A bush pilot wants to fly her plane to a lake that is 250.0 km [N30.0°E] from her starting point. The plane has an air speed of 210.0 km/h, and a wind is blowing from the west at 40.0 km/h. (a) In what direction should she head the plane to fly directly to the lake? (b) If she uses the heading determined in (a), what will be her velocity relative to the ground? (c) How long will it take her to reach her destination?​

The correct answer is The object must be at equilibrium position. So, the displacement is obtained zero.

Given,

The simple harmonic motion has a time period of T = 2s

The amplitude of oscillation is A = 0.5 m

The displacement of the object from the equilibrium position at time t= 1.5 s should be determined.

At time t = 0 , the displacement of the object is maximum. For objects in SHM, the maximum displacement is equal to its amplitude.

The general equation of a particle in simple harmonic motion can be written as x = A sin(ωt + Φ) where A is the amplitude ω = 2π/T is the angular frequency and Φ is its initial phase which can be determined considering time t= 0 as follows,

x = A sin(ωt + Φ)

A = A sin ( ω × 0 + Φ )

sin Φ = 1

Φ = π/2

Therefore, the equation of the object in SHM becomes,

x = A sin(ωt + π/2)

x = A cos ωt ______(1)

Substituting, t = 1.5s the displacement can be obtained as,

x = 0.5 cos (2π/T × 1.5)

x = 0.5 cos (2π/2 × 1.5)

x = 0.5 (1.5 π)

x = 0

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When pressure is decreased, a substance is more likely to undergo an expansion process.

The total applied force per unit of area is known as the pressure.

The pressure depends both on externally applied force as well the area on which it is applied.

For constant pressure, the pressure of a substance would decrease with the increase in volume which clearly represents the process of expansion.

Thus, when pressure is decreased, a substance is more likely to undergo an expansion process.

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The frequency of 0.5 kg mass oscillating on a spring with spring constant k = 5 n/m will be 0.50 Hz.

The oscillation of a spring is governed by the following formulas :

ω =  √k/√m

T = 2π/ω = 2π (√m√/k)

f = 1/T = 1/2π(√k/√m)

Here ω represents the angular frequency

T is the time period

And f is the frequency

We can use the third formula to calculate the frequency by putting the given values in it.

f = 1/2π  √k/√m

f = 1/2π √5/√0.5

f = 1/2π x √10

f = 1/2 x 3.16/3.14

f = 0.50 Hz

Hence, the frequency of 0.5 kg mass oscillating on a spring with spring constant k = 5 n/m will be 0.50 Hz.

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Larry's acceleration at take-off is  23.38 m/s.

Acceleration is the name we give to any process where the velocity changes. Since velocity is a speed and a direction, there are only two ways for you to accelerate: change your speed or change your direction—or change both.

Formula for acceleration ->

a= Δu / Δt = [tex]u_{f} - u_{i}[/tex] / Δt

Now, Given

m = 200Lb = 90.71kg

D = 2m / s

[tex]N_{0}[/tex] = 42

volume of balloon = (4/3)π[tex]r^{3}[/tex]

= 4/3 * pi * (1) ^ 3 = 4 . 188 m  t ^ 3

Total volume 42 x 4-188 = 175.9 mt3

Buoyancy force = P g x volume of air displaced

= 1.229 * 9.81 * 175 * 9

= 2121N

Force =  mass x acceleration

acceleration = F /m = 2121 / 96.71 = 23.38 m/s

Therefore, the required acceleration is 23.38 m/s.

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When the magnitude remains came and the direction changes the particle is moving in a circular motion. Speed is equal to the arc length traveled (S) divided by the change in time (Δ),

A particle travels in a uniform circular motion while maintaining a constant speed. The radius R of the circle sweeps out the angle, and the particle's velocity vector v in the illustration has a constant magnitude but changes direction as it advances from location B to position C.

The isosceles triangles OBC and DEF are identical because OB and OC are perpendicular to the velocity vectors, and as a result, the ratio of the chord BC to the radius R is the same as the ratio of the magnitudes of v to v. The chord BC and the arc BC approach one another as approaches zero, and the chord can be replaced by the arc in the ratio.

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The temperature of 21.6 g of a metal rises by 6.04 o c when the metal receives 60.0 j of heat , the identity of the metal is 0.46J/gC.

The amount of heat energy needed to raise a substance's temperature by one degree Celsius per unit mass of that substance is known as its specific heat.

The amount of energy required to raise or lower a substance's temperature by 1 unit of 1 kg of material is its specific heat capacity.

Specific heat and specific heat capacity are measured in SI units of J/Kg.

Mass of the metal = m =2.16g

the temperature of metal =ΔT=6.04C

Energy of metal = Q= 60.0J

c∝Q/ΔT

c=q/mΔT

c=60.0J/(21.6g)(6.04)

c=60.0J/130.464g.C

c=0.459896J/g.C

Hence the specific heat capacity is 0.46J/gC.

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The electromagnetic energy emitted by an excited sodium atom is 3.47 x 10¯¹⁹ joules.

We need to know about electromagnetic energy to solve the problem. The electromagnetic energy of radiated photons can be calculated by wavelength. It can be determined as

E = h . c / λ

where E is energy, h is Max Planck's constant (6.6 x 10¯³⁴ Js), c is the speed of light (3 x 10⁸ m/s) and λ is the wavelength.

From the question above, the given parameter is

λ = 570 nm = 570 x 10¯⁹ m

By using the equation, we can calculate the energy generated from an sodium atom

E = h . c / λ

E = 6.6 x 10¯³⁴ . 3 x 10⁸ / 570 x 10¯⁹

E = 3.47 x 10¯¹⁹ joules

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The watercraft with an initial velocity of 6.4 m/s and an average acceleration of 2.0 m/s2 [s] for 2.5 s will have a final velocity of: 11.4 m/s

The formula for Uniformly varied rectilinear motion (UVRM) and procedure we will use to solve this exercise is:

vf = vi + (a* t)

Where:

Information about the problem:

Applying the final velocity formula, we have:

vf = vi + (a* t)

vf = 6.4 m/s + (2.0 m/s²* 2.5 s)

vf = 6.4 m/s + 5 m/s

vf = 11.4 m/s

It is a physical quantity that indicates the variation of velocity as a function of time, it is expressed in units of distance per time squared e.g.: m/sec2 ; km/h2

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45.7 °F  is the Fahrenheit scale reading equal to  3 times that of the Celsius

-4 °F is 1/6 times that of the Celsius

The relationship between temperature in degrees Fahrenheit, F, and degrees Celsius, C, is

F = 1.8°C + 32

Part a.

If F = 6°C, then

6°C = 1.8°C + 32

6°C - 1.8°C = 32

4.2°C = 32

C = 7.62

Therefore, F = 6×7.62 = 45.71

= 45.7 °F (nearest tenth)

Part b.

When F = (1/5)C, then

0.2°C = 1.8°C + 32

0.2°C - 1.8°C = 32

-1.6°C = 32

C = - 20

Therefore, F = 0.2 × -20 = -4

                      =   -4 °F

Celsius and Fahrenheit are two scales won't to measure temperature. The temperature within the centigrade scale will be expressed in degrees Celsius. The temperature within the Fahrenheit scale will be expressed in degrees Fahrenheit. The relation between Celsius and Fahrenheit is proportional.

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A voltage sensor was used to probe and find the surfaces of electric potential.

One of the most widely utilized electrical quantities is electrical potential, which is essential for both storing and releasing electrical energy.

By dividing the potential energy by the total charge, the electric potential of any charge is calculated.

To measure the electrical potential difference between two locations in an electric circuit, a voltmeter is employed.

The electric potential difference between two places is determined using a voltmeter.

The electrical component whose potential difference is being measured is connected in parallel to voltmeters, which have high resistance.

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The average acceleration of the ball, while it is in contact with the wall, is -3969.27 m/s².

Acceleration is the rate of change of velocity per unit of time. Its S.I. unit is m/s². It is equal to the change in velocity divided by the time taken to change the velocity.

Acceleration a =  Change in velocity/ Time taken

Given in the question

Initial Velocity = u = + 20.6 m/s ( towards the wall is positive direction )

Final Velocity = v = - 11.948 m/s (away from the wall is negative direction)

Change in Velocity = Final Velocity - Initial Velocity

                                = (- 11.948) - ( + 20.6)

                                = -11.948 - 20.6

                                = -32.548 m/s

So Change in velocity = 32.548 m/s

Time Taken = Time of contact with the wall

                    = 0.0082 seconds

Put in the Formula: a =  Change in velocity/ Time taken

a = -32.548/0.0082

a = -3969.27 m/s²

Therefore the average acceleration of the ball, while it is in contact with the wall, is -3969.27 m/s².

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Coal gas is produced by using the following equation: 2C (s) + 2 H,O (g) CH, (g) + CO.

Coal gas is a mixture of methane and carbon dioxide that is created when coke and steam are combined. Gas from coal can be burned as fuel or employed as a catalyst in other chemical reactions.

When heating coal without the presence of air. It generates gas known as coal gas. It creates a substance known as coal tar. Additionally, coke, a solid residue, is created.

Coal gas is a fuel composed of hydrogen, oxygen, and carbon.

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The entropy change when 2.00 kg of water at 100°C is heated to form steam at 100°C is 12.1kJ/K.

Entropy is a metric for a system's unpredictability or disorder. The mass of a system affects the value of entropy. It has units of joules per kelvin and is represented by the letter S. The value of entropy can be either positive or negative.

Total energy change = latent heat of of vapourization × mass

Total energy change = [tex]2.26[/tex] × [tex]10^{6}[/tex] × 2

Total energy change = 4520kJ

Now, entropy change is given as:

Δ[tex]S = \frac{Total energy change}{Temperature}[/tex]

Δ[tex]S = \frac{4520}{273.15+100}[/tex]

Entropy = 12.1kJ/K

Therefore, the entropy change when 2.00 kg of water at 100°C is heated to form steam at 100°C is 12.1kJ/K.

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The fundamental frequency is 102.06 Hz m/s.

We need to know about the fundamental resonant frequency to solve this problem. When the string is vibrating at its lowest resonant frequency, it should follow the rule

λ = 2L

where λ is wavelength and L is the length of string

The transverse waves on a string also can be defined as

v = √(F . l/m)

where v is velocity, F is string tension, l is the length of string and m is mass

From the question above, we know that

l = 60 cm = 0.6 m

m = 8 g = 8 x 10¯³ kg

F = 200 N

By substituting the following equation, we can calculate the wavelength

λ = 2L

λ = 2 . 0.6

λ = 1.2 m

Find the speed of the wave

v = √(F . l/m)

v = √(200 . 0.6/(8 x 10¯³))

v = 122.47 m/s

Find the frequency

v = λ . f

122.47 = 1.2 . f

f = 102.06 Hz

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Since the angle of incidence is 45° using the law of reflection we can conclude the reflective ray will also make an angle equal to the angle of incidence i.e. 45° with the normal.

1)The angle between the incident ray and the normal is equal to the angle between the reflected ray and the normal.

2)The incident ray, the normal and the reflected ray are all in the same plane.

3) Incident ray and refracted ray are on different sides of the normal.

Given:

Light rays strike at an angle of 45° to the plane.

Using the law of reflection we can easily draw the reflective wave.

Important terms:

Angle of incidence - it is the angle at which the light way strikes the plane mirror.

Angle of reflection- it is the angle at which the light way is reflected back by the plane mirror.

Now since the angle of incidence is 45° using the law of reflection we can conclude the reflective ray will also make 45° with the normal.

Hence the angle of incidence is 45° and also the angle of reflection is equal to the angle of incidence i.e.45°.

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J. J. Thompson created an apparatus composed of a sealed glass tube with electrodes of different polarities fixed at each end. By passing a high voltage through the gas in the sealed tube, he was able to create a cathode ray. J.J. Thompson called the particles that makeup cathode rays as negatively charged particles.

In the experiment, the flow of particles was from the negative terminal (cathode) to the positive terminal (anode). He also placed two plates of opposite charges around the cathode rays. The cathode rays were deflected towards the positive place.

J.J Thompson concluded that the cathode rays were composed of negatively charged particles.

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Answer:

25 m/s

Explanation:

1.25*20=25

The car acceleration at the rate of 1.25 m/s² in the time period of 20 seconds, then the change in velocity will be equal to 25 m/s.

Acceleration is the speed of change in both speed and distance of velocity over time. Anything is said to be propelled when it goes quickly or slowly in a straight line. So because direction is always moving, motion on a circle accelerate even while the speed is increased. Both effects add to, the accelerated for all other types of motion.

It is a vector field because accelerating has both a direction and magnitude. Another vector quantity is velocity. The velocity vector change during a certain period of time, divided by that period of time, is the definition of acceleration.

The given data according to the question is,

Acceleration, a = 1.25 m/s² and,

Time, t = 20 s

Velocity, v = 1.25 × 20

v = 25 m/s.

Therefore, the change in velocity will be equal to 25 m/s.

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Some of the coal's energy was turned into other forms of energy.

According to the first law of thermodynamics, energy can neither be created nor destroyed but is converted from one form to another. We know that from the first law of thermodynamics, the energy that originally in the coal does not  vanish into thin air but undergoes a conversion.

Thus, want to find out what accounts for the energy of the coal. Thus, we could say that some of the coal's energy was turned into other forms as this is in consonance with the first la of thermodynamics.

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The magnitude of the resultant displacement of your boat will be 33.5 m

Displacement is the distance travelled in a specific direction. It is a vector quantity and it is measured in meter.

If starting from one shore you row a boat across a narrow river to the other shore. the river is 30.0 m wide as u row the river current moves your boat down the river a distance of 15.0 m

The resultant displacement of your boat can be calculated by using Pythagoras theorem.

The horizontal component = 15 m, while the vertical component = 30 m

The magnitude of the resultant displacement D = √(x² + y²)

D = √(15² + 30²)

D = √(225 + 900)

D = √1125

D = 33.5 m

Therefore, the magnitude of the resultant displacement of your boat will be 33.5 m

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Percentage of the solar constant is received at a location if insolation is measured at 343 w/m2  is 25%.

The flux density, or measuring mean of solar electromagnetic radiation, is the solar constant, represented by the symbol GSC. It refers to the sun irradiation per square meter.

At Earth's separation from the Sun, the light has an intensity of 1372 W/m2 —this is also known as the solar constant,  and the fact that it will not change over the long run.

So it would be 100%

But as mentioned in question Solar Constant is received at a location if insolation is measured at 343

W/m^2

Therefore,

Percentage of the Solar Constant is received = (343 / 1372) × 100

                                                                        = 25 %

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The volume of an element in n[tex]m^{3}[/tex] is 3×[tex]10^{27}[/tex] n[tex]m^{3}[/tex].

How are cubic nanometers converted from cubic meters?

When converting cubic meters to cubic nanometers, one must use the following conversion factor:

1 [tex]m^{3}[/tex] = 1×[tex]10^{27}[/tex] n[tex]m^{3}[/tex]

Given that the volume of an element is 3 [tex]m^{3}[/tex]

By using above conversion formula we can now convert as

⇒ 1 [tex]m^{3}[/tex] = 1×[tex]10^{27}[/tex] n[tex]m^{3}[/tex]

⇒ 3 [tex]m^{3}[/tex] = V

    V = (3×1×[tex]10^{27}[/tex]) [tex]m^{3}[/tex] n[tex]m^{3}[/tex] / 1 [tex]m^{3}[/tex]

     By canceling [tex]m^{3}[/tex] we get,

      V = 3×[tex]10^{27}[/tex] n[tex]m^{3}[/tex]

So the volume of an element after conversion is  3×[tex]10^{27}[/tex]n[tex]m^{3}[/tex].

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Produces no change in the energy because total energy is independent of the mass.

Mechanical  energy = [tex]\frac{1}{2} \times K V^2[/tex]

K = Spring constant

A = Amplitude of oscillation

Mechanical energy is the sum of kinetic energy and potential energy in an object that's utilized to do a specific work. In other words, it describes the energy of an object since of its movement or position, or both. mechanical energy, sum of the kinetic energy.

Mechanical energy is the energy of either an object in movement or the energy that's put away in objects by their position.

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The impedance of the headphones can be chosen to be 32 ohms impedance.

           Z = V/I

The perceived resistance to the flow of an alternating current in an electrical circuit, which is comparable to the real electrical resistance to a direct current and which equals the ratio of effective electromotive force to effective current.

The magnitude of the impedance Z of a circuit is equal to the maximum value of the potential difference, and  voltage, V (volts) across the circuit, divided by the maximum value of a current I (amperes) through the circuit, or simply Z = V/I. The unit of impedance, such  that of resistance, is the ohm.

Case 1 :

I²R = 2P

p = 50nW

R = 8 ohm

so, on solving,

V = 0.89442 V

Case 2 :

I²R = 2P

p = 50nW

R = 32 ohm

so, on solving,

V = 1.788 V

Case 3 :

I²R = 2P

p = 50nW

R = 1000 ohm

so, on solving,

V = 10 V

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The gas temperature change if the volume is halved and the pressure is tripled by factor 6.

An ideal gas is theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics.

Considering combined law equation:

Temperature increases by factor of 6.

Gay-Lussac's Law

Gay-Lussac's Law indicates that, as long as volume of the container containing the gas is constant, as the temperature increases, the gas molecules move faster. Then number of shocks against the walls increases, that is, the pressure increases. That is, gas pressure is directly proportional to its temperature.

In summary, when there is constant volume, as the temperature increases, the gas pressure increases. And when temperature decreases, gas pressure decreases.

Gay-Lussac's law can be expressed as mathematically as follows:

where:

P= pressure

T= temperature

k= Constant

Boyle's Law

Pressure and volume are related by Boyle's law, which says that volume occupied by a given mass of gas at constant temperature is inversely proportional to pressure.

Boyle's law is expressed mathematically as follows:

P× V=k

where:

P= pressure

V= volume

k= Constant

Charles's Law

Finally, Charles's Law consists of the relationship that exists between the volume and the temperature of certain amount of ideal gas, which is maintained at a constant pressure.

This law says that for given sum of gas at constant pressure, as the temperature increases, the volume of the gas increases and as the temperature decreases, the volume of the gas decreases. That is, volume is directly proportional to the temperature of the gas.

In summary, Charles' law is a law that says that when amount of gas and pressure are kept constant, the ratio between volume and temperature will always have the same value:

where:

V= volume

T= temperature

k= Constant

Combined law equation

Combined law equation is combination of three gas laws called Boyle's, Charlie's and Gay-Lussac's law:

Studying the two different states, an initial state 1 and an final state 2, the following will be true:

In this case, you know that:

Volume is double: V2= 2×V1

Pressure is tripled: P2= 3×P1

So, replacing in combined law equation:

Solving:

T2= 6×T1

Finally, temperature increases by a factor of 6.

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Answer:

Is this psychology or something?

A company can calculate its profit by using the foreign currency exchange rates prevailing in the market. The cost incurred in foreign currency can be converted into domestic currency first. The spot rates prevailing in the market can be used for such conversion. Once the expenses are converted into the domestic currency, the profits can be computed in the normal manner as now both the revenues and the cost are in domestic currency.

Foreign Exchange Rate is defined as the cost of the residential currency with regard to another currency. The reason of foreign trade is to compare one currency with another for appearing their relative values.

Foreign exchange rate can also be said to be the rate at which one currency is traded with another or it can be said as the price of one currency that's expressed in terms of another currency.

Exchange rates of a currency can be either fixed or floating. Fixed trade rate is decided by the central bank of the nation whereas the floating rate is decided by the flow of market request and supply.

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The symbol of the element Carbon is C, its proton number is 6, its atomic mass is 12, its neutron number is 6 and finally carbon belong to period 2 of the periodic table.

This is defined as a substance cannot be further broken down by any chemical reaction and examples include oxygen, nitrogen etc.

Carbon is an element and has an atomic number of 6 with a mass number of 12 and is present in period 2 in the periodic table.

For all atoms with no charge, the atomic number is equal to the number of proton. The number of proton is also equal to the number of electron which is why they all have the same value of 6.

Neutron = atomic mass - atomic number

         = 12 - 6 = 6

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The pressure is  2.43456 atm.

An atom or molecule has electrons all over it. Additionally, electrons are always traveling. Uneven electron distributions are possible at any time. The result is the creation of a transient dipole. Another transient dipole may develop in an atom next to this one as a result of this dipole. It causes a cascade of transient dipoles, which causes the atoms or molecules to attract one another. It's referred as Vander wall force.

We have van der waals equation and values given

use R = 0.0821 l atm/mol/k

[tex][P+an^2/V^2][v-nb] = nRT[/tex]

[tex][P+an^2/V^2] = nRT/[V-nb][/tex]

[tex][P+an^2/V^2]  = 1\times0.0821 l atm/mol/k\times298 K/[10 L ^{- 1}\times 0.04278 Lmol^{-1}][/tex]

[tex][P+an^2/V^2] = 24.4658/9.95722 = 2.45709[/tex]

[tex][P +2.253\times 1^2/(10)^2] = 2.45709[/tex]

P+ 0.02253 = 2.45709

P = 2.45709-0.02253 = 2.43456 atm

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It it takes the rock a time of 3.2 s with an initial velocity of 10 m / s, the height of the cliff is 82.12 m

s = ut + 1 / 2 at²

s = Height

u = Initial velocity

a = Acceleration due to gravity

t = Time

u = 10 m / s

t = 3.2 s

a = g = 9.8 m / s²

s = ( 10 * 3.2 ) + ( 1 / 2 * 9.8 * 3.2² )

s = 32 + 50.18

s = 82.18 m

The equation used to find the solution is an equation of motion. Equations of motion are discovered to describe the position of an object in motion at any given time.

Therefore, the height of the cliff is 82.12 m

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Answer:

V = m / s           correct units for V

x = V * t = m / s * s = m    where x is in meters

Thus t = x / V = m / (m / s) = sec

A) has to be the correct equation