A ball rolling down a hill for 9 seconds accelerates from 3 m/s to 34.5 m/s

Wavelength = c/f = (3 × [tex]10^{8}[/tex]) / (9076 × [tex]10^{9}[/tex]) = 0.0307 m.

The distance between identical points (adjacent crests) in adjacent cycles of a waveform signal propagated in space or along a wire is defined as the wavelength.

Therefore,

Wavelength = c/f = (3 × [tex]10^{8}[/tex]) / (9076 × [tex]10^{9}[/tex]) = 0.0307 m.

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An energy unit known as a kilowatt-hour is one kilowatt of power for one hour. It is 3.6 megajoules, or in conventional units.

The Formula for Calculating Watts Into Kilowatt-Hours:

kWh = (watts × hrs) ÷ 1,000

[tex]= ( 16*6)/1000[/tex]

=0.096 kwh

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The fundamental frequency of a 0.672-m-long tube, open at both ends, on a day when the speed of sound is 344 m/s is 256 Hz.

The fundamental frequency is the lowest frequency that any given instrument can produce. The instrument's first harmonic is another name for the fundamental frequency.

Given,

Length of the tube = 0.672-m

Speed of sound = 344 m/s

Tube open at both the ends

Solution:

Since the tube is open at both ends,

[tex]f_{n}[/tex] = n ([tex]V_{w/2L}[/tex])

n = 1, 2, 3, 4,...

[tex]f_{1}[/tex] = 1(344/2*0.672)

   = 256 Hz

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The rocket is still moving at 30 Km/s after 60 seconds

Speed is the distance travelled per unit. Mathematically, it can be expressed as:

Speed = distance / time

The follwing data were obtained from the question:

From the data given, we were told that the rocket experience no forces.

This simply implies that the rocket was still moving at the said speed (i.e 30 Km/s)

Thus, we can conclude that the speed of the rocket after 60 seconds is 30 Km/s since it experience no forces.

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The net force is zero due to the direction.

We need to know about force resultant to solve this problem. The force resultant is the total net force applied to the object according to the direction. It can be written as

R = F1 + F2 + ... + Fn

where R is force resultant (net force)

From the question above, we know that

F1 = F2 = F N

Because the direction is the same, the force will be minus each other.

R = F1 - F2

R = F - F

R = 0 N

Hence, the net force is 0 N

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The acceleration of the following given forces and masses are Mass = 50 kg, Force = 150N, Acceleration = 3m/s², Mass = 50 kg, Force = 200N, Acceleration = 4m/s², Mass = 50 kg, Force = 250N, Acceleration = 5m/s², Mass = 50 kg, Force = 300N, Acceleration = 6m/s².

According to Newton's second law of motion, the rate of change of momentum is directly proportional to the force.

F = ma                                ----(1)

where,

m is the mass of the body

a is the acceleration by which body move

F is the force

From 1 equation,

a = F/ m

By substituting all the values, we get

For (1),

a = 150/ 50

a = 3m/s²

For (2),

a = 200/50

a = 4 m/s²

For (3),

a = 250/50

a = 5m/s²

For (4),

a = 300/50

a = 6 m/s²

Thus, we concluded that the acceleration of the following given forces and masses are

Mass = 50 kg, Force = 150N, Acceleration = 3m/s²

Mass = 50 kg, Force = 200N, Acceleration = 4m/s²

Mass = 50 kg, Force = 250N, Acceleration = 5m/s²

Mass = 50 kg, Force = 300N, Acceleration = 6m/s²

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The heat developed per hour is 2896740 J/h.

The electric potential of the electric iron is V.

V = 121 v

The current drawn by the electric rod is I.

I = 6.65 A

The heat developed is,

Power = Electric potential × Current

P = V × I

= 121 × 6.65

= 804.65 watts

Heat developed developer in watts is 804.65 watts.

The heat developed in joules per second is,

= 804.65 J/s

The heat developed in joules per second is 804.65 Joules per second.

The heat developed per hour is,

[tex] = \frac{804.65}{ \frac{1}{3600}hour } [/tex]

= 2896740 J/h

Therefore, the heat developed per hour is 2896740 joules per hour.

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The wavelength of the line corresponding to n=n= 4 in the Balmer series is 486 nm .

A periodic wave's wavelength is its spatial period, or the length over which its shape repeats. A waveform signal that is carried in space or down a wire has a wavelength, which is the separation between two identical places (adjacent crests) in the consecutive cycles.

This length is typically defined in wireless systems in meters (m), centimeters (cm), or millimeters (mm) (mm). The distance between two successive crests or troughs of a wave is known as its wavelength. It is measured in the wave's direction.

Expression for the Balmer series to discover the wavelength of the spectral line is as follows:

1 / λ = R [tex](1/2^{2}-1/n^{2} )[/tex]

Where λ stands for the wavelength, R stands for the Rydberg constant, and n is the integral value (4 here → the Fourth level)

Substitute 1.097 x 10⁷ m⁻¹ for R and 4 for n in the above equation

1 / λ = (1.097 x 10⁷ m⁻¹) [tex](1/2^{2}-1/4^{2} )[/tex]

 = 0.20568 x 10⁷ m⁻¹

λ = 4.86 x 10⁻⁷ m

since 1 m = 10⁹ nm

λ = 486 nm

Hence, The wavelength of the line corresponding to n=n= 4 in the Balmer series is 486 nm .

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The power does the razor consume as it is ruined 160 watt.

From joules law of heating, current flows through a resistor, converts a part of electric energy into heat energy.

The rate at which the power dissipated through a resistor is,

[tex]P = V^2/R[/tex]

Here,V is the applied voltage or voltage from source Ris the resistance of the resistor, Resistance of the device Ac razor)is,

[tex]R = V^2/P[/tex]

[tex]= (120)^2/ 40[/tex]

= 14400/40

= 360 ohm

NOW, the input voltage is change to V1, new power consumed by the razor is

[tex]P_1 = V_1^2/R[/tex]

[tex]= (240)^2/360[/tex]

= 57,600/360

=160 watt

Joule's law is the e rate at which heat is produced in a conductor is directly proportional to the square f the current provided is resistance is constant.

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The liquid density is 1.25 g/ml.

We need to know about the density to solve this problem. Density is a unit that measures how dense an object is. Density can be measured by dividing mass by volume. It can be written as

ρ = m / V

where ρ is density, m is mass and V is volume

From the question above, we know that

m = 10.47 lb

V = 1 gal

Convert mass to grams

m = 10.47 lb

m = 10.47 x 453.592 grams

m = 4749.11 grams

Convert volume to milliliters

V = 1 gal

V = 1 x 3785.41 ml

V = 3785.41 ml

By substituting mass and volume, we can determine the density

ρ = m / V

ρ = 4749.11 / 3785.41

ρ = 1.25 g/ml

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When Diego is in the race, he would be using only aerobic exercise.

The term aerobic exercise has to do with the type of exercise that require brisk repetitive movements in which the consumption of oxygen is elevated during the process.

A person tends to breath faster and more deeply when carrying out an aerobic exercise and the rapid movements is the reason why there is an intense demand for oxygen in the process.

As such, when Diego is in the race, he would be using aerobic exercise.

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Answer:

1what is the first who derived car

Varactors provide a tunable capacitance with the bias voltage across the varactor, a reverse biased diode, changing the capacitance of the diode. The applied bias voltage also changes the series resistance of the diode

The choke inductors provide a DC short and an RF opens

The resonator network is designed to be resonant at a frequency above the operating frequency. At the oscillation frequency, the resonator network must present an inductance to resonate with the capacitance of the active device in an oscillator. In addition, for oscillator stability, the effective inductance must have a particular derivative of admittance with respect to frequency.

The combination of the resonator and the active device forms an oscillator. The intersection of the active device and resonator loci selects the oscillation frequency of the oscillator. The oscillator presents a capacitance to the resonator and so the resonator must present an inductance to the active device

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Increasing the frequency of supply will decrease the current through the inductor.

When an inductor is connected to an ac supply, it develops a resistance known as inductive reactance.

The inductive resistance/reactance(XL) is given by the following formula

XL = ω X L

As  ω =2πf

XL = 2πf x L

Where ω is the angular frequency and f is the frequency of the AC supply.

When the frequency of AC supply is increased i.e, f is increased, the inductive reactance (XL) is also increased because it is directly proportional to the frequency.

As the resistance of the inductor is increased, the current through it will decrease.

Thus, increasing the frequency of supply will decrease the current through the inductor.

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The fact that voyager 1 continues to speed out of the solar system even though its rockets have no fuel is an example of Newton's first law of motion.                                                                                                                                                  

Newton's first law of motion states that "an object will continue to be in a state of rest, or will continue to move at constant speed, unless it is acted upon by a force". In other words, if an object is already moving, it won't slow down or speed up on its own, unless it collides with another object, or a force acts on it.

Voyager 1 was launched in 1977 in an attempt to study the outer solar system. While it was being launched, rockets were used in order to break free from the gravitational pull of the earth. After that, the rockets continued to propel voyager 1 away from the earth, until it eventually ran out of fuel.

Even though its rocket is out of fuel, the satellite will continue to speed out of the solar system. This is because, according to Newton's first law of motion, voyager 1 will still continue in uniform motion out to space, unless it collides with an asteroid, or it enters the gravitational field of another planet, but for now, it will just continue to move.

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Critical angle. Angle of refraction from. Diamond to hear is 90 degree.

Using Snell's law.

[tex]\frac{sini}{sin90} =\frac{1}{n} \\ or, n=2.42[/tex] index of refraction

Refraction is the term for the bending of light as it passes through transparent materials (it also occurs with sound, water, and other waves).

We are able to create lenses, magnifying glasses, prisms, and rainbows because to this bending caused by refraction. Even our eyes rely on this light bending. We wouldn't be able to concentrate light onto our retina without refraction.

Two factors determine how much bend occurs:

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Answer: Ask the rest of the question.

Explanation:

Increase in wavelength of light leads to decrease in the radiation energy.

Radiation energy is inversely proportional to the wavelength of light. Thus, an increase in the wavelength of light will decrease the radiation energy and a decrease in the wavelength of light will increase the radiation energy.

Radiation energy is calculated by the formula:

E = hυ

where,

E is the radiation energy

h is the Planck’s constant

υ is the frequency

But,

υ = c / λ

where,

c is the speed light travels at in vacuum

λ is the wavelength of light

Therefore,

E = hc/λ

And thus, radiation energy and wavelength of light are inversely proportional.

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Answer:

16.55 km

Explanation:

to find the displacement use the Pythagorean theorem to find the distance between the starting position and the ending position

15 becomes 225 when squared

7 is 49 when squared

225+49=274

sqrt of 274 is 16.55

The speed of raindrops hitting your face when thy fall vertically at 3m/s while you’re running horizontally at 4 m/s is 5 m/sec.

Consider one drop of rain falling vertically. The velocity  of the rain and the velocity of the man both  are taken as vectors.

The result of the above statement is the vector is sum.

Let us consider two vectors : a and b.

Then a and b are added.

The magnitude of the sum is the root of the sum of squares of the individual vectors.

We know that

a = 3

b = 4

On substituting the given values in the above equation, we get as

Underroot of 3^2 + 4^2 we get 25.

Therefore the square root of 25 is 5

Therefore, it hit fast your face is 5 m/s.

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Answer:

A metamorphic rock

Explanation:

The angle in radians between the central maximum  is 0.04 .

The central maximum is the brightest central portion of the diffraction pattern. The central maximum is the widest and has the maximum intensity.

When the crest of a wave coincides with the crest of another wave then that interference is called the bright fringe. The same thing happens with the dark fringe also, when the trough of one wave coincides with the trough of another wave then results in dark fringes.

Formula used:

nλ = d sin(θ)

Given,

n = 1, and d = 25λ, so:

λ = 25λsin(θ)

on Dividing through by λ, and we get:

1 = 25sin(θ)

1/25 = sin(θ)

θ = 2.29 degrees = 0.04 radians.

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The energy would be obtained if 44 g of carbon were irradiated is  5.8863 x 10^5 J.

Assume each carbon atom emits one photon. For each photon.

E=hc/lambda

Where h = Plank's constant

C = speed of light

E = (6.625×10^-34)×(3×10^8)/(7.45×10^-7)

E = 2.66819x10^-19 J

So the total energy emitted is

E = E1xn

E = (2.66819x10^-19)×(6.022x10^23)/ 1 mol of carbon atom

E = 5.8863 x 10^5 J

Black body radiation is a type of radiation in which a body is in thermodynamic equilibrium, emitted by a black body. It has a specific, continuous spectrum of wavelength. Photons are energy stored in bundles.

In above question,

Wavlength (lambda)=745nm = 7.45x10^-7m.

Mass of carbon = 44 gram

Assume each carbon atom emits one photon. For each photon.

E=hc/lambda

Where h = Plank's constant

C = speed of light

E = (6.625×10^-34)×(3×10^8)/(7.45×10^-7)

E = 2.66819x10^-19 J

So the total energy emitted is

E = E1xn

E = (2.66819x10^-19)×(6.022x10^23)/ 1 mol of carbon atom

E = 5.8863 x 10^5 J

Therefore, The energy would be obtained if 44 g of carbon were irradiated is  5.8863 x 10^5 J.

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Answer:

If the gas is ideal while volume and temperature stay unchanged, there would be a five-fold increase in the pressure of this gas.

Explanation:

Let [tex]V[/tex] denote the volume of this gas, let [tex]P[/tex] denote the pressure of the gas, let [tex]n[/tex] denote the number of particles in this gas, let [tex]T[/tex] denote the temperature of this gas, and let [tex]R[/tex] denote the ideal gas constant.

If this gas is an ideal gas, it would satisfy the ideal gas law:
[tex]P\, V = n\, R\, T[/tex].

Assuming that this gas is uniform. The mass of this gas will be directly proportional to the number of particles [tex]n[/tex] in this gas. Hence, a five-fold increase in the mass of this will increase the number of particles in this gas by five folds.

Rearrange this equation to separate pressure [tex]P[/tex] from the number of particles in this gas [tex]n[/tex]:

[tex]\begin{aligned} P &= \left(\frac{R\, T}{V}\right) \, n\end{aligned}[/tex].

In other words, if the temperature and volume of this gas stays the same, the pressure [tex]P[/tex] of this gas will be proportional to the number of particles [tex]n[/tex] in this gas. Thus, the five-fold increase in the number of particles (from a five-fold increase in mass) will increase the pressure of this gas by five folds.

The amplitude of the electric field in a plane electromagnetic wave is 100  v/m then the amplitude of the magnetic field is 3.34×[tex]10^{-7}[/tex].

Electromagnetic waves, or EM waves, are produced by the oscillations of an electric field and a magnetic field. In other words, electromagnetic (EM) waves are created when magnetic and electric fields oscillate.

Electromagnetic waves are produced when an electric field and a magnetic field interact. They are referred to as "electromagnetic" waves as a result. The electric field and magnetic field of an electromagnetic wave are perpendicular to one another (at right angles). They are also parallel to the direction of the EM wave.

According to the question,

Electric Field, E₀= 100 v/m and,

B₀/E₀=1/c

The amplitude of the magnetic field  will be :

B₀=E₀/c

=100/(3×[tex]10^{8}[/tex])

B₀=3.34×[tex]10^{-7}[/tex]

Hence, the amplitude of the magnetic field is 3.34×[tex]10^{-7}[/tex].

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The transformer secondary turns should be 83 turns.

We need to know about the transformer to solve this problem. Transformer is a device that can increase or reduce the voltage. The changed voltage depends on the current and number of coil turns. It can be written as

Vi / Vs = Ni / Ns = Is / Ii

where Vi is input voltage, Vs is output voltage, Ni is primary turn, Ns is secondary turn, Is i output current and Ii is input current.

From the question above, we know that

Vi = 120 V

Ni = 1000 turns

Vs = 10V

By substituting the following parameters, we can calculate the secondary turns

Vi / Vs = Ni / Ns

120 / 10 = 1000 / Ns

Ns = 1000 / 12

Ns = 83 turns

Hence, the transformer secondary turns should be 83 turns.

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(a) The probability that we roll the die n times is (5/6) n−1 = (1/6)

(b) The expected number of times we roll the die is 6

We would have to roll (n – 1) numbers that are not 6 followed by a 6. In other words, other five numbers are expected to be rolled each, and since there are five other numbers aside 6, so the probability is

(5/6) n−1 = (1/6)

The expected number of dies to be rolled is given by the relation:

E(N) = ∑_(n=1)^∞▒n

= (5/6) n−1* (1/6)

= (1/6) (1/(1-(5/6)))2

= 6

This is the correct answer since after 6 rolls we would expect to have rolled exactly one 6 while other numbers appear once per time.

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The density of wood is 118.095 gram/liter.

We need to know about the density to solve this problem. Density is a unit that measures how dense an object is. Density can be measured by dividing mass by volume. It can be written as

ρ = m / V

where ρ is density, m is mass and V is volume

From the question above, we know that

m = 62 grams

V = 0.525 liter

By substituting the following parameters, we can calculate the density

ρ = m / V

ρ = 62 / 0.525

ρ = 118.095 gram/liter

Hence, the density of wood is 118.095 gram/liter.

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If 4.71 l of nitrogen gas and 24.96 l of hydrogen gas were allowed to react, in total 16.616 L of ammonia could form.

The balanced reaction for this would be:

N2(g) + 3H2(g) → 2NH3(g)

assuming STP:

∴ V N2(g) = 4.71 L

∴ V H2(g) = 24.96 L

The ideal gas equation is stated as:

PV = RTn

∴ moles N2(g) = PV/RT

⇒ mol N2(g) = (1 atm) (4.71L)/ (0.082 atm.L/K.mol)(298 K)

⇒ mol N2(g) = 0.007 mol

∴ moles H2(g) = PV/RT

⇒ mol H2(g) = (1) (24.96) / (0.082) (298) = 1.021 mol (limit reagent)

∴ moles NH3(g) = (1.021 moles H2(g)) (2 moles NH3 / 3 mol H2) = 0.680 mol

∴ V NH3(g) = RTn/P

⇒ V NH3(g) = ((0.082 atm.L/K.mol)(298 K) (0.680 mol))/(1 atm)

⇒ V NH3(g) = 16.616 L

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