A plane starts out at rest. 100 seconds later, its velocity is 300 m/s. What
vas its average acceleration during this time?

To increase the boiling temperature of 2051 g of water by 1.500 °C, approximately 3.431 grams of NaCl would need to be added.

Explanation:

The boiling point elevation is determined by the molality of the solute in the solution. The equation for boiling point elevation is:

ΔTb = Kb * m

Where:

ΔTb is the boiling point elevation,

Kb is the boiling point elevation constant for water (0.5100 °C/m),

m is the molality of the solute.

To calculate the molality, we can use the formula:

m = (moles of solute) / (mass of solvent in kg)

Given that we want to increase the boiling temperature by 1.500 °C, and the Kb value is 0.5100 °C/m, we can rearrange the equation to solve for the molality:

m = ΔTb / Kb

m = 1.500 °C / 0.5100 °C/m

m ≈ 2.941 m

To convert molality to mass, we need to know the molecular weight of NaCl. The molecular weight of NaCl is approximately 58.44 g/mol.

Using the formula:

mass of solute = molality * molecular weight of solute * mass of solvent in kg

mass of solute = 2.941 m * 58.44 g/mol * 2.051 kg

mass of solute ≈ 3.431 g

Therefore, approximately 3.431 grams of NaCl would need to be added to 2051 g of water to increase the boiling temperature of the solution by 1.500 °C.

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The equation for free fall at the surface of some planet (s in meters, t in seconds) is s=1.33t^(2), the long it take a rock falling from rest to reach a velocity of 27.2(m)/(s) on this planet is 1.414 seconds.

Free fall is a type of movement that an object undergoes when it falls freely under the effect of gravity. Gravity is a force that acts on every object and makes it move towards the center of the earth or any other celestial body. The acceleration due to gravity is expressed as g, and it is equal to 9.8 m/s² on earth. The time it takes a rock falling from rest to reach a velocity of 27.2 m/s on this planet can be calculated by equating the acceleration due to gravity with the given velocity.

The formula for velocity is given by V=U+at, where V is the final velocity, U is the initial velocity, a is the acceleration, and t is the time taken to reach the final velocity. Under free fall, the initial velocity is zero; therefore, the formula can be simplified to V = at.

Substituting the given values in the formula, we get 27.2=1.33t² × g or 27.2=1.33t² × 9.8.

We can simplify this equation to t² = (27.2)/(1.33 × 9.8) or t² = 2.

The square root of 2 is 1.414. Therefore, the time taken for the rock to reach a velocity of 27.2 m/s on this planet is 1.414 seconds.

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The current through the new resistor will be half of the original current.

The resistance of a conductor depends on its material, length, and cross-sectional area, and is given by: R = (ρL) / A

Where R is the resistance, ρ is the resistivity of the material, L is the length, and A is the cross-sectional area.

Since the new resistor has twice the cross-sectional area of the original, its resistance will be half that of the original, assuming the length and material are the same.

According to Ohm's Law, the current through a resistor is directly proportional to the potential difference across it, and inversely proportional to its resistance: I = V / R

where I is the current, V is the potential difference, and R is the resistance.

Since the potential drop across the resistor is the same for the new resistor as for the original, and the new resistor has half the resistance, the current through the new resistor will be twice the current through the original resistor.

Therefore, the current through the new resistor will be half of the original current.

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Answer:

11. Food Chain

12. Food web

13. Habitat

Explanation:

The difference between food chain and food web is;

In a food chain, it shows one path of energy in one ecosystem.

In a food web, it shows various food chains in many ecosystems and how they are connected.

The type of galaxy which has arms that contain sites of active star formation and start close to a bulge in the center is: D. normal spiral.

A star can be defined as a giant celestial (astronomical) object that is made up of a luminous sphere of plasma bounded together by its own gravitational force.

Generally, a star comprises two (2) main interstellar hot gases and these include:  

I. Hydrogen (H).

II. Helium (He).

A galaxy refers to a collection of billions of stars, which are existing independently.

This ultimately implies that, the greatest number of stars are found in a galaxy.

According to astronomers, the galaxy is classified into four (4) main categories and these are:

Furthermore, spiral galaxies are divided into two (2) major groups such as:

I. Barred spiral.

II. Normal spiral.

A normal spiral is typically made up of arms containing sites of active star formation and it start close to a bulge in the center.

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Answer:

D) normal spiral

Explanation:

Whoever answered it practically wrote a life story. There's no need for an explanation; just get to the point and tell us the answer. But anways, the answer is D.

The stratosphere absorbs over 95% of incoming ultraviolet radiation.

The stratosphere is the second layer of the atmosphere and it is composed

of ozone layer.

The ozone layer is composed of ozone which helps to shield the earth from

the ultraviolet radiations from the sun. The absence of this layer will result

in skin burns, cancer etc .

This is why special attention is given to prevent further depletion of the

layer which will most likely cause harmful effects and threaten existence of

life on earth.

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Answer:

The stratosphere absorbs over 95% of incoming ultraviolet radiation.

The stratosphere is the second layer of the atmosphere and it is composed

of ozone layer.

The ozone layer is composed of ozone which helps to shield the earth from

the ultraviolet radiations from the sun. The absence of this layer will result

in skin burns, cancer etc .

This is why special attention is given to prevent further depletion of the

layer which will most likely cause harmful effects and threaten existence of

life on earth.

The period of oscillation, if at a given time the magnitude of acceleration of a mass is 9 m/s² when its position is 4 meters from equilibrium is 4.188 s

Acceleration can be expressed as,

a ( t ) = - ω² x ( t )

ω² = a ( t ) / - x ( t )

ω² = 9 / - ( - 4 )

ω² = 9 / 4

ω = 3 / 2

ω = 1.5 rad / s

T = 2 π / ω

T = Time period

ω = Angular velocity

T = 2 * 3.14 / 1.5

T = 4.188 s

Therefore, the period of oscillation is 4.188 s

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Answer: Solenoid

Explanation:

Answer:

Solenoid

Explanation:

To read text at a near-point distance of 22 cm, a person who has had cataract surgery would need a corrective lens with a refractive power of +4.5 diopters.

If a person has had the surgical removal of the variable lens of the eye, they would have lost the ability to accommodate (change the shape of the lens to focus on objects at different distances). Therefore, they would require corrective lenses to see clearly at different distances.

To determine the power of the corrective lenses required to read text at a near-point distance of 22 cm, we can use the following formula:

\(1/f = 1/d_o + 1/d_i\)

where:

f = focal length of the corrective lens

\(d_o\) = object distance (distance from the eye to the object)

\(d_i\)= image distance (distance from the eye to the image formed by the corrective lens)

We want to find the power of the corrective lens, which is given by:

\(P=1/f\)

The near-point distance \((d_o)\)  is 22 cm = 0.22 m. Since the cornea's refractive power focuses objects at infinite distances onto the retina, we can assume that the object distance is effectively at infinity, i.e., \(d_o = \infty\)

Therefore, the formula becomes:

\(1/f = 1/\infty + 1/d_i\)

\(1/f = 0 + 1/d_i\)

\(f = d_i\)

We want to find the focal length \((d_i)\)  of the corrective lens required to form an image of the text at a distance of 22 cm from the eye.

Using the formula, we get:

\(f = d_i = \frac{1}{(1/d_o + 1/d_i)}\)

\(d_i = \frac{1}{(1/d_o + 1/f)}\)

\(d_i = \frac{1}{(1/0.22 + 1/\infty)}\)

\(d_i = 0.22 m\)

Now, we can calculate the power of the corrective lens required as follows:

\(P = 1/f\)

\(P = 1/0.22\)

\(P = +4.5\)  diopters (to the nearest tenth of a diopter)

Therefore, the power of the corrective lenses required to read text at a near-point distance of 22 cm is +4.5 diopters (convex lenses).

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Answer: Manipulated Variable

Explanation:

The thing that is changed on purpose is called the manipulated variable. Sometimes it is also called the independent variable, the scientist may change this to discover something new or change it for better results.

The creation of space between particles with opposing charges is known as charge separation, sometimes known as static electricity.

When the positive and negative charges are out of balance, static electricity is produced. While electrons like to hop all over the place, protons and neutrons don't move around very much. A negative charge is present when an object (or person) possesses more electrons. A common electric phenomena called static electricity occurs when charged particles are transmitted from one body to another. For instance, when two insulators are rubbed together and the air around them is dry, the resulting charges are equal and opposite to one another. The term "static electricity" describes an imbalance of electric charges in a body, more precisely, the imbalance of negative and positive charges.

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To find the velocity of the plane relative to the ground, we need to use vector addition. The eastward airspeed of the plane is one vector, while the southward wind speed is another vector. The resulting vector is the velocity of the plane relative to the ground.

Using the Pythagorean theorem, we can find the magnitude of the resulting vector:

Velocity^2 = (156 m/s)^2 + (20.0 m/s)^2

Velocity = sqrt[(156 m/s)^2 + (20.0 m/s)^2]

Velocity = 158.1 m/s

The direction of the resulting vector can be found using trigonometry. We can use the tangent function to find the angle between the eastward direction and the direction of the resulting vector:

tan(theta) = opposite/adjacent

tan(theta) = (20.0 m/s)/(156 m/s)

theta = 7.3 degrees south of east

Therefore, the velocity of the plane relative to the ground is 158.1 m/s at an angle of 7.3 degrees south of east.

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3440 KG/m3 is the same as 3.44 g/ cm3As the SI unit of density is kilogram per cubic meter so, we need to convert g/cm3 to kilogram per cubic meter

As density is the property of matter that deals with the mass per cubical unit place it occurs or places it is required. Or we can say it also deals with the floating property of a substance. Density decides the floating of an object. The less the density more floating the object is and it does not sink easily. it has a formula as

d= m/v..........(Mass/Volume)

To convert gram/ cm3

1 g/cm3 is the same as 1000kg/meter cubic

as

10 gram to kg, divide it by 1000, and 10/1000 = 0.01 kg

so 1000 gram = 1 kg

for cm to m, we need to multiply by 100

so

3.44* (100)*100*100/1000

3440000/1000

3440kg/m3

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No. A dog chasing its tail is just an animal running around in circles.

The dog's MOTION, however, IS accelerated motion, since the DIRECTION of its motion is constantly changing.

A a dog chasing its tail cannot be considered as acceleration.

Acceleration is the rate at which velocity changes over time, both in terms of speed and direction.

A point or object moving in a straight line is accelerated if it accelerates or decelerates. Even if the speed is constant, motion on a circle is accelerated because the direction is constantly changing.

For example, if a car accelerates as it turns a corner at constant speed, it is doing so because its direction is changing.

The faster you turn, the faster you accelerate. When velocity changes in magnitude (increase or decrease in speed), direction, or both, there is an acceleration.

Thus, as there is no change in either speed or direction in scenario in which a dog chases its tail, it is not considered as acceleration.

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Answer:

La velocidad del sistema bala-bloque es 5 metros por segundo.

Explanation:

El enunciado tiene una omisión gramatical. La forma correcta es la siguiente:

Una bala de 0.8 kilogramos de masa se mueve horizontalmente con una velocidad de 30 metros por segundo y se introduce en un bloque de 4 kilogramos, inicialmente en reposo. ¿Cuál es la velocidad de la bala y el bloque después del impacto?

Esta situación es un caso clásico de colisión enteramente inelástica, en donde el sistema bala-bloque no tiene influencia de fuerzas externas, entonces la situación queda descrita por la siguiente ecuación:

\(m_{b}\cdot v_{b,o} = (m_{b}+m_{B})\cdot v\) (1)

Donde:

\(m_{b}\) - Masa de la bala, en kilogramos.

\(v_{b,o}\) - Velocidad inicial de la bala, en metros por segundo.

\(m_{B}\) - Masa del bloque, en kilogramos.

\(v\) - Velocidad del sistema bala-bloque, en metros por segundo.

Si sabemos que \(v_{b,o} = 30\,\frac{m}{s}\), \(m_{b} = 0.8\,kg\) y \(m_{B} = 4\,kg\), entonces la velocidad del sistema masa-bloque es:

\(v = \frac{m_{b}}{m_{b}+m_{B}}\cdot v_{b,o}\)

\(v = 5\,\frac{m}{s}\)

La velocidad del sistema bala-bloque es 5 metros por segundo.

Answer:

The strength of gravity decreases.

An example of that would be if you were in space; you float around because there's no gravity.

The effect that changing plate separation and surface area has on your capacitor is that if the distance between the plates is increased then the capacitance of the capacitor will decrease. If the distance between the plates is decreased, then the capacitance of the capacitor will increase.

Similarly, if the surface area of the plates is increased, the capacitance of the capacitor will increase. If the surface area of the plates is decreased, the capacitance of the capacitor will decrease.The addition of a dielectric effect the capacitance by increasing the capacitance of the capacitor by a factor equal to the dielectric constant. The capacitance of the capacitor is given by the formula C = Kε0A/d  Therefore, the capacitance of the capacitor increases.Charge Q is stored on a capacitor in such a way that there is an equal and opposite charge on each plate. If the magnitude of the charge on one plate is q, then the magnitude of the charge on the other plate is -q.

The capacitance of a parallel-plate capacitor is given by the formula:C = ε0A/dWhere:C = capacitance of the capacitorε0 = permittivity of free spaceA = area of the platesd = distance between the platesIf the distance between the plates is increased, then the capacitance of the capacitor will decrease. If the distance between the plates is decreased, then the capacitance of the capacitor will increase.If the voltage across the equivalent capacitor is 3V, the charge on the equivalent capacitor is given by:Q = CeqV = (0.2F)(3V) = 0.6CIf the charge on the equivalent capacitor is 0.6C, the charge on capacitor C2 is given by:q2 = C2V = (0.05F)(3V) = 0.15CIf the charge on the equivalent capacitor is 0.6C, the charge on capacitor C3 is given by:q3 = C3V = (0.15F)(3V) = 0.45CTherefore, the capacitor that stores less charge is capacitor C2, because its capacitance is smaller than the capacitance of capacitor C3.

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Answer:

The water would rise because of displacement in the water

Explanation:

Answer:

Reflected

Explanation:

During the process of reflection whatever that is sent forth e.g light comes back (reflects)

Answer:

transmitted

Explanation:

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A pulsar is a neutron star that sweeps a beam of radiation past the Earth each time it rotates. So, option D is correct.

A pulsar is a highly magnetized, rotating neutron star that emits beams of electromagnetic radiation. It is formed from the remnants of a massive star that has undergone a supernova explosion.

As the neutron star spins rapidly, its intense magnetic field causes beams of radiation to be emitted from its magnetic poles. These beams are observed as regular pulses of radiation as the pulsar rotates.

Pulsars are characterized by their precise and regular periods of pulsation, which can range from milliseconds to several seconds.

The emission of radiation occurs along the magnetic axis of the neutron star, and if this axis is not aligned with the rotation axis, the beams of radiation sweep across space like a lighthouse, leading to periodic pulses of radiation detected on Earth.

The discovery of pulsars in 1967 by Jocelyn Bell Burnell and Antony Hewish provided evidence for the existence of neutron stars and opened up new avenues for studying stellar remnants and extreme astrophysical phenomena.

Pulsars are important objects in astrophysics and continue to be studied for their contributions to our understanding of stellar evolution, gravity, and the behavior of matter under extreme conditions.

So, option D is correct.

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Answer:

\(a=916\ km/h^2\)

Explanation:

Given that,

Initial speed, u = 65,640 km/h

Final speed, v = 120,600 km/h

Time, t = 2.5 days = 60 h

We need to find the acceleration of the hyperdrive. We know that, acceleration is equal to the change in velocity per unit time. So,

\(a=\dfrac{v-u}{t}\\\\a=\dfrac{120,600-65,640 }{60}\\\\=916\ km/h^2\)

So, the acceleration of the hyperdrive is equal to \(916\ km/h^2\).

The current through R1 immediately after the switch is opened which has been closed for a long time is 0.5 A ( up )

Vc = V30Ω + V10Ω

Vc = I R2

Vc = Voltage across capacitor

V30Ω = Voltage across 30Ω resistor

V10Ω = Voltage across 10Ω resistor

I = Current

R2 = Resistance across resistor 2

I = 2 A

R2 = 10 Ω

Vc = 2 * 10

Vc = 20Ω

V = I R

V30Ω = 30 I

V10Ω = 10 I

Vc = V30Ω + V10Ω

20 = 30 I + 10 I

20 = 40 I

I = 1 / 2

I = 0.5 A ( up )

Therefore, the current through R1 immediately after the switch is opened is 0.5 A ( up )

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Answer:

The brick was traveling at 49 m/s the instant before hitting the ground.

Explanation:

When an object is dropped from rest in a free-falling motion, it falls with a constant acceleration called the acceleration of gravity, which value is \(g = 9.8 m/s^2\).

The final velocity of a free-falling object after a time t is given by:

\(vf=g.t\)

The distance traveled by a dropped object is:

\(\displaystyle y=\frac{gt^2}{2}\)

The brick takes 5 seconds to land from the high scaffold. The speed at which it lands is:

\(vf=9.8\cdot 5\)

vf=49 m/s

The brick was traveling at 49 m/s the instant before hitting the ground.

The speed of the  Toyota Corolla would have  been 143.9 mph.

The acceleration of the F-15 can be calculated as follows:

Acceleration = Velocity Change / Time = (Take-off Speed) / Time

where;

Take-off Speed = √(2dg /t²)

Take-off Speed = √(2 x  (270 ft)  x 32.2 ft/s² / (2 s)²)

T  = √(17496) = 131.6 ft/s

Acceleration = Velocity Change / Time

= (131.6 ft/s) / (2 s) = 65.8 ft/s²

We can use the same acceleration to launch the Toyota Corolla, and calculate its final velocity:

Final Velocity = Initial Velocity + Acceleration x Time

where;

Final Velocity = 0 + (65.8 ft/s²) * (2 s) = 131.6 ft/s

Finally, we can convert the velocity from feet per second to miles per hour:

Velocity (mph) = Velocity (ft/s) x (1 hour/3600 s) x (5280 ft/mile)

= 131.6 ft/s x  (1 hour/3600 s)  x (5280 ft/mile)

= 143.9 mph

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The charge on the capacitor at t = 9 ms is approximately 31.8 μC. To find the charge on the 7.0 μF capacitor at t = 9 ms when connected in series with a 5.0 kΩ resistor and a 20-V DC source,

We will use the formula for the charge on a charging capacitor in an RC circuit:

Q(t) = Q_max * (1 - e^(-t/RC))

where Q(t) is the charge at time t, Q_max is the maximum charge on the capacitor, R is the resistance (5.0 kΩ), C is the capacitance (7.0 μF), and t is the time (9 ms).

First, calculate Q_max: Q_max = C * V = 7.0 μF * 20 V = 140 μC.
Next, calculate RC: RC = 5.0 kΩ * 7.0 μF = 35 ms.
Finally, calculate Q(9 ms): Q(9 ms) = 140 μC * (1 - e^(-9 ms / 35 ms)) ≈ 31.8 μC.

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To solve this problem, we can use the formula Q = CV, where Q is the charge on the capacitor, C is the capacitance, and V is the voltage across the capacitor.

Initially, when the switch is open, there is no current flowing through the circuit and the voltage across the capacitor is zero. Therefore, the charge on the capacitor is also zero.

When the switch is closed at t = 0 s, the capacitor starts to charge up through the resistor. The voltage across the capacitor increases gradually and the current flowing through the circuit decreases exponentially with time.

The total resistance in the circuit is the sum of the resistance of the resistor and the capacitive reactance of the capacitor, which is given by Xc = 1/(2πfC), where f is the frequency of the source (which is DC in this case). Using the given values, we get:

Xc = 1/(2π*20*10^6*7.0*10^-6) ≈ 1.1 kΩ

Therefore, the total resistance in the circuit is Rtot = R + Xc = 5.0 kΩ + 1.1 kΩ = 6.1 kΩ

Using Ohm's law, we can calculate the current flowing through the circuit at t = 9 ms:

I = V/Rtot = 20/6100 ≈ 3.28 mA

The charge on the capacitor at t = 9 ms is then given by:

Q = CV = 7.0*10^-6 * 3.28*10^-3 ≈ 22.9 μC

Therefore, the charge on the capacitor at t = 9 ms is approximately 22.9 microcoulombs.

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Answer:

C

Explanation:

(C) Positively charged particles moved upward, causing the top of the rod to have a positive charge and the bottom of the rod to have a negative charge.

When a neutral and non-polarized conducting rod moves through a magnetic field, it will experience a force known as the Lorentz force. This force acts on the moving charges within the rod, and causes them to move perpendicular to both the direction of motion and the magnetic field. In this case, since the rod is moving to the right, and the magnetic field is pointing into the screen, the Lorentz force will act upward on the positively charged particles within the rod. This motion will cause a separation of charges in the rod, with the top having a positive charge and the bottom having a negative charge.

For a 998-kg satellite orbits the Earth at a constant altitude of 102 km,

a. The energy that must be added to the system to move the satellite into a circular orbit with an altitude of 203 km is approximately 1.48 × \(10^{10}\) J.

b. The change in the system's kinetic energy is zero.

c. The change in the system's potential energy is approximately -2.96 × \(10^9\) J.

a. To move the satellite into a circular orbit with an altitude of 203 km, the potential energy of the satellite needs to be increased by an amount equal to the difference in potential energy between the two orbits. The potential energy of an object in orbit is given by U = -G M m / r, where G is the gravitational constant, M is the mass of the Earth, m is the mass of the satellite, and r is the distance between the center of the Earth and the satellite. At an altitude of 102 km, the potential energy of the satellite is U1 = -G M m / (r1 + R), where R is the radius of the Earth and r1 = R + 102 km.

At an altitude of 203 km, the potential energy of the satellite is U2 = -G M m / (r2 + R), where r2 = R + 203 km.

Therefore, the energy that must be added to the system to move the satellite into the new orbit is:

ΔE = U2 - U1 = -G M m [(1 / (r2 + R)) - (1 / (r1 + R))]

Plugging in the values, we get:

ΔE = -6.67 × \(10^{-11}\) Nm²/kg² × 5.97 × 10^{24} kg × 998 kg [(1 / (203 km + 6371 km)) - (1 / (102 km + 6371 km))]

ΔE ≈ 1.48 × \(10^{10}\) J

b. The kinetic energy of the satellite in both orbits will be the same since the altitude and speed of the satellite are the same in both cases.

c. From the formula for potential energy, we can see that the potential energy of an object in orbit is negative and becomes more negative as the distance from the center of the Earth decreases. Therefore, moving the satellite from an altitude of 102 km to an altitude of 203 km will result in a decrease in potential energy. The change in potential energy is:

ΔU = U2 - U1 = -G M m [(1 / (r2 + R)) - (1 / (r1 + R))]

Plugging in the values, we get:

ΔU = -6.67 × \(10^{-11}\) Nm²/kg² × 5.97 × \(10^{24}\) kg × 998 kg [(1 / (203 km + 6371 km)) - (1 / (102 km + 6371 km))]

ΔU ≈ -2.96 × \(10^9\) J

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Liquid containers are necessary to store liquids or other fluids, and are manufactured using various materials. These materials have unique properties and physical characteristics to meet the diverse requirements of different fluids and their storage conditions. Two of the materials used to make liquid containers are covalently bonded and metal.

1) Covalently bonded materials:Covalent bonds are strong bonds formed between atoms by sharing electrons. Covalently bonded materials are non-metallic materials that use a covalent bond between atoms to form the material. Examples of covalently bonded materials that can be used to manufacture liquid containers include:

- Polyethylene Terephthalate (PET): PET is a plastic material used to make water bottles and soft drink bottles. PET is lightweight and unbreakable, making it ideal for shipping and storing liquids.

- Polypropylene (PP): PP is a popular plastic material that is lightweight, durable, and resistant to chemical reactions. PP is used to make containers that store harsh chemicals and strong acids, as well as food containers, such as yogurt cups and margarine tubs.

In conclusion, there are many materials available that can be used to manufacture liquid containers, including covalently bonded materials and metals. The choice of material used depends on the type of liquid being stored and the storage conditions.

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When a material in liquid state is given energy, it changes its phase from liquid to vapor; the energy absorbed in this process is called heat of vaporization. The heat of vaporization of water is about 2,260 kJ/kg, which is equal to 40.8 kJ/mol. The vaporization is the opposite process of condensation.

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(a) the angle the sailor should steer his ship is 53°.

(b) The magnitude (speed) of the resultant velocity is approximately 5.26 ms-1.

(a) Since the wind is blowing towards the South of East, the course the sailor should steer the ship in order to travel directly East is given by the bearing of the vector sum of the wind and the boat's velocity vector. We need to find this bearing.

From the diagram below, the resultant vector, R, is the vector sum of the boat's velocity vector, B, and the wind vector, W. The direction of the R is given by the bearing of the line QR.

Since PR = 6 and PQ = 8, the angle between PQ and QR is given by:

tan θ = PR / PQ

= 6 / 8

= 0.75θ

= 37° (to the nearest degree)

Therefore, the bearing of the resultant vector R is 90° - θ = 90° - 37°

= 53° (to the nearest degree).

Hence, the angle the sailor should steer his ship is 53°.

(b) The magnitude of the resultant velocity can be found by finding the magnitude of the resultant vector R.

From the diagram above,

\(cos \theta = PQ / PR\cos  \theta \\= 8 / 6\\\cos \theta = 1.333R^2 \\= PQ^2 + PR^2 - 2PQPR\\\cos  \theta R^2 = 8^2 + 6^2 - 2(8)(6)\\\cos  \theta R^2 = 64 + 36 - 96\\\cos  \theta R^2= 100 - 96(1.333)\\R^2 = 100 - 127.68\\R = \sqrt{(-27.68)}\\R = 5.26\)ms-1 (to 3 significant figures)

Therefore, the magnitude (speed) of the resultant velocity is approximately 5.26 ms-1.

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The magnitude (speed) of the resultant velocity is 10 m/s.

To find the angle (as a bearing) the sailor should steer his ship to and the magnitude (speed) of the resultant velocity, we can use vector addition.

Let's break down the given information:

Boat's speed in still water (no wind): 8 m/s.

Wind's direction: 150° (measured clockwise from the North).

Wind's magnitude: 6 m/s.

a) To determine the angle (bearing) the sailor should steer his ship to, we need to find the resultant direction by adding the vectors representing the boat's velocity and the wind's velocity.

Since the wind's direction is 150°, and the boat wants to travel east (90°), the resultant direction should be the sum of

these two angles.

Resultant direction = 150° + 90° = 240° (measured clockwise from the North).

Therefore, the sailor should steer his ship to a bearing of 240°.

b) To find the magnitude (speed) of the resultant velocity, we need to calculate the magnitude of the resultant vector by using the Pythagorean theorem.

Let the magnitude of the resultant velocity be V.

Using the Pythagorean theorem:

V^2 = (Boat's velocity)^2 + (Wind's velocity)^2

V^2 = (8 m/s)^2 + (6 m/s)^2

V^2 = 64 m²/s² + 36 m²/s²

V^2 = 100 m²/s²

Taking the square root of both sides:

V = √(100 m²/s²)

V = 10 m/s

Therefore, the magnitude (speed) of the resultant velocity is 10 m/s.

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Answer:

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