Five seconds into her run, Selina sees a rabbit and decides to chase it. She accelerates at a rate of 0. 1m/s2. What would be her pace at 10s? Show your work

The distance between point A and the point charge is approximately 1.815 micrometers.

The electric potential at a point in the electric field created by a point charge is given by the formula V = kq/r, where V is the electric potential, k is the Coulomb constant (9.00 x [tex]10^{9}[/tex] [tex]Nm^{2}/C^{2}[/tex]), q is the point charge, and r is the distance from the point charge.

Rearranging this equation, we get r = kq/V. Plugging in the given values, we get: r = (9.00 x [tex]10^{9}[/tex] [tex]Nm^{2}/C^{2}[/tex])(3.3 x [tex]10^{-11}[/tex] C)/(0.6 V)

Simplifying this expression, we get: r = 1.815 x [tex]10^{-6}[/tex] m

Therefore, the distance between point A and the point charge is approximately 1.815 micrometers.

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It would require an additional 1.35 J of work to stretch the spring by an additional 4.0 cm.

The work required to stretch a spring is given by the equation:

W = (1/2)kx²

where W is the work done, k is the spring constant, and x is the displacement from the equilibrium position.

To find the spring constant k, we can use the equation:

k = F/x

where F is the force required to stretch the spring by a certain amount.

Given that it requires 6.0 J of work to stretch the spring by 2.0 cm, we can find the spring constant as follows:

6.0 J = (1/2)k(0.02 m)²

k = 750 N/m

To stretch the spring an additional 4.0 cm, the displacement from the equilibrium position would be:

x = 0.02 m + 0.04 m = 0.06 m

Using the equation for work done, we can find the additional work required:

W = (1/2)kx²

W = (1/2)(750 N/m)(0.06 m)²

W = 1.35 J

As a result, stretching the spring by 4.0 cm would need an additional 1.35 J of labour.

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The observer hears a frequency of 374 Hz when the car is approaching and 293 Hz when it is moving away.

The frequency of sound heard by an observer is affected by the motion of the source of the sound relative to the observer. This effect is known as the Doppler effect. The Doppler effect can be described by the equation: f' = f (v±vo)/(v±vs)

where f is the frequency of the sound emitted by the source, v is the speed of sound, vo is the speed of the observer, and vs is the speed of the source. The ± sign is positive when the source is moving toward the observer and negative when it is moving away.

(a) When the car is approaching, the frequency of sound heard by the observer is higher than the frequency emitted by the car. Applying the Doppler effect equation, we get: f' = f (v+vo)/(v+vs), f' = 320 Hz (343 m/s + 0)/(343 m/s - 35.0 m/s), f' = 374 Hz

(b) When the car is right next to the observer, the frequency of sound heard by the observer is the same as the frequency emitted by the car. This is because there is no relative motion between the observer and the source.

(c) When the car is moving away, the frequency of sound heard by the observer is lower than the frequency emitted by the car. Applying the Doppler effect equation, we get:

f' = f (v-vo)/(v-vs)

f' = 320 Hz (343 m/s - 0)/(343 m/s - 35.0 m/s)

f' = 293 Hz

Therefore, the observer hears a frequency of 374 Hz when the car is approaching and 293 Hz when it is moving away.

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The approach to motivation that emphasizes the role of species-specific instincts in directing behavior is called the Instinct Theory of Motivation.

This theory suggests that certain innate, fixed patterns of behavior, known as instincts, are responsible for motivating actions and reactions within specific species. These instincts have evolved over time due to their contribution to the survival and reproductive success of the species.

For example, the fight or flight response, which is a common instinct among many animals, helps protect them from predators and ensures their survival. Another example is the maternal instinct observed in many mammal species, which promotes nurturing and protective behaviors towards their offspring, ultimately benefiting their survival and reproduction.

Instinct Theory of Motivation has its roots in the work of early psychologists like William James and Sigmund Freud, who believed that instincts played a significant role in shaping human behavior. However, it is important to note that while instincts do influence motivation, they are not the only factors at play. Other approaches, such as the drive-reduction theory and cognitive theories, also contribute to our understanding of motivation and behavior.

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During a new moon, the moon is located between the sun and the Earth. The illuminated side of the moon is facing away from the Earth and towards the sun, so it is not visible from the Earth.

The side of the moon facing the Earth is in shadow, which is why a new moon is not visible in the night sky. The alignment of the sun, Earth, and moon during a new moon is also what causes a solar eclipse, when the moon passes directly in front of the sun, blocking its light from reaching the Earth.

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A 2 kg ball is thrown upward with an initial speed of 12 m/s. After rising 3.0 meters, it is moving upwards at 5 m/s. The average force of air resistance on the ball is 32.3 N.

When an object is thrown upward, it experiences air resistance that opposes its motion. In this scenario, a 2 kg ball is thrown upward with an initial velocity of 12 m/s.

After rising a vertical distance of 3.0 meters, its velocity reduces to 5 m/s. We need to find the average force the ball experiences due to air resistance during this time.

To solve this problem, we can use the work-energy principle which states that the net work done on an object is equal to its change in kinetic energy. Since the ball is moving upward, the net work done on the ball is the work done by gravity and air resistance.

We can assume that the work done by gravity is negligible because the vertical displacement of the ball is small. Therefore, the work done by air resistance is equal to the change in the ball's kinetic energy.

The change in kinetic energy of the ball can be calculated using the equation: [tex]\Delta KE = 1/2 \times m \times (vf^2 - vi^2)[/tex], where m is the mass of the ball, vi is the initial velocity, and vf is the final velocity. Substituting the given values, we get [tex]\Delta KE = 1/2 \times 2 kg \times (5 \;m/s)^2 - (12 \;m/s)^2) = -97 J[/tex].

Since the change in kinetic energy is negative, the work done by air resistance is negative. Therefore, the average force the ball experiences due to air resistance is [tex]F = -\Delta KE/d = -(-97 J)/3 m = 32.3 N[/tex].

In summary, we can calculate the average force the ball experiences from air resistance during its upward journey using the work-energy principle. The force is negative as it opposes the motion of the ball, and its magnitude is 32.3 N.

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Option (d) translation, rotation, and vibration is the correct answer for energies contributing to the molar specific heat of 29. 1 J/mol · K of a diatomic gas is measured at constant volume.

The molar specific heat of a diatomic gas is measured at constant volume and found to be 29.1 J/mol·K. To determine the types of energy contributing to the molar specific heat, let's consider the options: translation, rotation, and vibration.

For a diatomic molecule, the translational degrees of freedom are 3, as it can move in the x, y, and z directions. The rotational degrees of freedom are 2, since it can rotate around two axes. The vibrational degrees of freedom for a diatomic molecule are 1, as there is only one mode of vibration.

According to the equipartition theorem, each degree of freedom contributes (1/2)R to the molar specific heat at constant volume (Cv), where R is the gas constant (8.314 J/mol·K).

Let's calculate the molar specific heat (Cv) for each type of energy:

(a) Translation only:
Cv = (3/2)R = (3/2)(8.314) = 12.471 J/mol·K

(b) Translation and rotation only:
Cv = (3/2 + 2/2)R = (5/2)(8.314) = 20.785 J/mol·K

(c) Translation and vibration only:
Cv = (3/2 + 1/2)R = (4/2)(8.314) = 16.628 J/mol·K

(d) Translation, rotation, and vibration:
Cv = (3/2 + 2/2 + 1/2)R = (6/2)(8.314) = 24.942 J/mol·K

Comparing the calculated molar specific heat values with the given value of 29.1 J/mol·K, none of the options match exactly. However, option (d) is the closest, which includes translation, rotation, and vibration. While it doesn't perfectly match the given value, it is the most plausible answer based on the available options.

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Answer:

a. The two balloons will repel

Explanation:

when stephen rubs the balloon on his head, the balloon collects a negative charge. this will happen to both balloons and because the balloons are both negatively charged they will repel

As the loop moves away from the magnet, the force weakens and is greatest when it is directly beneath the magnet.

When a conducting circular loop moves downwards beneath a stationary magnet with its north pole pointing upward, an induced current is produced in the loop. This induced current flows in a counterclockwise direction, as seen from above.

Additionally, the loop experiences a force due to the magnet. This force is perpendicular to both the direction of motion of the loop and the direction of the magnetic field produced by the magnet. The force is given by the formula F = BIL, where B is the strength of the magnetic field, I is the current induced in the loop, and L is the length of the loop that is in contact with the magnetic field.

Since the loop is moving downwards, the force on it is upwards, opposite to the direction of motion. The force is strongest when the loop is directly under the magnet and decreases as the loop moves away from the magnet.

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Knowing a combination of grappling and striking martial arts is advantageous during a street self-defense scenario because it provides a well-rounded skill set to address various types of threats.

Grappling techniques, such as those found in Brazilian Jiu-Jitsu or Judo, focus on controlling, submitting, or immobilizing an opponent, which can be especially helpful in close-quarters situations.

Striking martial arts, such as Muay Thai or Boxing, emphasize powerful punches, kicks, and knee strikes to deter or incapacitate an attacker from a distance.

By mastering both grappling and striking disciplines, one can adapt to different situations, maintain control, and maximize their chances of successfully defending themselves in a street scenario.

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The blades in the blender decelerate at a rate of approximately: 4.32 rps² when the motor is turned off during operation, taking 2.7 seconds to come to a complete stop from an initial rotational speed of 700 rpm or 11.67 rps.

To answer your question, let's first convert the given rotational speed from rpm to revolutions per second (rps) by dividing by 60, as there are 60 seconds in a minute:

700 rpm ÷ 60 = 11.67 rps

Next, we need to determine the rate at which the blades are decelerating, which is the change in rotational speed over the 2.7 seconds. Since the blades come to a stop, the final rotational speed is 0 rps. We can calculate the deceleration as follows:

Deceleration = (Final Rotational Speed - Initial Rotational Speed) ÷ Time
Deceleration = (0 rps - 11.67 rps) ÷ 2.7 s
Deceleration ≈ -4.32 rps²

This means that the blades in the blender decelerate at a rate of approximately 4.32 rps² when the motor is turned off during operation, taking 2.7 seconds to come to a complete stop from an initial rotational speed of 700 rpm or 11.67 rps.

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Based on the given scaling rules, a 450 kg bear should be able to run approximately 1.38 times faster than the top speed of a 45 g rodent.

To determine how many times faster a 450 kg bear can run compared to a 45 g rodent, we can use the given scaling rules.

First, we need to calculate the speed ratio based on the maximum metabolic rate scaling and the cost of transport scaling. Since the maximum metabolic rate varies with body mass^0.81, we can calculate the ratio of bear to rodent metabolic rate:

450^0.81 / 45^0.81 ≈ 14.07

Next, since the cost of transport varies with body mass^0.68, we can calculate the ratio of bear to rodent cost of transport:

450^0.68 / 45^0.68 ≈ 10.20

Now, we can calculate the speed ratio by dividing the metabolic rate ratio by the cost of transport ratio:

14.07 / 10.20 ≈ 1.38

So, based on the given scaling rules, a 450 kg bear should be able to run approximately 1.38 times faster than the top speed of a 45 g rodent.

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Because universal laws are principles that apply consistently across the universe, regardless of place or culture, the findings of scientific inquiries into universal laws would be comparable regardless of where they were done.

These principles are founded on empirical observations and experiments, thus they may be tested and repeated in many circumstances. Scientists perform their research using the same rigorous standards and procedures, regardless of where they are done, to guarantee that their findings are legitimate and credible. As a result, the rules of physics, chemistry, biology, and other disciplines would be the same in any area of the planet, as would the results of scientific inquiries into them.

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The electric field in the copper wire is approximately 7.63 x [tex]10^{-5}[/tex] V/m. The drift velocity of free electrons in a copper wire is given as 8.32 x [tex]10^{-4}[/tex] m/s.

The electric field in a conductor is directly proportional to the drift velocity. The relationship between drift velocity and electric field is given by:

vd = (eEτ)/(m)

where,

vd = drift velocity of electrons

e = charge of an electron

E = electric field

τ = relaxation time of electrons

m = mass of an electron

Assuming the values of e, m, and τ for copper, we can solve for the electric field:

E = (vd x m)/(eτ)

E = (8.32 x [tex]10^{-4}[/tex] m/s x 9.11 x [tex]10^{-31}[/tex] kg)/(1.6 x [tex]10^{-19}[/tex] C x 2.3 x [tex]10^{-14}[/tex] s)

E ≈ 7.63 x [tex]10^{-5}[/tex] V/m

Therefore, the electric field in the copper wire is approximately 7.63 x [tex]10^{-5}[/tex] V/m.

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The angle from the center of the Airy disk to the first dark ring is 0.0363 degrees, and the distance between the center of the disk and the first dark ring on a screen 2 meters away from the aperture is: 1.268 mm.

a. To find the angle from the center of the Airy disk to the first dark ring, we will use the formula sin(p) = (wavelength) / (aperture diameter). Plugging in the values, we get sin(p) = 632.8 * 10^-9 / 0.001. Then, we calculate the inverse sine, sin^-1(0.0006328) = 0.0363 degrees.

b. To determine the distance between the center of the Airy disk and the first dark ring on a screen that is 2 meters from the aperture, we will use the formula distance = (angle) * (distance to screen).

In this case, distance = 0.0363 degrees * 2 meters.

First, convert the angle to radians: 0.0363 degrees * (pi / 180) = 0.000634 radians.

Then, multiply by the distance to the screen: 0.000634 radians * 2 meters = 0.001268 meters or 1.268 mm.

In summary, the angle from the center of the Airy disk to the first dark ring is 0.0363 degrees, and the distance between the center of the disk and the first dark ring on a screen 2 meters away from the aperture is 1.268 mm.

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Complete question:

A laser beam is aimed through a circular aperture of diameter 1 mm.

a. If the laser beam is red with a wavelength of 632. 8 nm, what is the angle from the center of the Airy disk to the first dark ring? (2 points)

sin(p) = 632. 8*10^-9 /. 001

sin^-1(. 0006328) =. 0363 degrees

b. If the screen you are projecting the Airy disk onto is 2 m from the aperture, what is the distance between the center of the disk and the first dark ring? (2 points)

The distance between the golf tube and the balloon is approximately 53.9 millimeters.

To solve this problem, we can use Coulomb's Law, which states that the electrical force (F) between two charges (q1 and q2) is proportional to the product of their charges divided by the square of the distance (r) between them:

F = k * (q1 * q2) / r²

where k is Coulomb's constant, approximately 8.99 x 10^9 Nm²/C².

In this case, the electrical force (F) is -1.0 x 10^-5 N, the charge of the balloon (q1) is -1.0 x 10^-6 C, and the charge of the plastic golf tube (q2) is +4.0 x 10^-6 C. We want to find the distance (r) between them.

First, let's rearrange the formula to solve for r:

r = √(k * (q1 * q2) / F)

Now, substitute the given values into the equation:

r = √((8.99 x 10^9 Nm²/C²) * (-1.0 x 10^-6 C) * (4.0 x 10^-6 C) / (-1.0 x 10^-5 N))

Solve for r:

r ≈ 0.0539 meters or 53.9 millimeters

So, the distance between the golf tube and the balloon is approximately 53.9 millimeters.

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ans. forward baised

The resistance measurement is high when the diode is forward-biased because current from the multimeter flows through the diode, causing the high-resistance measurement required for testing.

The type of lightning that extends up to 95 kilometers above the top of a thunderstorm and resembles a jellyfish is called a sprite. Option B is correct.

Sprites are electrical discharges that occur high above thunderstorms and are often red or orange in color. They are caused by the same type of electrical breakdown that produces lightning, but they occur in the mesosphere, rather than the troposphere where lightning occurs. Sprites are relatively short-lived, lasting only a few milliseconds, and are difficult to observe from the ground due to their high altitude.

They were first documented in 1989, and since then, they have been observed and studied extensively by scientists using high-speed cameras and other specialized equipment. Sprites are still not fully understood, but their study is providing valuable insights into the physics of lightning and the behavior of the Earth's atmosphere. Option B is correct.

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According to the law of conservation of momentum, the total momentum of a system remains constant if no external forces act on it. In this scenario, the boat and the person are initially at rest, so their total momentum is zero.

When the person on the dock tosses the watermelon to you, the watermelon will have an initial momentum in the direction of the throw. Since there are no external forces acting on the system, the total momentum of the system must still be zero after the toss.

To maintain the total momentum at zero, you and the boat must acquire an equal but opposite momentum to balance out the momentum of the watermelon. As a result, the boat will move backward in response to the forward momentum acquired by you when you catch the watermelon.

This outcome demonstrates the law of conservation of momentum in action, where the total momentum of the system (you, the boat, and the watermelon) remains constant before and after the toss.

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The tension on the rope is 886 N. We can use Newton's second law to solve this problem:

ΣF = ma

where

ΣF is the net force acting on the hero,

m is the mass of the hero, and

a is the acceleration of the hero.

In this case, the hero is being pulled upward by a rope, so the net force acting on the hero is the tension in the rope minus the weight of the hero:

ΣF = T - mg

where

T is the tension in the rope and

g is the acceleration due to gravity.

Substituting the given values, we get:

T - mg = ma

T - (75.0 kg)(9.81 m/s²) = (75.0 kg)(2.00 m/s²)

Simplifying, we get:

T = (75.0 kg)(2.00 m/s² + 9.81 m/s²)

T = 75.0 kg × 11.81 m/s²

T = 886 N

Therefore, the tension on the rope is 886 N.

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3. If the mass is doubled, then acceleration will be halved. If both the net force and the mass are doubled, the acceleration will be unchanged.

4. If we reduce the length of the string by half then the time period will be ✓2 of the initial time period

From 1880 to 2010, there was a substantial increase in both global temperature and atmospheric CO2 levels, with a positive correlation between the two. The temperature reached its highest point in 2010, and its lowest point in the late 1800s.

1. The increase in temperature from 1880 to 2010 is approximately 0.8°C (1.4°F) according to NASA's Goddard Institute for Space Studies. This increase in temperature has been attributed to human activities such as burning fossil fuels, deforestation, and agriculture.

2. The amount of carbon dioxide in the atmosphere has significantly increased from 1880 to 2010. According to the National Oceanic and Atmospheric Administration (NOAA), the concentration of carbon dioxide has increased from 280 parts per million (ppm) in 1880 to over 400 ppm in 2010. This increase is due to the burning of fossil fuels and deforestation.

3. There is a strong correlation between the amount of carbon dioxide and global temperature. As the amount of carbon dioxide increases, it traps more heat in the Earth's atmosphere, leading to an increase in global temperature. This is known as the greenhouse effect.

4. The temperature was at its highest in 2016, with an average global temperature of 1.78°F (0.99°C) above the 20th-century average. The temperature was at its lowest in 1904, with an average global temperature of 1.46°F (0.81°C) below the 20th-century average. However, it is important to note that these temperature fluctuations are within the range of natural variability, and it is the overall upward trend in temperature that is of concern.

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Explanation:

To find the absolute pressure on the base area of the cylinder, we need to use the formula for absolute pressure:

P(abs)​=P(atm​)+P(gauge)​

where P(abs)​ is the absolute pressure, P(atm​) is the atmospheric pressure, and P(gauge​) is the gauge pressure.

The gauge pressure is the pressure exerted by the water column on the base area. It depends on the height and density of the water column, and can be calculated using the formula:

P(gauge​)=ρgh

where ρ is the density of water, g is the acceleration due to gravity, and h is the height of the water column.

Given that the height of the water column is 0.5 m, and assuming that the density of water is 1000 kg/m^3 and the acceleration due to gravity is 9.8 m/s^2, we can find the gauge pressure as:

P(gauge​)=1000×9.8×0.5

P(gauge)​=4900 Pa

The atmospheric pressure at sea level is approximately 101325 Pa. Therefore, we can find the absolute pressure on the base area as:

P(abs​)=101325+4900

P(abs)​=106225 Pa

Hence, the absolute pressure on the base area of the cylinder is 106225 Pa.

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The new weight of the object from the description would now be  2  × 10^2 N.

Given that the force between two bodies is inversely proportional to the square of their distance, doubling that distance results in a force that is one-fourth of what it was before.

We would now know that the force that is now acting on the object is;

Weight = 1/4 * 8.00 × 10^2 N

Weight = 2  × 10^2 N

This is true when we consider the universal gravitational law that governs the force on the object.

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Kinetic energy depends on the mass and the motion

The equilibrium of the plank is maintained: when the net torque and net force are both equal to zero.

In this scenario, we have a uniform plank AB with a mass of 20 kg. It is supported horizontally at points 20 cm and 70 cm from point A. The plank is in equilibrium when additional masses of 50 kg and 70 kg are suspended at points A and B, respectively. Furthermore, a weight of 100 N is suspended at the 40 cm mark from point B.

To maintain equilibrium, the net torque and the net force on the plank must be zero. The torque produced by each mass and weight on the plank can be calculated as the product of the force and the distance from the pivot point. The force due to the mass of the plank and the suspended masses can be calculated using the formula F = mg, where m is the mass and g is the acceleration due to gravity (approximately 9.81 m/s^2).

The torque balance equation will involve the torques produced by the 20 kg plank, the 50 kg and 70 kg suspended masses, and the 100 N weight. By calculating these torques and setting the net torque to zero, we can analyze the equilibrium state of the plank. Additionally, we need to ensure that the net force acting on the plank is also zero, which can be confirmed by summing the forces due to each mass and weight and setting the total equal to zero.

In summary, the equilibrium of the plank is maintained when the net torque and net force are both equal to zero. This involves balancing the torques produced by the 20 kg plank, the 50 kg and 70 kg suspended masses, and the 100 N weight, as well as the forces acting on the plank.

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The difference between the head and point of a nail when pushed against your skin with the same force is due to the difference in pressure. Pressure is calculated as force divided by area (P = F/A).

The point of the nail has a smaller area, which results in higher pressure, allowing it to pierce your skin. On the other hand, the head of the nail has a larger area, resulting in lower pressure, and therefore does not pierce your skin.

Pressure is defined as the force applied per unit area. It can be calculated using the equation P = F/A, where P represents pressure, F represents the force applied, and A represents the area over which the force is distributed.

When a nail is pushed against your skin with the same force, the pressure exerted by the nail depends on the area of contact between the nail and your skin.

The point of the nail has a smaller area compared to the head. Since the force applied remains the same, the pressure exerted by the nail point is higher because the force is distributed over a smaller area. This higher pressure allows the point of the nail to pierce through your skin.

On the other hand, the head of the nail has a larger area of contact. When the same force is applied, the pressure exerted by the nail head is lower because the force is distributed over a larger area. This lower pressure is why the head of the nail does not pierce your skin.

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The ratio of the area at this location to the entrance area can also be determined. The temperature at this location is 291.7K, the pressure is 1.058 MPa, and the area ratio is 1.603.

To solve this problem, we can use the isentropic flow equations and the speed of sound formula. The first step is to determine the Mach number at the nozzle entrance. We can use the following formula:

Mach number = velocity of air/speed of sound

Using the given values, we can calculate that the Mach number is 0.407. Since the flow is isentropic, we can assume that the entropy of the air remains constant throughout the nozzle.

a) To determine the temperature of the air where the velocity is equal to the speed of sound, we can use the following formula:

Temperature ratio = [tex]$1 + \frac{(\gamma - 1)}{2} \times M^2$[/tex]

where gamma is the ratio of specific heats of air, which is 1.4. At the speed of sound, the Mach number is 1. Using the formula, we get:

Temperature ratio = [tex]$1 + \frac{(1.4-1)}{2} \times 1^2 = 1.2$[/tex]

The temperature at the nozzle entrance is given as 350K. Therefore, the temperature where the velocity is equal to the speed of sound is:

Temperature = temperature at entrance / temperature ratio = 350 / 1.2 = 291.7K

b) To determine the pressure of the air where the velocity is equal to the speed of sound, we can use the following formula:

Pressure ratio = [tex]$\left(1 + \frac{(\gamma - 1)}{2} \times M^2 \right)^\frac{\gamma}{\gamma-1}$[/tex]

At the speed of sound, the Mach number is 1. Using the formula, we get:

Pressure ratio = [tex]$\left(1 + \frac{(1.4-1)}{2} \times 1^2 \right)^\frac{1.4}{0.4} = 1.891$[/tex]

The pressure at the nozzle entrance is given as 2MPa. Therefore, the pressure where the velocity is equal to the speed of sound is:

Pressure = pressure at entrance / pressure ratio = 2 / 1.891 = 1.058 MPa

c) To determine the ratio of the area at this location to the entrance area, we can use the following formula:

Area ratio = [tex]$\frac{1}{M} \times \left(\frac{2 + (\gamma-1) \times M^2}{\gamma+1}\right)^{\frac{\gamma+1}{2(\gamma-1)}}$[/tex]

At the speed of sound, the Mach number is 1. Using the formula, we get:

Area ratio = [tex]$\frac{1}{1} \times \left(\frac{2 + (1.4-1) \times 1^2}{1.4+1}\right)^{\frac{1.4+1}{2(1.4-1)}} = 1.603$[/tex]

Therefore, the ratio of the area at the location where the velocity is equal to the speed of sound to the entrance area is 1.603.

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The y component of puck B's momentum after the collision is 0 g cm/s.

Momentum is the quantity of motion of a moving object, measured as a product of its mass and velocity. In physics, it is a conserved quantity, meaning that the total momentum of a closed system remains constant, regardless of the interactions within the system. Momentum can be transferred from one object to another, or between objects and their environment. Momentum is the driving force behind many physical phenomena, including collisions, friction, rocket propulsion, and the orbits of planets and stars.

[tex]p_A[/tex]  (before) = [tex]m_A[/tex] * [tex]v_A[/tex] = 165.0 g * 55.0 cm/s = 9077.5 g cm/s
[tex]v_A[/tex] (x) = [tex]v_A[/tex] * cos(27.0°) = 29.0 cm/s * cos(27.0 °) = 27.61 cm/s
[tex]v_A[/tex] (y) = [tex]v_A[/tex] * sin(27.0 °) = 29.0 cm/s * sin(27.0 °) = 14.26 cm/s
Using these components, we can calculate the momentum of puck A after the collision:
[tex]p_A[/tex]  (after) = [tex]m_A[/tex] * [tex]v_A[/tex] = 165.0 g * 27.61 cm/s = 4562.1 g cm/s
[tex]p_A[/tex] (before) + [tex]p_B[/tex] (before) = [tex]p_A[/tex]  (after) + [tex]p_B[/tex] (after)
9077.5 g cm/s + [tex]p_B[/tex] (before) = 4562.1 g cm/s + [tex]p_B[/tex] (after)
[tex]p_B[/tex] (before) = 4562.1 g cm/s - 4562.1 g cm/s = 0
Since the momentum of puck B before the collision was 0, its momentum after the collision must also be 0. Therefore, the y component of puck B's momentum after the collision is 0 g cm/s.

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The caloris basin on mercury covers a large region of the planet, but few craters have formed on top of it. from this we conclude that iii) the caloris basin formed toward the end of the solar system's period of heavy bombardment.

From the observation that the Caloris Basin on Mercury covers a large region of the planet, but few craters have formed on top of it, we can conclude that the Caloris Basin likely formed toward the end of the solar system's period of heavy bombardment (option iii). This is because the basin has not accumulated a significant number of craters on top of it, suggesting that it was created after most of the intense impacts had occurred.

The other options are less likely: option i, that the Caloris Basin was formed by a volcano, is not as plausible since the basin is generally thought to have been formed by a massive impact event. Option ii, that erosion destroyed smaller craters on the basin, is unlikely as Mercury lacks the significant atmosphere and geological processes necessary for substantial erosion to occur. Finally, option iv, that Mercury's atmosphere prevented smaller objects from hitting the surface, is incorrect because Mercury's extremely thin atmosphere is not capable of shielding the surface from impacts. The correct option is iii) the caloris basin formed toward the end of the solar system's period of heavy bombardment.

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