaces, the object will float. The fraction of the object that is submerged depends on the density of the object relative to the density of the fluid.

In this case, copper has a density of 8.96 g/cm3, while mercury has a density of 13.53 g/cm3. The ratio of the densities is 8.96/13.53 = 0.662.

Therefore, when a piece of copper floats in mercury, approximately 66.2% of the volume of the copper will be submerged in the mercury.

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The glasses needed are again diverging lenses, with a focal length of 666.7 cm. The near point of a person is the closest distance from the eye at which an object can be seen clearly. For this farsighted person, the near point is 60 cm, which means that she has difficulty seeing objects that are closer than that.

To correct her vision, the person needs glasses that will create an image of nearby objects at a distance of 25 cm from her eyes. We can use the thin lens formula to find the focal length of the glasses needed:

1/f = 1/d_o + 1/d_i

where f is the focal length of the lens, d_o is the object distance (distance of the object from the lens), and d_i is the image distance (distance of the image from the lens). For a converging lens, the focal length is positive, and for a diverging lens, it is negative.

If the glasses are 2 cm from her eyes, the object distance is:

d_o = 60 cm - 2 cm = 58 cm

The image distance is:

d_i = -25 cm

since the image is formed on the same side as the object, and the image distance is negative for a virtual image. Therefore, we can solve for the focal length:

1/f = 1/d_o + 1/d_i

1/f = 1/58 cm - 1/25 cm

1/f = -0.0012 [tex]cm^{(-1)}[/tex]

f = -833.3 cm

Since the focal length is negative, the glasses needed are diverging lenses, with a focal length of 833.3 cm.

If the glasses are 3 cm from her eyes, the object distance is:

d_o = 60 cm - 3 cm = 57 cm

The image distance is still:

d_i = -25 cm

We can again solve for the focal length:

1/f = 1/d_o + 1/d_i

1/f = 1/57 cm - 1/25 cm

1/f = -0.0015 [tex]cm^{(-1)}[/tex]

f = -666.7 cm

Therefore, the glasses needed are again diverging lenses, with a focal length of 666.7 cm.

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The fundamental frequency of the pipe filled with helium will be 7.2 times the fundamental frequency of the pipe filled with air.

The fundamental frequency of a pipe filled with helium can be calculated using the formula:
fhe = fair * (Mair / Mhe) * (1/2)
Where fhe is the fundamental frequency of the pipe filled with helium, fair is the fundamental frequency of the pipe filled with air, Mair is the molar mass of air and Mhe is the molar mass of helium.
We are given that the molar mass of air is 28.8 g/mol and the molar mass of helium is 4.00 g/mol. The fundamental frequency of the pipe filled with air can be calculated using the formula:
fair = v / (2L)
Where v is the speed of sound in air and L is the length of the pipe. Since the temperature is the same, the speed of sound in air will be constant. Therefore, we can write:
fair = constant / L
The fundamental frequency of the pipe filled with helium can now be calculated as follows:
fhe = (constant / L) * (28.8 / 4.00) * (1/2)
fhe = (constant / L) * 7.2
Thus, the fundamental frequency of the pipe filled with helium will be 7.2 times the fundamental frequency of the pipe filled with air.

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