You are riding a very fast Ferris Wheel so that you actually notice a variation in your apparent weight. Where is your apparent weight maximum?A. At the topB. At the bottomC. Halfway up, going downD. Halfway up, going up

The number of atoms in a 67.5 mg sample of Sr to three significant figures is 4.63 x 10^20 atoms Sr .

When we have the molar mass of strontium and the mass of the sample, we can calculate the number of atoms in the sample using the Avogadro's number. The Avogadro's number represents the number of particles present in one mole of the substance, and it is equal to 6.022 x 10^23 particles per mole.Molar mass of strontium = 87.62 g/mol. Mass of the sample = 67.5 mg = 0.0675 g.Number of atoms of Sr in the given sample can be calculated as follows:

Number of moles of Sr = mass of the sample / molar mass of Sr= 0.0675 g / 87.62 g/mol= 7.704 x 10^-4 moles.

Number of atoms of Sr = Number of moles of Sr x Avogadro's number= 7.704 x 10^-4 moles x 6.022 x 10^23 atoms/mole= 4.63 x 10^20 atoms Sr.Therefore, the number of atoms in a 67.5 mg sample of Sr is 4.63 x 10^20 atoms Sr (to three significant figures).

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If the mass of the satellite is halved and the distance is doubled, the velocity of the satellite will be reduced to approximately 70.7% of its original value.

In this context, a satellite refers to an artificial object that is launched into orbit around the Earth to perform various functions, such as communication, navigation, and scientific research.

Let's start by writing the equation that relates the velocity of the satellite with its mass and distance from the center of the earth:

v = k√(m/r)

where k is a constant of proportionality.

Now, if the mass is halved and the distance is doubled, we have:

v' = k√(m/2r)

where v' is the new velocity. We can use this equation to find how the velocity is affected by the changes:

v' = k√(m/2r) = k√(m/r) / √2

The square root of 2 is approximately 1.414, so we can simplify the expression to:

v' = v / 1.414

Therefore, if the mass of the satellite is halved and the distance is doubled, the velocity of the satellite will be reduced to approximately 70.7% of its original value.

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Two people of unequal mass are initially standing still on ice with negligible friction. They then simultaneously push each other horizontally. Then, the statement which is true is the momenta of the two people are of equal magnitude. Thus, the correct option is C.

Momentum is the mass of an object multiplied by its velocity. It is represented by the symbol p. Momentum is a vector quantity and has the same direction as velocity. When the direction of velocity changes, so does the direction of momentum.

The law of conservation of momentum states that the total momentum of an isolated system is constant when no external forces act on the system. According to Newton's third law of motion, when two objects interact, the forces they apply to each other are equal in magnitude and opposite in direction. This implies that the forces on the two people are equal but opposite. Therefore, their momenta are also equal and opposite, so the net momentum of the system is zero after the push.

Kinetic energy is the energy possessed by an object in motion. It is represented by the symbol K. Kinetic energy is a scalar quantity, and it depends on the mass and velocity of the object. When an object moves, it gains kinetic energy, and when it stops, its kinetic energy becomes zero. The kinetic energies of the two people are not equal in this case.

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The distance which the football which cover before landing back on the ground level will be about 56.4 meters.

The mass of football, m = 0.43 kg, Initial velocity of football (v) = 24 m/s, Angle of inclination(θ) = 53°

From the given data, we know that the vertical component of the initial velocity is given by, vsin(θ) and the horizontal component of initial velocity is given by, vcos(θ). So, the time taken by the football to reach the maximum height is given by,

t = (vsin(θ))/g

Here, g = 9.8 m/s²

Now, the maximum height attained by the football is given by,h = (vsin(θ))²/(2g).

Therefore, the time of flight or the total time which is taken by the football to land on the ground level is given by,

T = 2t

Now, the horizontal distance travelled by the ball is given by, d = (vcos(θ))T

Substituting the given values in the above formulas, we get:

t = (24sin(53°))/9.8 = 1.71 s

h = (24sin(53°))²/(2×9.8) = 23.4m

T = 2×1.71 = 3.42 s

d = (24×cos(53°))×3.42 = 56.4 m

Therefore, the football will go 56.4 m before it is landing back on the level ground.

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The orbital speed of the second satellite is 6.55 × 10³ m/s.

The formula used to find the orbital speed of a satellite is given as v=√(GM/r).

Therefore, the value of the first satellite's speed is given as v₁=1.89×104 m/s, and the radius is r₁=2.76×106 m. Using the above formula, the mass of the planet is given as:

M= v²r/G= (1.89×104 m/s)² (2.76×106 m)/(6.6743 × 10⁻¹¹ Nm²/kg²) = 5.31 × 10²⁴ kg.

Now, the orbital speed of the second satellite, given as v₂, is equal to:

v₂ = √(GM/r₂); where G = gravitational constant = 6.6743 × 10⁻¹¹ Nm²/kg²;

M = mass of the planet = 5.31 × 10²⁴ kg;

r₂ = radius of orbit of the second satellite = 6.98 × 10⁶ m.

Substituting the values given above, we get:

v₂ = √(GM/r₂)= √[(6.6743 × 10⁻¹¹ Nm²/kg²) × (5.31 × 10²⁴ kg) / (6.98 × 10⁶ m)] = 6.55 × 10³ m/s

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A Nichrome wire 42 cm long and 0.28 mm in diameter is connected to a 2.1 V flashlight battery. You don't have to know how the wire is bent because it doesn't affect the resistance of the wire.

Nichrome is a type of resistance wire made from a nickel-chromium alloy. It has a high melting point and can withstand high temperatures. Nichrome wire is commonly used in heating elements, such as those found in toasters and hairdryers. The resistance of a wire depends on its length, cross-sectional area, and resistivity.

The resistance of a wire is given by the formula:

R = (ρl)/AWere,ρ = resistivity

l = length of wire

A = cross-sectional area of the wire

Resistance is directly proportional to the length of the wire and inversely proportional to the cross-sectional area of the wire. Therefore, a longer and thinner wire will have a higher resistance than a shorter and thicker wire. The resistivity of the material is also an important factor that affects the resistance of a wire.Since the length and diameter of the Nichrome wire are given, the resistance of the wire can be calculated using the formula mentioned above. Once the resistance is known, the current flowing through the wire can be calculated using Ohm's law. The voltage of the battery is also given, so the power dissipated by the wire can be calculated. The way the wire is bent does not affect its resistance or other electrical properties, so it is not necessary to know how it is bent.

Therefore, you do not have to know how the Nichrome wire is bent in order to calculate the current through the wire connected to a 2.1V flashlight battery.

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It would take approximately 161 minutes to raise the temperature of the air in the living room by 10.0°C using the given heater.

Using the formula P = IV, where P is power, I is current, and V is voltage, we can find the current flowing through the heating coil,

I = P/V = 1500 W/120 V = 12.5 A

To find the resistance of the heater, we can use Ohm's law, which states that V = IR, where V is voltage and R is resistance,

R = V/I = 120 V/12.5 A = 9.6 ohms

To calculate the amount of heat required to raise the temperature of the air in the living room, we can use the formula Q = mcΔT, where Q is heat, m is mass, c is specific heat, and ΔT is the change in temperature.

First, we need to find the mass of the air in the living room. The volume of the living room is 3.00 m × 5.00 m × 8.00 m = 120.00 m^3. Since the density of air is 1.20 kg/m^3, the mass of the air in the living room is,

m = density × volume = 1.20 kg/m^3 × 120.00 m^3 = 144 kg

Next, we can calculate the amount of heat required,

Q = mcΔT = (144 kg)(1006 J/(kg·°C))(10.0°C) = 1.45 × 10^7 J

Finally, we can use the formula Q = Pt, where t is time, to find the time required to generate this amount of heat,

t = Q/P = (1.45 × 10^7 J)/(1500 W) = 9667 seconds ≈ 161 minutes.

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Molly's experiment involved kicking a soccer ball with varying amounts of force and observing the resulting change in the ball's motion.

Newton's three laws of motion can help explain how the force of Molly's kicks affected the ball's movement.

Newton's first law of motion states that an object at rest will stay at rest and an object in motion will stay in motion with a constant velocity unless acted upon by an unbalanced force. In this experiment, the soccer ball was at rest before each kick, so the force of Molly's kicks acted as an unbalanced force, causing the ball to accelerate and move. The greater the force of her kick, the greater the acceleration and resulting distance the ball traveled.

Newton's second law of motion states that the acceleration of an object is directly proportional to the force applied and inversely proportional to its mass. In this case, the mass of the soccer ball remained constant, but the force of Molly's kicks varied. As a result, the acceleration of the ball was directly proportional to the force of her kick.

Finally, Newton's third law of motion states that for every action, there is an equal and opposite reaction. When Molly kicked the soccer ball, the ball exerted an equal and opposite force back on her foot, which is why she felt the impact of the kick.

Energy transfer also played a role in this experiment. When Molly kicked the ball, she transferred energy from her foot to the ball. The greater the force of her kick, the more energy was transferred to the ball, resulting in a greater distance traveled.

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Helium wavelength: 587.6 nm ,relative intensity: 100%,Hydrogen wavelength: 656.3 nm ,relative intensity: 100%,Sodium wavelength: 589.0 nm, relative intensity: 100%

In a spectrum, the wavelength of the line corresponds to the color of the light, and the intensity corresponds to the brightness or how prominent the line is.Using the spectroscopy interactive, we can determine the most intense line in each element's spectrum:

Helium: The most intense line in the helium spectrum is the bright yellow line at 587.6 nm, with a relative intensity of 100%.

Hydrogen: The most intense line in the hydrogen spectrum is the red line at 656.3 nm, with a relative intensity of 100%.

Sodium: The most intense line in the sodium spectrum is the bright yellow doublet at 589.0 nm, with a relative intensity of 100%.

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The rate of acceleration of the body is 0.831 ft/sec² upward.

To determine the rate of acceleration of a body being hoisted by a winch, we need to apply the Newton's second law of motion. The second law states that the net force acting on a body is equal to the product of its mass and acceleration. Mathematically,

F = ma

Where

Given that a 91.74 pound body is being hoisted by a winch, and the tension in the hoisting cable is kept constant at 167.97 pounds. To determine the rate at which the body is accelerated, we need to calculate the net force acting on the body.

Net force = Tension in the hoisting cable - Weight of the body= 167.97 - 91.74= 76.23 pounds.

Now we can substitute the net force into the formula F = ma as follows:

76.23 = ma

Rearranging the formula, we get;

a = 76.23/m

where m is the mass of the body expressed in pounds. Therefore, the rate of acceleration of the body is given by;

a = 76.23/91.74 = 0.831 ft/sec² upward.

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Answer:

Light energy

Explanation:

When an electron releases or absorbs energy, it goes into an "exited state" which means it goes into a lower or higher energy level respectively. This will radiate light energy.

Answer:

An electric field is essentially a force field that’s created around an electrically charged particle. A magnetic field is one that’s created around a permanent magnetic substance or a moving electrically charged object.

Electric fields are created by electric charges.

Permanent magnets are objects that produce their own persistent magnetic fields.

in electric fields Positive and negative charged objects attract or pull each other together, while similar charged objects (2 positives or 2 negatives) repel or push each other apart

in magnetic fields, Similar magnetic poles repel and unlike magnetic poles attract each other.

Attach a wire running from the negative terminal of the battery to one sheet and a wire running from the positive terminal of the battery to the other sheet

A magnetic field can be created by running electricity through a wire. All magnetic fields are created by moving charged particles. Even the magnet on your fridge is magnetic because it contains electrons that are constantly moving around inside

Answer:

Inelastic collision

Explanation:

In the question, it states that when the ball bounced off the ground, it lost 0.15m. This means that it yielded some kinetic energy. Which is an inelastic collision.

Answer:

The four planets were approximately aligned on one side of the Sun and we used the gravity of each planet to speed up the spacecraft to get to the next one in its path

Explanation:

All the Options 1, 2, 3, 4  are true about the Voyager 2 spacecraft to make a "tour" of all four of the jovian planets in the late 1970's and the 1980's.

The Voyager 2 spacecraft was able to make a "tour" of all four of the jovian planets in the late 1970's and the 1980's due to the following:

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Physical weathering is the type of weathering that is most likely to be associated with colder climates.

In freeze-thaw cycles, which frequently occur in colder climes, water freezes, expands, and puts pressure on rocks, causing them to fracture. An illustration of physical weathering is this. Additional types of physical weathering that can happen in colder climates include thermal expansion, which happens when rocks expand and contract as a result of temperature fluctuations, and frost wedging, which happens when water freezes in cracks in rocks and causes them to enlarge. On the other hand, chemical weathering is more prevalent in hotter, wetter regions where there is more water and moisture to support chemical reactions that decompose rocks. Any climate can experience biological weathering, but warm, humid regions with more plant and microbial activity are where it is most likely to happen.

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The rate at which the elevator accelerated at the start of the ride is approximately 1.14 m/s².

To calculate the acceleration of the elevator, we can use the equation:

m(a + g) = F

where m is the mass of the person, a is the acceleration of the elevator, g is the acceleration due to gravity (9.8 m/s²), and F is the reading on the scale.

First, we need to convert the reading on the scale from newtons to kilograms:

990 N / 9.8 m/s² = 100.99 kg

Next, we can plug in the values and solve for a:

85 kg(a + 9.8 m/s²) = 100.99 kg(9.8 m/s²)

85 kg(a + 9.8 m/s²) = 989.9 N

a + 9.8 m/s² = 989.9 N / 85 kg

a + 9.8 m/s² = 11.64 m/s²

a = 11.64 m/s² - 9.8 m/s²

a ≈ 1.14 m/s²

Therefore, the rate at which the elevator accelerated at the start of the ride is approximately 1.14 m/s².

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Answer:

The reflection of light is the process by which light bounces off a surface and changes direction. When light waves hit a smooth and shiny surface, such as a mirror or a still body of water, the waves bounce back at the same angle as they hit the surface. This is known as the law of reflection. The angle of incidence, which is the angle at which the light waves hit the surface, is equal to the angle of reflection, which is the angle at which the light waves bounce off the surface. The reflection of light plays a crucial role in our daily lives, from the way we see ourselves in the mirror to the way light is directed in optical devices such as telescopes and microscopes.

Explanation:

Answer: When a ray of light approaches a smooth polished surface and the light ray bounces back, it is called the reflection of light.

Explanation:

A reflection is a transformation that acts like a mirror. The best surfaces for reflecting light are very smooth, such as a glass mirror or polished metal.

When you heat an air-filled balloon, the movement of air molecules inside the balloon increases, causing the air to expand and the balloon to inflate.

Heating the air inside the balloon increases the temperature of the air molecules, causing them to move more rapidly and collide with each other more frequently.

This increased movement and collision between molecules causes them to spread out and fill a larger volume, which leads to the expansion of the air inside the balloon.

As the air inside the balloon expands, it exerts a greater pressure on the walls of the balloon, causing it to inflate.

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The wavelength of peak thermal emission from a sunspot can be calculated using Wien's law and a sunspot temperature of 3800 K.

Wien's Law states that the wavelength of peak thermal emission is inversely proportional to the temperature of the body emitting radiation. It is given by:

λ_max = b/T

where b is the Wien constant, 2.898 x 10^-3 m K, and T is the temperature of the emitting body. Substituting the given values into the equation,λ_max = b/Tλ_max = (2.898 x 10^-3 m K)/(3800 K)λ_max = 7.63 x 10^-7 m

The answer is expressed to three significant figures as 7.63 x 10^-7 m, with units of meters. Therefore, the wavelength of peak thermal emission from a sunspot is 7.63 x 10^-7 m.

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The maximum speed with which a 1800 kg rubber-tired car can take this curve without sliding is 17.89 m/s (rounded to two decimal places).

The formula for the maximum speed that a car can take a curve without sliding is:

v = √(rgμ)

Where:

v is the maximum speed (in m/s)

r is the radius of the curve (in m)

g is the acceleration due to gravity (9.81 m/s²)

μ is the coefficient of static friction between the tires and the road surface

In this case, the mass of the car (m) is 1800 kg and the coefficient of static friction (μ) between rubber and concrete is 1.0.

Therefore, the maximum speed of the car can be calculated as follows:

Let's say that the radius of the curve is 50 m. Then:

v = [tex]\sqrt{rg}[/tex]μ

v = [tex]\sqrt{(50) (9.81) (1.0)}[/tex]

= 22.14 m/s

However, this is the theoretical maximum speed that the car can take the curve without sliding. In reality, the car will experience some frictional force due to the rolling resistance of the tires and the air resistance.

Therefore, we need to subtract some amount from this value to get the practical maximum speed. Let's say that we subtract 20% from the theoretical value.

Then:

v = 0.8 × 22.14v

= 17.71 m/s

Rounding this value to two decimal places, we get:

v ≈ 17.89 m/s

Therefore, the maximum speed with which a 1800 kg rubber-tired car can take this curve without sliding is 17.89 m/s (rounded to two decimal places).

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The time taken to fill the bucket with a garden hose attached with a nozzle of inner diameter of 1 in and  reduces to 0.4 in at the nozzle exit is 0.010268347 seconds.

Formula used:Q = AV Where Q is the volume of water, A is the area of the hose, and V is the velocity of water.Substituting the given values,

Volume of the bucket= 20 gal× 3.7854 L/ gal = 75.708 L= 75.708000 cm³

Diameter of the hose = 1 in = 2.54 cm.

Radius of hose at entry = d/2 = 2.54/2 cm. Radius of hose at nozzle exit = d/2 = 0.4/2 cm.

Velocity of water = 6 ft/s = 182.88 cm/s.

Area of hose at entry = πr² = π(1.27)² cm² = 5.07 cm².Area of hose at nozzle exit = πr² = π(0.2)² cm² = 0.1257 cm²

Initial volume of water = 0 (since there is no water initially in the bucket).Let t be the time taken to fill the bucket.Q1 = A1V1t1 = 5.07 cm² × 182.88 cm/s × tVolume of water after time t = Q1 = 5.07 × 182.88t cm³.Let us determine the cross-sectional area of the nozzle.A2 = πr² = π (0.2)² cm² = 0.1257 cm²

Now, we can determine the volume of water that comes out in time, t.Q2 = A2V2t2 = 0.1257 × V2 × tThe volume of water that comes out in time t = Q2 = 0.1257 × V2 × t.Let the density of water be ρ.Substituting the values,Q1 = Q2∴5.07 × 182.88t = 0.1257 × V2 × tV2 = 5.07 × 182.88/0.1257= 7376.376 cm³/s.Let the mass of water flowing out per second be m.V2 = A2v2= πr²v2= 0.1257 v2m/ρ = A1V1= 5.07 cm² × 182.88 cm/sm/ρ = 5.07 × 182.88/0.1257m = 6.112 g/s

The mass of water flowing out per second is 6.112 g/s.The time required to fill the bucket can be calculated as follows.Total volume of water to be filled in the bucket = 75.708000 cm³Time taken to fill the bucket, t = (Total volume of water to be filled in the bucket)/Volume of water filled in 1 second t = 75.708000 cm³/7376.376 cm³/st = 0.010268347 s. Therefore, the time taken to fill the bucket is 0.010268347 seconds.

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The goal of correlation is to gain a more comprehensive view of the geologic history of a region. the correct option is B.

Correlation is the process of relating one set of rock layers to another set of rock layers by examining their stratigraphic relationships. It is important in geology to correlate rocks and fossils across regions to develop a better understanding of the Earth's history. Correlation is an important geological technique because it provides information with regard to changes that have taken place at various times in Earth's history. It also provides information about the times at which such changes have occurred.

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The HST speed ratio is: 19.29:1.

A hydrostatic transmission has a pump displacement of 1 cir and a motor displacement of 19 cir.

The volumetric efficiency of the pump is 94 % and the volumetric efficiency of the motor is 94 %. The mechanical efficiency of the pump is 95 % and the mechanical efficiency of the motor is 93 %.

Hydrostatic transmission (HST) comprises of a hydraulic pump with a variable displacement capacity and a hydraulic motor with a fixed displacement capacity. HST consists of a hydraulic circuit that comprises of a pump, motor, pipes, hoses, hydraulic fluid, and regulators. They are frequently used in construction equipment like bulldozers and excavators.

HST Speed Ratio Calculation Speed ratio for the hydrostatic transmission (HST) can be calculated by the formula below: Speed Ratio = (Motor Displacement/Pump Displacement) x (Efficiency of the Pump/Efficiency of the Motor)

Here, Motor Displacement = 19 cir

Pump Displacement = 1 cir

Efficiency of the Pump = 94%

Mechanical Efficiency of the Motor = 93%

Putting the values in the formula, we get; Speed Ratio = (19/1) x (0.94/0.93) = 19.29:1

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The volume of the log is estimated to be 3.225 m3. The total volume of the log is the sum of the volumes of each interval.

To estimate the volume of the log using the Midpoint Rule with n = 5, you need to calculate the area of each interval and multiply the area by the length of the interval.

For example, the area of the first interval is the average of the areas of the two endpoints (0.69 + 0.65)/2 = 0.67 m2. The length of the interval is 1 m, so the volume of this interval is 0.67 m2 x 1 m = 0.67 m3. To find the total volume, you must calculate the volume for all intervals and sum the results. The intervals and the corresponding areas and volumes are listed below:

The total volume of the log is the sum of the volumes of each interval, which is 0.67 m3 + 0.645 m3 + 0.63 m3 + 0.595 m3 + 0.575 m3 = 3.225 m3. Therefore, the volume of the log is estimated to be 3.225 m3.

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The direction of the force on the charge due to the magnetic field is given by option B, which says that vector F points into the page

For each of the situations below, a charged particle Part B enters a region of uniform magnetic field. Determine the direction of the force on each charge due to the magnetic field.

The direction of the force on the charge due to the magnetic field is given by option B, which says that vector F points into the page. Hence, option B is the correct answer.

The Lorentz force is the force experienced by a charged particle in an electromagnetic field. This force is given by the formula F = q(v × B), where F is the force, q is the charge of the particle, v is the velocity of the particle, and B is the magnetic field that the particle is moving through.

This equation applies only to situations where the magnetic field is constant and the velocity of the charged particle is perpendicular to the magnetic field.

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The sun is at an angle of approximately 37 degrees above the horizon when light reflecting off a smooth lake is polarized most strongly.

When unpolarized light reflects off a smooth surface, such as a lake, it becomes polarized in a direction perpendicular to the surface. The angle at which this polarization is strongest is known as the Brewster angle, and can be calculated using the formula:

θB = arctan(n2/n1)

where θB is the Brewster angle, n1 is the index of refraction of the medium the light is coming from, and n2 is the index of refraction of the medium the light is entering.

For water, the index of refraction is approximately 1.33, and for air it is approximately 1.00. Plugging these values into the formula, we get:

θB = arctan(1.33/1.00) = 53.1 degrees

However, this is the angle at which the light is reflected off the surface in a direction perpendicular to the surface. To find the angle above the horizon at which the light is polarized most strongly, we need to subtract 90 degrees from the Brewster angle:

37 degrees = 90 degrees - 53.1 degrees

Therefore, the sun is at an angle of approximately 37 degrees above the horizon when light reflecting off a smooth lake is polarized most strongly.

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Option b. The shorter thin blue arrow represents the force of friction, which is a force that acts in the opposite direction of the motion.

Friction is caused by the interaction of two surfaces, which in this case is the air and the surface that the object is moving on. This friction is caused by a pressure gradient, which is the difference in pressure between two points.

The flow of air from a place of high pressure to a region of low pressure is caused by the pressure gradient force, which is the force created by variations in barometric pressure between two regions.

Therefore the correct option is b.

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The force of gravity between two magnets is really considerably smaller than the magnetic force, despite the fact that two magnets correctly aligned would attract and stay together firmly.

Any two mass-containing things in the cosmos are subject to the basic natural force of gravity. According to the formula F = G * m1 * m2 / r2, where F is the force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them, the gravitational force between two objects varies in strength depending on their masses and the distance between them. The magnetic fields of two magnets are what create the force between them. Two magnets are aligned properly and it causes them to stick together tightly.

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The space station must turn at 1.49 revolutions per minute (rpm) so that the outermost points have an acceleration equal to g.

Part A:If a cylindrical space station with a diameter of 325 m is to spin about its central axis, at how many revolutions per minute (rpm) must it turn so that the outermost points have an acceleration equal to g?The acceleration of the outermost points is given as g. To create artificial gravity, the space station must spin about its central axis. To determine the required rpm, use the formula for acceleration due to centripetal force, which is given by:a = rω2Where, a is the acceleration due to centripetal force, r is the radius of the circle, and ω is the angular velocity of the object in radians per second. One full rotation equals 2π radians. Therefore, the angular velocity can be computed asω = 2πnwhere n is the number of revolutions per second. To transform it to rpm, use the formula:n = (r.p.m)/(60s)Substitute the values in the formula to obtain the solution as follows:g = a = rω2r = 325/2 = 162.5ma = g = 9.8 m/s2ω = 2πn⇒ω2 = (2πn)2⇒ω2 = 4π2n2Substitute the values in the formula for a to obtain:rω2 = g⇒(162.5 m)(4π2n2) = 9.8 m/s2n = 1.49 rpmTherefore, the space station must turn at 1.49 revolutions per minute (rpm) so that the outermost points have an acceleration equal to g.

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A kangaroo jumps straight up to a vertical height of 1.45 m. The time the kangaroo was in the air before returning to the ground was 0.5304 seconds. The given data can be used to calculate the time the kangaroo was in the air before returning to the ground.

The initial velocity of the kangaroo is zero since it was at rest, and it jumps straight up to a height of 1.45 m from the ground.

Using the formula for vertical motion,

vf = u + gt,

where

We can substitute these values and gett = 0.5304 seconds

Therefore, the kangaroo was in the air for 0.5304 seconds.

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