consider a projectile fired vertically in a constant gravitational field. for the same initial velocities, find the times required for the projectile to reach its maximum height (a) with no resisting force and (b) for a resisting force proportional to the instantaneous velocity of the projectile. (c) show that the result in (a) can be recovered from the result in (b).

At a half moon, this means the Suns light is falling on exactly half of the moon. So the angle must be a right angle (same as between the moon and sun, earth and sun, and earth and moon).So ,he choose the time of a half moon for calculating the earth -sun distance

The moon and the sun appear to have the same size and have the same angle of taper. He was able to determine the distance to the sun by using the right triangle that the sun made with the moon. At a distance 100,000 times closer than the Oort cloud, the Earth orbits the sun. It is only 92,955,807 miles (149,597,870 kilometres) away on average. Astronomical unit, or AU, is the name for the distance between the earth and the sun. Additionally, we utilise it to calculate distances throughout the solar system.

He calculated the angle between the Sun and a quarter-phase moon. He discovered the angle to be 87° and deduced that the Sun was between 18 and 20 times farther distant from the moon using the mathematics available at the time.

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This indicates that the moon is exactly halfway illuminated by the Sun at a full moon. The angle must therefore be a right angle (same as between the moon and sun, earth and sun, and earth and moon).

He therefore chose a half moon to calculate the Earth-Sun distance. Both the moon and the sun seem to be the same size and have a similar tapering angle. The right triangle formed by the sun, moon, and earth allowed him to calculate the distance to the sun. The distance between the Earth and the sun is 100,000 times closer than that of the Oort cloud. On average, it is only 149,597,870 kilometers (92,955,807 miles) away.

The distance between the earth and the sun is known by the abbreviation astronomical unit (AU). We also employ it to determine distances within in the solar system.

He determined the Sun's angle with a quarter-phase moon. Using the mathematics known at the time, he calculated the angle to be 87° and concluded that the Sun was between 18 and 20 times farther away from the moon.

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The same power plant could supply approximately 270,000 homes if the average electricity consumption rises to 1,200 kWh/month in the summer.

This is due to the fact that there is now a significant increase in the demand for electricity, which must be met by power plants.

500 mW x 24 hours/day x 30 days/month x 0.9 = 324,000 MWh/month.

The number of homes that the same power plant can serve, however, may vary based on how much electricity each household has.

324,000 mWh/month x 1,000 kWh/MWh = 324,000,000 kWh/month.

324,000,000 kWh/month/1,200 kWh/month/home = 270,000 homes.

The number of homes that can be served by the same power plant in hotter parts of the United States may rise significantly if air conditioning is kept up.

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The electric force between these two sets of charges is: -3.6*10^6 N

In physics the electric force is the force that attracts or repels two charges (q) separated at a distance called (r), this is expressed in the international system of units in Newton.

To solve this exercise the electric force formula and the procedure we will use is:

F = (k * q1 * q2)/r²

Where:

Information about the problem:

By converting the the separation distance of the charges from (km) to (m) we have:

r = 2.0 km * 1000 m/1 km

r= 2000 m

Applying the electric force formula we have:

F = (k * q1 * q2)/r²

F = [(9 *10^9 N*m²/C² * (40 C) * (-40 C)]/ (2000 m)²

F = -1.44*10^13 N*m² /4*10^6 m²

F = -3.6*10^6 N

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If the hiker moves at a constant 500 Watts per meter, it will take 2.4 hours to ascend the hill (1200 meters x 500 Watts).

The way a body's orientation or position changes over time. Translation describes motion along a line or a curve. Rotation is a motion in which a body's orientation is altered.

An object moving or being moved is referred to as motion. It's said that motion follows a pattern when it repeats. Making predictions about future motion requires the observation of patterns of motion. Friction is the name for the force that prevents moving objects from moving.

The fundamental kinematics equation of motion, which states that the distance travelled divided by the object's speed equals the amount of time required to travel that distance.

Following are the steps to determine how long it took to climb the hill:

To start, figure out the hiker's power output.

500 Watts are being produced continuously by the hiker.

Step two is to compute the climbing time.

By dividing the distance travelled by the time it took to climb the slope.

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Heat rates, thermal efficiencies, capacity factors, load factors, economic efficiencies, operational efficiencies, and energy efficiencies are all elements in power plants. A power plant's performance may be expressed using several typical performance factors: heat rate (energy efficiency) and thermal efficiency.

Water, light, temperature, and nutrients are the four most important factors influencing plant development. You might be asking where dirt comes into all of this. Plants may grow without soil using a technique known as hydroponics. Plants, on the other hand, cannot grow if they are not provided with the necessary nutrients.

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The extensive property among the following is mass. So, option A) is correct.

The property of a material known as the widespread property is dependent on the mass (or amount of matter) of the substance. Mass is the extensive property solely in the possibilities that are presented. Other than mass, all other attributes are independent of mass.

Divide the substance in half to determine the extensive property quickly and easily. It depends on mass and is an extensive property if it also applies to both of the separate portions. When a property remains constant for each half, it is said to be an intense property and is independent of mass. Examples of an intensive property include density, temperature, pressure, etc.

Hence, the answer is mass.

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When a material tends to obstruct the flow of electrons, electrical energy is converted into heat energy and light. All materials have a characteristic called electrical resistance. Ohms, or, are used to measure resistance.

The flow of electrons is in the opposite direction from the flow of current. Resistance is a conductor quality that prevents current from flowing. Electrons and ions collide as they pass across a conducting wire. The current is decreased as a result of these collisions, which convert some kinetic energy into thermal energy. The ohm is the SI unit of resistance. Regarding the movement of electrons, they naturally gravitate towards the +ve side due to their -ve charge, which is the opposite of the traditional direction of current flow (from +ve to -ve).

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The signs of the charge qX on X is positive and qY on Y is positive after ball carrying the negative charge is removed and the balls X and Y are separated.

At the time when the third ball carrying a negative charge is brought near the first two, it gets polarized such that X contains +ve charge and Y contains a +ve charge.  After this the ball X is connected to the ground when  the positions of these balls are fixed and the electron move up from the ground. After that the ground wire should be disconnected. The ball carrying the negative charge is removed and the ball X and Y are separated. Due to this the electron has cancelled the net +ve charge on Y. Hence the charge on both X and Y is positive.

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The mass of one pill measured was 461 mg and for the same pill, the mass in kilograms of 100 pills will result to 46l*100/100000 => 0.046l kg.  As there are 1 ms = 10^-5 kg.

What is a pharmacy technician? A pharmacy technician is a person in pharma who decides the composition of the chemicals in medicine and the size of medicine from manufacturing.

The mass of one pill is given as 461 mg and the number of pills required is 100So the total mass will be, mass of 1 pill*100 = 461 mg × 100 = 46100mg

one kilogram = 1000 grams, so the mass in kilograms will be, The same mass in kg will be 46100mg / 1000 grams

which results in 0.046l kg.

This simply shows, the mass of 1 pill was 461 mg the mass in kilograms of 100 pills will be 0.046l kg for measurements of the mass in kg of a pill.

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The magnitude of the force that the curler is exerting on the stone (ii) greater in Case B

Thus Force is directly proportional to acceleration of an object.

Here , Case (B) has higher acceleration. So, It will have greater force.

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The angle between the incident and reflected beam is 46° when a beam of light strikes a mirror at angle of 23° to the normal.

Given the angel of incidence (∠i) = 23°

Since the beam of light strikes the mirror at normal it is the angle of incidence. The incident ray's angle with the normal at the point where it contacts the mirror surface is used to calculate the angle of reflection.

From mirror laws we know that the angle of incidence is equal to the angle of reflection. Then, ∠i = ∠r

Hence, as angle of incidence is 23° and the angle of reflection is 23° . So, the angle between the incident ray and the reflected ray is 23° + 23° = 46°.

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The combination of cloudy skies, quiet winds, and humid air would encourage the greatest temperature shift from sunrise to mid-afternoon.

The location of a place in relation to the sea is the primary factor that affects temperature. Compared to land, the sea both gains and loses heat gradually. Rapid warming and cooling occur on land.

Latitude, height, distance from the sea, and ocean currents are the four unavoidable factors that affect temperature.

Compared to land, oceans warm up and cool down considerably more gradually. This indicates that, for the same latitude and elevation, coastal areas tend to be warmer in the winter and cooler in the summer.

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The greatest temperature change from sunrise to mid-afternoon would be caused by a mix of gloomy skies, calm winds, and humid air.

The main factor affecting temperature is where a place is in proximity to the sea. The sea progressively warms and cools compared to land. On land, there is a sudden warming and cooling.

The four unavoidable factors that affect temperature are latitude, height, distance from the sea, and ocean currents. Oceans warm up and cool down much more gradually than land does. This shows that coastal places typically experience warmer winters and cooler summers for the same latitude and elevation.

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The amount of energy transferred as light is 73.5 J (350 J x 21%).

A lumen is a unit of size for the quantity of mild that is emitted through a source. Lumens are frequently used to evaluate the brightness of different light sources. The efficiency of a mild bulb is regularly measured in phrases of the quantity of lumens in line with watt of electricity fed on. A light bulb that has a higher lumen output consistent with watt is considered to be more green. As an example, a mild bulb that produces one hundred lumens in step with watt is more efficient than a light bulb that produces eighty lumens in line with watt. That is because it produces greater light according to unit of electricity fed on.

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An electric light bulb has an efficiency of 21% 350 J of energy contains the 73.5 J  of energy transferred as light.

Amount of energy transferred by light =( 21/100)×350

                                           = 2.1 × 35

                                                = 73 .5 J

A lumen is a unit of size for the quantity of mild that is emitted through a source. Lumens are frequently used to evaluate the brightness of different light sources. The efficiency of a mild bulb is regularly measured in phrases of the quantity of lumens in line with watt of electricity fed on. A light bulb that has a higher lumen output consistent with watt is considered to be more green. As an example, a mild bulb that produces one hundred lumens in step with watt is more efficient than a light bulb that produces eighty lumens in line with watt. That is because it produces greater light according to unit of electricity fed on.

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The statement that the direction of a vector can be different in different coordinate systems, is true.

It can be possible to add a coordinate system to a vector and identity components of that vector in that particular system, but the orientation and the type of the coordinate system with the respect to the vector can be different. The choice of a particular coordinate system usually does not change the direction of the vector.

However the magnitude of a vector may or may not be different in different coordinate systems. It is possible to attach a scalar to a vector. A  vector may have its magnitude equal to zero while having one of its components is nonzero. The direction of a vector can be different in a different particular coordinate system.

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Mutations occur in the genetic material due to alterations in the sequence of nucleic acids of the genome. Mutations are harmful as they lead to many disorders and conditions which are life-threatening.

A mutation can be defined as an alteration in the sequence of nucleic acids of the genome of a living organism, virus, or the extrachromosomal DNA material such as the mitochondrial DNA or the chloroplast DNA. Viral genomes are different from that of other living organisms as they contain either DNA or RNA as genetic material.

The guanine-thymine (G-T) mutation is the single most common mutation which occurs in the DNA of human. This mutation occurs about once in every 10,000 to 100,000 base pairs in the DNA.

Mutations are of different types. From which, the deletion mutations are opposite types of point mutations. These mutations involve the removal of a base pair from the sequence. Both of these mutations lead to the creation of one of the most dangerous type of point mutations which is known as the frameshift mutation.

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If the Earth's sideways velocity becomes zero the Earth would still continue to orbit as before.

Sideways velocity of the earth is the rotational speed of the earth in terms of linear velocity. That is 1100 miles an hour approximately. If the sideways velocity of the earth becomes zero, objects on the earth will start flying eastward. This is due to the momentum possesses by the object on the surface of the earth. Flying of the rocks and oceans would cause the earthquakes and tsunamis. But there will not be any effect on the orbital velocity of the earth as it is governed by the gravitational force between the earth and the sun. Which ultimately depends on the masses of the sun and the earth and the distance between them.

So the correct option will be that the earth would continue to orbit as before.

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Charges a and d, on the other two corners, have equal charge, while both b and c have a charge of 1.0 c, so the charge so that the force on b is zero is -2.8.

Charge is the material's physical quality that results in a force being applied to it when it is exposed to an electromagnetic field. You can have a positive or negative electric charge. Opposite charges attract one another while like charges repel one another. Neutral refers to an object that carries no net charge.

A square is a geometric shape with four equal-length sides and four right-angled corners. When diagonally opposite charges are paired, the fields inside every duo cancel in examples 1 and 2, leaving no net field at the centre.

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A) The electric field at 1.0 cm above the center of the sheet is 2.5 × 10⁵ N/C, B) the electric field 15 m above the center of the sheet is 11 N/C.

Side of the square sheet, l =25 cm = 0.25 m

Uniformly distributed charge, Q = 275 × 10⁻⁹ C

ε₀ = 8.8 × 10⁻¹²

a) When close to the sheet, we assume it as an infinite sheet, So,

E = σ/2ε₀,

σ = Q/l²

E = Q/(2ε₀l²)

E = (275 × 10⁻⁹)/(2×8.8 × 10⁻¹²×0.25²)

E = 2.5 × 10⁵ N/C

B) When far from the sheet, we assume it as a point charge, if R = 15 m

E = Q/(4πε₀R²)

E = (275 × 10⁻⁹)/(4π×8.8 × 10⁻¹²× 15²)

E = 11 N/C

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The measurement have 4 significant figures. Hence, option (b) is correct.

The number that is given as digits is established using significant figures. A meaningful representation of numbers is carried by these digits.

Frequently, significant digits are employed in place of figures. By counting all of the values beginning with the first non-zero digit on the left, we may determine the number of significant digits.

The certain chemical reaction produces 0.0450grams of product.

In 0.0450, there have 4 significant figures.

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Answer: The answer is 3 sig figs, option A

Explanation:

The driving frequency that will set up a standing wave with five equal segments is 600 Hz.

It is given that frequency observed for a stretched string with four equal segments in a standing wave is 480Hz.

That is,  f₄ = 480 Hz

      Fundamental frequency, f₀, can be calculated as,  

              f₀ = [tex]\frac{480}{4} = 120 Hz[/tex]

Therefore, the driving frequency that will set up a standing wave with five equal segments, f₅, is

            f₅ = f₀ × 5

            f₅= 120 × 5

            f₅ = 600 Hz.

Hence, the driving frequency, f₅, is 600 Hz.

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A significant burn can happen in as little as five seconds at a hot liquid's temperature climb to 140° F.

Is the water hot at 140 degrees Fahrenheit?

A major reason to keep hot water at 120 degrees, especially if you have young children, is because hot water exceeding 140 degrees can potentially cause scorching. Scalding can have serious consequences and is more likely to happen to children and elderly people.

What is temperature?

Temperature is a measurement of how hot or cold something is on a specific scale.

What temperature causes the skin to burn?

According to studies, a full-thickness skin burn can occur at a temperature of 52 degrees Celsius (125 degrees Fahrenheit) in 2 minutes and a temperature of 54 degrees Celsius (130 degrees Fahrenheit) in 30 seconds.

Burn Exposure chart

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It just takes five seconds or less for a major burn to develop when a hot liquid is raised to a temperature of 140° F.

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When a volleyball is tossed over a net, starting from a height of 1.5 meters above the ground, where  after reaching the top of its trajectory it returns to its original height as it falls, the ball's speed is the same as when it was tossed, but its velocity is different.

As ball 1 gets to the top of its trajectory, its velocity becomes zero.

since not stated otherwise, we assume that both balls have the same properties

If ball 2 is released at this instance, then they both will travel down at the same time interval and have initial velocity as zero.

since vertical travel is downwards, then acceleration due to gravity g is positive for both balls.

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Answer:

250.025 Newtons

Explanation:

Fnet=ma

Answer:

Below

Explanation:

The trailing edge has to fall 6.14 inches   ( mass is irrelevant)

 d = 1/2 a t^2

 6.14/12  ft   = 1/2 (32.2  ft/s^2 )(t^2) shows   t = .178 s

The final temperature of the whisky is  10.95∘C when 55.0g of whisky at 22∘C room temperature, and then three stones to cool it are added.

Given the mass of whisky (m1) = 55g = 55x10^-3kg

Initial temperature of whisky (T1) = 22∘C

The final temperature of mixture = T

The mass of stone cube (m2) = 32g = 32x10^-3kg

The temperature of stone (T2) = -11∘C

The specific heat of stone is (Cs) = 980J/kg.K

The specific heat of whisky is (Cw) = 3400J/kg⋅K

Let the number of stones = 3

Following the combination, the stone cube gains hatred while the whisky loses heat.

Let the heat lost by whisky = Qw

Qw = 55 x 10^-3 x 3400J/kg⋅K x (22 - T)

Qw = 187(22 - T)

Let the heat gained by stones = Qs

Qs = 3 x 32 x 10^-3 x 980J/kg⋅K x (T-(-11))

Qs = 94.080(T+11)

We know that Qw = Qs such that

187(22 - T) = 94.080(T+11)

4114 - 1034.88 = 94.080T + 187T

T = 3079.12/281.08 = 10.95∘C

Hence the final temperature of the drink is  10.95∘C

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The most practical application of sonar is measuring the distance between objects in the ocean.

option A.

Sonar is a technique that uses sound propagation to navigate, measure distances, communicate with or detect objects on or under the surface of the water, such as other vessels.

So basically, sonar is applied under water to measure the distance of objects such minerals, vessels , etc.

Thus, we can conclude that the most practical application of sonar is found under water, for measuring the distance between objects in the ocean.

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After 2.00 billion seconds you will be around 63 years assuming a 365 day year.

To know the answer you need to know the number of seconds in a year.

First, you need to multiply, 60 × 60

to find the number of seconds in an hour, which is 3600 seconds.

Then, multiply = 3600 × 24

to find the number of seconds in a day, which is 86,400 seconds.

Next, multiply = 86400 × 365

to find the number of seconds in a year, which is 31,536,000 seconds.

Finally, divide 2,000,000,000 by 31,536,000 and you will get about 63 years.

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The reference height form the ground level is 30.6m.

Let us note that when we are talking about the gravitational potential energy, we would have to look at the energy that is possessed by the object because the object is placed at a given height on earth.

Now, we have to note that the gravitational potential energy of the object can be obtained by the use of the formula;

E = mgh

E = gravitational potential energy

m = mass of the object

g = acceleration due to gravity

h = height

Then;

2.4 =  0.008 * 9.8 * h

h = 2.4/0.008 * 9.8

h = 30.6m

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The force particle b exerts on a is -2.72 N to the left.

The force particle b exerts on a can be determined by using Coulomb's law, which states that the force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

Since the charges of the particles are the same, we can assume that the force is proportional to the inverse of the distance squared. By increasing the distance between the particles from 13.0 mm to 18.5 mm, we can assume that the force has decreased.

Using the formula F = k(q1*q2)/r^2, we can calculate the new force by substituting the new distance and assuming the charges are equal. Since the force was 2.72 N to the right, and the distance has increased, the force particle b now exerts on a would-be -2.72 N to the left.

This is because the force is inversely proportional to the distance squared, and since the distance has increased the force has decreased.

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31.08 N will be the weight of that object on mars which has a mass of 8.4 kg as the gravitational field strength is 3.7 n/kg on Mars.

As we know that weight is nothing just force a body exerts on the surface so in a similar way the weight will be mass* acceleration due to the planet(Mars in this case) (g) which is 3.7 n/kg given. So

W = mass* g

w = 8.4 * 3.7 => 31.08N

Each planet has different gravitational field strength that we call (g) in the case of earth it is calculated as 9.8 n/kg but generally, we take as 10 n/kg for simplifying the calculation, and Mars has 3.7 n/kg and moon has as just 1.4 n/kg.

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