A potato gun fires a potato straight up with an initial velocity of 16 m/s. How high will it rise?

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 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:

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 temperature to increase from to 29.75℃.

When heat is transferred from your body by moving air, convection takes place. The air will rise if it absorbs your heat and is colder than the environment. Cooler air flows in to take its place and absorb more of your warmth as the warmed air rising around you increases. You feel colder as this air flows more quickly.

When absorbed by a substance, heat results  inter-particle bonds to weaken and break which result  to a change of state (solid to liquid for example). Heat causing a phase change is NOT sufficient to cause an increase in temperature

amount of heat absorbed ,

q = m* c* ΔT

specific heat of water is = 4.186J/g ⁰C

ΔT = 7.5⁰C

mass of water = 948.0g

there for,

q =  948.0g *  7.5⁰C * 4.186J/g ⁰C

q = 29.762 KJ

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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 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 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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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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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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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 average acceleration is a = 1.3158 m/s²

The average acceleration.

V₀ = 2.0 m/s,

V = 4.5 m/s,

t = 1.9 s,

a =?

a = V-V₀/t

a = 4.5 m/s - 2.0 m/s / 1.9 s

a = 2.5 m/s /1.9 s

a = 1.3158 m/s²

∴ The average acceleration is a = 1.3158 m/s²

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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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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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Answer:

1what is the first who derived car

(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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Answer:

A metamorphic rock

Explanation:

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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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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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 speed is the distance covered by an object at a particular time. The average cycling speed of Liam is 2.91667 meters/sec.

The speed is the distance covered by an object at a particular time. Therefore, it is the ratio of distance and time.

Speed = Distance Covered / Time taken

Given that Liam rides his bicycle to the near park that is 1.75 kilometers away from his home and it takes Liam 10 minutes to reach the park. Therefore, we can write,

Distance covered by Liam = 1.75 kilometers

                                            = 1.75 × 1000 meter

                                            = 1750 meters

Time taken by Liam = 10 minutes

                                 = 10 × 60 seconds

                                 = 600 seconds

Now, Liam's average cycling speed can be written as,

Liam's average cycling speed

 = Distance covered by Liam/Time taken by Liam

 = 1750 meters / 600 seconds

 = 2.91667 meters/seconds

Hence, the average cycling speed of Liam is 2.91667 meters/sec.

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The semi - major axis is a = 2.43 A.U

The semi-major axis, a, is half of the longest diameter of an ellipse. Together with the semi-minor axis , b, and eccentricity, e, it forms a set of related values that completely describe the shape of an ellipse.

Now,

We have to find the semi major axis which we represents as "a".

Aphelion = a( 1+e ) = 1.5 AU.

Perihelion = a( 1−e )= 3.36 AU .

a = ( 1.5 + 3.36 )/2 AU = 2.43 AU .

e = 3.36 - 1.5 /2a

= 1.86 /2 ( 2.43 ) = 1.86 /4.86  

=0.3827.

The semi - major axis is a = 2.43 A.U

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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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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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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 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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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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