an emerald has an index of refraction of 1.57. the light from a red laser of wavelength 633nm in vacuum travels within the emerald. what is the maximum angle with respect to the normal that this light can strike the emerald/air interface such that the light wave exits into the air?

When a rigid object rotates about a fixed axis, it is true about all the points in the object.

The idea of a body that does not deform or alter shape is a hard body. It is described as a collection of particles having the property that the distance between them stays constant throughout the body's motions.

The rotation of a rigid body, or an item that does not deform when it moves around a fixed axis is referred to as fixed axis rotation. We'll demonstrate how to apply the theories we've discovered so far regarding translational motion to a rotating object around a fixed axis.

Every body experiences the same angular acceleration.

Therefore, when a rigid object rotates around a fixed axis, it is true about all the points in the object.

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The work done have been calculated as : Wgravity = 15,250 joules, W rope1 = - 9667.158 joules and W rope2 = - 5584.94 joules

Given ; Force of gravity on piano = 2500 N

r = distance of the ground =  6.10 m

As the angles are mentioned in the diagram, thus we can write

Work done can be calculated by ;

Wgravity = 2500 N . 6.10m . cos 0 = 15,250 joules

W rope1 = 1830 N . 6.10 m . cos 150 = - 9667.158 joules

W rope2 = 1295 N . 6.10 m . cos 135 = - 5584.94 joules

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Answer:

W = 12500 J

T1 = -7920 J

T2 = - 4580 J

Explanation:

The angle between the force w and the displacement is 0 degrees, therefore:

[tex]W_{w} = wdcos(0) = (2500)(5)(1) =[/tex] 12500 J

The angle between the force T1 and the displacement is 90 + 60 = 150 degrees, therefore:

[tex]T_{1}= T_{1} dcos (150) = (1830)(5)(cos(150)) =[/tex] - 7920 J

The angle between the force T2 and the displacement is 90 + 45 = 135 degrees, therefore:

[tex]T_{2} = T_{2} dcos(135) = (1295)(5)(cos (135)) =[/tex] - 4580 J

The original mass of the Argon-37 sample (N₀) was 14.98651g or approximately 15g. We Use the equation for first-order kinetics for determining the original mass of the given Argon-37 sample.

If the rate of radioactive decay is first order, we can write r = k[N]1, where N is the quantity of radioisotope present at the time the rate is recorded, k is the isotope's first order rate constant, and r is the rate of decay as observed.

According to First-Order Rate Equation,

[tex]ln(\frac{N}{N_{0} } )=-kt[/tex]

Here,

N = The amount of radioisotope left after "t" time.

N₀= The initial amount of radioisotope,

k = Rate constant of the radioisotope.

t = Time

Given,

N = 2. 14 g.

N₀ = ?

k = 0. 0198

t = 98. 3 days

Now, substituting these values in the first order rate equation we get,

[tex]ln(\frac{N}{N_{0} } )=-kt\\ln(\frac{2.14}{N_{0} } )=-0.0198*98.3\\ln(\frac{2,14}{N_{0} } )=-1.94634\\\frac{2.14}{N_{0} } =e^{-1.94634} \\\frac{2.14}{N_{0} }=0.142795\\N_{0} = 14.98651g[/tex]

Hence, the original mass of the sample (N₀) was 14.98651 g or approximately 15 g.

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The magnitude is 10.2. The two unit vectors parallel to PQ are (6i+2j+8k)/10.2 and  -(6i + 2j+ 8k)/10.2.

What is vector?

A quantity with magnitude and direction, typically represented by a directed line segment whose length indicates the magnitude and whose orientation in space represents the direction.

What is unit vector?

These unit vectors are frequently used to denote direction, with the magnitude being provided via a scalar coefficient. The sum of unit vectors and scalar coefficients can then be used to represent a vector decomposition.

P = (11,4,9)

Q = (5,2,1)

So,

PQ = (11,4,9) - (5,2,1) = (6, 2, 8)

PQ= 6i + 2j+ 8k

PQ mag = 10.2

unit vector = non zero vector / magnitude of vector  

1st unit vector = (6i + 2j+ 8k)/10.2

2nd unit vector = -(6i + 2j+ 8k)/10.2

The magnitude is 10.2. The two unit vectors parallel to PQ are (6i+2j+8k)/10.2 and  -(6i + 2j+ 8k)/10.2.

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The inductance is 680µH if the induced emf is 17 v and the rate of change of the current is 25 ka/s.

The magnetic field will change as a result of growing current, so the inductor will resist the flow of current through it, resulting in a decrease in current.

e=induced emf=17V

e=Ldi/dt [di/dt=25000a/s]

17=L×25000

17/25000=L

0.00068=L

680×10⁻⁶Henry

=680µH

Inductance=680µH

The amount of energy delivered per unit of electric charge by a power source, such as a generator or a battery, is known as electromotive force (abbreviated E or EMF).

Energy is converted from one form to another as the generator or battery operates on the electric charge that is carried inside itself. Positive charge is applied to the device's positive terminal, whereas negative charge is applied to the device's negative terminal. The work done on an electrical charge unit, or the energy acquired per electrical charge unit, is known as the electromotive force. It is also referred to as EMF and is denoted by the international metric system's letter E.

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The magnitude of the acceleration due to gravity on planet p is 5 meters per seconds squared.

From the Second Equation of Motion;

s = ut + (1/2)gt²

Where v is final velocity, u is initial velocity, g is acceleration due to gravity and t is time elapsed.

Given the data in the question;

Plug the given data in the above formula and solve for g.

s = ut + (1/2)gt²

40m = (0 × 4s) + ( (1/2) × g × (4s)²

40m =  (1/2) × g × 16s²

Multiply both sides by 2

2 × 40m = 2 × (1/2) × g × 16s²

80m = g × 16s²

g × 16s² = 80m

g = 80m / 16s²

g = 5m/s²

Therefore, the acceleration due to gravity is 5m/s².

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The final pressure of the gas will be 26.8 kPa when has a final volume of 78.0L.

Boyle's law, also known as the Boyle-Mariotte law, is an experimental gas law that explains the connection between a confined gas's pressure and volume. The pressure of a gas is inversely related to its volume at constant temperature, as well as its number of moles, according to Boyle's law.

P ∝ 1/V

[tex]PV=k[/tex] or [tex]P_{1} V_{1} =P_{2} V_{2}[/tex]

[tex]P_{1}[/tex]= initial gas pressure is 209 kPa

[tex]P_{2}[/tex]= final pressure which is unknown.

[tex]V_{1[/tex]= 10.0 L, which is the gas's initial volume.

[tex]V_{2}[/tex]= 78.0 L, which is the gas's final volume.

We can now use this formula to obtain the final gas pressure by entering all the specified variables.

[tex](209kPa)(10.0L)=P_{2}(78.0L)\\P_{2}=26.8kPa[/tex]

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Two vertical wires are used to hoist a 12 kilogram lantern from the ceiling; as a result, each wire is under 58.8 N of tension.

The phrase "wire transfer" dates back to a time when banks used telegraph wires to transmit this type of financial transfer. A bank wire stored procedures on who should receive the funds, along with the user's bank account information and the amount they should receive.

Well, we know from Newton that, if m is the mass of the lantern,

Fnet = ma

Additionally, it is clear that the two forces pulling on the candle are now the strain on the two wires and the gravitational force. Since the candle isn't moving, its speed is 0, which means that the final quantity of forces acting on it must likewise be zero.

The positive y-axis should point up, and also the negative y-axis should point below. Listing the forces reveals that

-mg + T1 + T2 = 0

The two wires' tensions are also equal because they are both straight and orbital angular momentum, or T1 = T2 = T. The preceding equation can be revised to say

-mg + 2T = 0, or

2T = mg.  

Thus,

T = mg/2 = (12kg*9.8m/s2) / 2 = 58.8N

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The maximum power that the siren can put out is of 4.74 dB.

Given that,

The height of the tower above the ground is, h = 105 m

Sound intensity from the siren is, I = 116 dB

We know that, the maximum intensity of sound allowed is 11.6 B.

Then the intensity of sound in terms of W/m² can be found as follows,

log(I / I₀) = 11.6

I / I₀ = 10¹¹°⁶

I = 10¹¹°⁶ * I₀

⇒ 10¹¹°⁶ * 10⁻¹²

⇒ 10⁻⁰°⁴

At 105 m above the ground the intensity will be 105² times.

Then the intensity at source point = 10⁻⁰°⁴ * 105²

⇒ 0.398 * 105² = 4387.95 W/m²

The energy of sound from the source is given as,

4π* intensity= 4* 3.14* 4387.95 = 55112.65 W/m²

To convert into decibels:

log(55112.65/ 10⁻¹²) = log(55112.65+12) = 4.74 dB

Thus, we can conclude that the maximum power that the siren can put out is of 4.74 dB.

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By decreasing M. Because its acceleration is in the same direction as its velocity, it accelerates as it moves closer to the equilibrium position.

The item moves at its fastest speed when it is in the equilibrium position, where there is no acceleration. Due to the acceleration now being in the opposite direction from the direction of its velocity, it overshoots the equilibrium position and begins to slow down. When the spring is squeezed by a distance A, it accelerates back towards the equilibrium position before coming to a stop, disregarding friction. When the spring is stretched by a distance A, it overshoots once more before stopping at the starting position. The movement continues. The thing swings back and forth.

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Ra = 32.1 m far is the speaker from each observe .

In physics, the power supplied per unit area is known as the intensities or flux of cosmic rays, where the area is expressed on a plane plane perpendicular of the energy's propagation.

Briefing :

Let's solve this problem in parts, let's start by finding the intensity of the sound in each observer

observer A β = 64 db

            β = 10 log Iₐ / I₀

where I₀ = 1 10⁻¹² W / m²

             Iₐ = I₀ 10 (β/ 10)

let's calculate

             Iₐ = 1 10⁻¹² (64/10)

             Iₐ = 2.51 10⁻⁶ W / m²

Observer B β = 85 db

            I_b = 1 10-12 10 (85/10)

            I_b = 3.16 10⁻⁴ W / m²

now we use that the emitted power that is constant is the intensity over the area of ​​the sphere where the sound is distributed

             P = I A

therefore for the two observers

            P = Ia Aa = Ib Ab

the area of ​​a sphere is

              A = 4π R²

we substitute

              Ia 4pi Ra2 = Ib 4pi Rb2

              Ia Ra2 = Ib Rb2

Let us call the distance from the observer be to the haughty R = ax, so the distance from the observer A to the haughty is R = 35 ax; we substitute

           Ia (35 -x) 2 = Ib x2

we develop and solve

         35-x = Ra (Ib / Ia) x

          35 = [Ra (Ib / Ia) +1] x

          x (11.22 +1) = 35

          x = 35 / 12.22

           x = 2,864 m

This is the distance of observer B

The distance from observer A

Ra = 35 - x

Ra = 35 - 2,864

Ra = 32.1 m

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When the height of the cylinder increased from 100 m to 1000 m, the heat generated is 10 times.

The energy of possessed by the body by virtue its position is called potential energy. This energy is converted in the form of heat.

The formula of potential energy is given by

P.E. = mgh

where, m is the mass of body, h be the height of body and g be the acceleration due to gravity.

The potential energy of the body when it is at a height of 100 m is

P = m x g x 100 = 100 mg

The potential energy of the body when it is at a height of 1000 m is

P' = m x g x 1000 = 1000 mg

The ratio of P' and P is 10.

So, the heat generated is 10 times.

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Answer:

D. It increased by a factor of 10.

Explanation:

Answer:

23 m/s

Explanation:

It is difficult for just any device that runs on a cycle to accept heat from a given fluid and create a net quantity of work, according to the Kelvin-Planck formulation of the second law.

A first rule, a second law, as well as the third law are the three fundamental laws that thermodynamics has traditionally acknowledged. They are each simply referred to by an ordinal designation.

the equations of thermodynamics. Hrxn is equal to H1, H2, H3, and H4. With a value of 1.38 10 23 J/K, k is indeed the Boltzmann constant, that is the same as the general gas steady, R, divided with Avogadro's quantity, NA. The figure you get in a thermodynamic table is called S°, or standard absolute entropy.

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It is difficult for just any device that runs on a cycle to accept heat from a given fluid and create a net quantity of work, according to the Kelvin-Planck formulation of the second law.

A first rule, a second law, as well as the third law are the three fundamental laws that thermodynamics has traditionally acknowledged. They are each simply referred to by an ordinal designation.

the equations of thermodynamics. Hrxn is equal to H1, H2, H3, and H4. With a value of 1.38 10 23 J/K, k is indeed the Boltzmann constant, that is the same as the general gas steady, R, divided with Avogadro's quantity, NA. The figure you get in a thermodynamic table is called S°, or standard absolute entropy.

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The moving plane is visible for 0.8 second.

Speed is distance travelled by the object per unit time. Due to having no direction and only having magnitude, speed is a scalar quantity. SI unit of speed be meter/second and CGS unit of speed be cm/s.

Given that:

Another plane lands and passes the stationary plane at a speed: v =  45 m/s.

length of the arriving plane be : L = 36 m.

So, Time the moving plane remains visible be: t = L/v = 36/45 s = 0.8 second.

Hence, the moving plane is visible for 0.8 second.

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Angle of the disk's momentum. 0881 kg*m^2/s.

Given:- mass is 2.00 kg, radius is 3.00 m, velocity of 4.00 rad/s.

The most important metric for determining an object's position and rate of movement is its velocity. The distance that an object travels in a certain amount of time might be used to define it. The object's movement in a unit of time is referred to as velocity.

In contrast to velocity, which describes the speed and direction of an object's movement, speed is the rate of movement along a path. Alternatively, velocity is a vector while speed is a scalar quantity.

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Internal energy associated with systems and particles is thermal energy.

What is Internal energy?

A thermodynamic system's internal energy is the entire amount of energy it contains. The energy required to construct or prepare the system in its current internal condition comprises both internal kinetic energy and potential energy contributions.

The internal energy has been described as the energy that has been assessed by the molecules and bonds at the STP. Thermal energy has been the energy of particular molecules and the system comprising all the molecules have the summation of the thermal energy.

Thus, internal energy associated with systems and particles is thermal energy.

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The net torque acting on it hen inserted into a player, the cd starts from rest and accelerates to an angular velocity of 21 rad/s in 0.52 s are 2.059[/tex.

The net torque is the force applied that is usually quite different from normal acting force.

Here solid disk =Torque[tex]Iα[/tex]

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The critical angle for the liquid when surrounded by air is 48.75°.

The critical angle is the maximum angle at which a light beam traversing a transparent media can collide with the surface of a second medium having a lower refractive index without being completely reflected within the first medium.

Given that:

Angle of incident: i = 30.0°.

Angle of refraction, r = 22.0°.

Hence, refractive index of the medium: n = sini/sinr

= sin 30.0°/sin22.0°

= 1.34.

Hence, the critical angle for the liquid when surrounded by air:

= sin⁻¹(1/n)

= sin⁻¹(1/1.33)

= 48.75°.

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The primary coil of a transformer, which has 59 turns, receives 80 v from a generator. The secondary voltage will be 530 if the secondary coil has 530 turns IS 718.644 V

For an ideal transformer

Vs/Vp=Ns/Np

Given that primary voltage V =80 V

Number of turns in primary N = 59 turns

Number of turns in srcondary Ng = 530 turns

Therefore

Vs/80=530/59

Hence voltage across secondary V = 8.98*80 V

=718.644 V.

Voltage is the quantity of potential charge that exists between two points on a circuit. One idea is charge more strongly than another. Voltage refers to the difference in charge between the two points. Volt, denoted by the symbol "V," is the accepted unit of measurement for the voltage expression.

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Two forces produce the same torque but this will not ensure that they have the same magnitude of torque because torque is the product of force times distance.

T = F * d

where:

T = torque [N*m]

F = force [N]

d = distance [m]

We can see in the above equation, that increasing the distance increases torque proportionally.

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The kinetic energy in the spring is equal to the mechanical work done by the spring

The kinetic energy in then spring is

E = 1 / 2 kA2

The mechanical work done by the spring is,

E= 1 / 2 mv2

Compare the above two equations to find the amplitude of oscillation:

1 / 1 kA2 = 1 / 2 mv2

A = v√ m/k

(3.58 m/s) √ 1.12 kg / 32.3 N/m

= 0.66m

The mechanical work done by the spring is,

E = 1/2 mv2

= 1 / 2 (1.12 kg) (3.58 m/s)2

= 7.17 J

Work modifications the quantity of mechanical and internal energy possessed by gadgets. Whole work is achieved on a machine or item, energy is introduced to it.

The character of work achieved can be categorised in three classes. they are +ve work, -ve work and zero work. The character of work relies upon on the perspective among pressure and displacement.

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If the expansion of the Universe is currently accelerating, can we conclude that the Universe will necessarily expand forever Since little is currently known about the source of the dark energy which is causing the present accelerated expansion of the Universe, it cannot be concluded that it will continue unchanged in the future? Thus, the Universe might, or might not expand forever.

According to the relativistic perspective, although the space around the Earth is contracting, its atoms are resisting this compression. This implies that the Earth's surface is moving higher at a constant rate. On Earth, falling would be the only option to avoid accelerating up. When you are at rest, you fall.

A falling apple, the moon orbiting the earth, and a car stopped at a stop sign are a few instances of acceleration. Through these illustrations, we can see that acceleration happens whenever a moving object changes its direction or speed, or both.

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A circular ring in the x y plane (radius r, centered at the origin) carries a uniform line charge λ. find the first three terms (n) is 2π λ ( 1 - (a/2r)² ( 3cos²0 -1).

Calculation:-

The first three of uniform charge carrying loop is.

V (r,theta) = q/r + 1/2r³ ( Q sin²0 cos²0 + q sin²0 sin²0 + Q cos²0)

= q/r - qa²/4r³ (3 cos²0 -1 )

= 2π λ ( 1 - (a/2r)² ( 3cos²0 -1)

A radius is a line section with one endpoint at the middle of the circle and the other endpoint at the circle. Radius = Diameter of a Circle: A line segment passing through the center of a circle, and having its endpoints at the circle, is referred to as the diameter of the circle. Diameter = 2 × radius.

underneath the Uniform rate techniques, we rate depreciation at the constant belongings which can be uniformly productive on a uniform basis every year. for this reason, the quantity of depreciation stays the same each 12 months.

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The maximum angle due to angular momentum measured from vertical, does the rod (with the attached ball of clay) rotate is 57°.

Given that,

Mass of the rod, [tex]\small M= 80\;g=0.08\; kg[/tex]

Mass of the clay ball, [tex]\small m=11\;g=0.011\;g[/tex]

Length of the rod, \small[tex]L=35\;cm=0.35\;m[/tex]

Initial speed of the ball, [tex]\small v_{i}=2.3\;m/s[/tex]

From law of conservation of angular momentum, Total initial angular momentum of the system = total final angular momentum of the system[tex]\small mv_{i}\frac{L}{2}=\frac{1}{2}(I_{rod}+I_{ball})\omega_{f}\small mv_{i}L=(I_{rod}+I_{ball})\frac{V_{f}}{(L/2)}[/tex].

[tex]\small mv_{i}L=\left (\frac{1}{12}ML^{2}+m\left (\frac{L}{2} \right )^{2} \right )\frac{V_{f}}{(L/2)}[/tex]

Now, From law of conservation of energy, Initial rotational kinetic energy = final potential energy:

[tex]\small \frac{1}{2}(I_{rod}+I_{ball})\left (\frac{V_{f}}{(L/2)} \right )^{2}=m(L/2)g(1-\cos\theta)[/tex]

[tex]\small \frac{1}{2}\left (\frac{1}{12}ML^{2}+m\left (\frac{L}{2} \right )^{2} \right )\left (\frac{V_{f}}{(L/2)} \right )^{2}=m(L/2)g(1-\cos\theta)[/tex]

[tex]\small \left (\frac{1}{12}M+m\left (\frac{1}{2} \right )^{2} \right )\left (\frac{V_{f}}{(1/2)} \right )^{2}=mLg(1-\cos\theta)[/tex]

[tex]\small \therefore \theta=\cos^{-1}\left (0.5496 \right )\small \boldsymbol{\therefore \theta=56.66^{o}}[/tex]

ROUNDING TO 2 SIGNIFICANT FIGURES

[tex]\small \boldsymbol{\therefore \theta=57^{o}}[/tex]

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Finally, Joe turns his attention to the mountain in the distance but finds that he cannot bring the mountain into focus. This is because he is nearsighted. But when Joe puts on his glasses, he can see the mountain clearly. To adjust for his nearsightedness, his glasses must contain less than lenses.

What is Lenses?

Lenses are essentially curved-sided magnifying glasses. A lens is a transparent piece of glass that, when light rays travel through it through refraction, either focuses or disperses them. Lenses are employed in telescopes and other magnifying equipment because of their enlarging capabilities. For the purpose of collecting light, they are used in cameras.

For the purpose of collecting light, cameras utilise a number of lenses rather than just one. The relationship between the size of the image generated by a lens and the size of the object is known as magnification. In order to prevent blurriness or distortion in the picture the lens creates, lenses can also be utilized in groups.

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Itis going to the speed of obstinacy.

speed is the fastest movement of something.

n the question time of flight of blocked ball time off flight of the ball that is represented by capital D This is the time of flight. It is given time of flight, height of time of flight, and hi of both ball, the same or equal, yet. We need to find out how fast production is. We need to find the projection that is represented by you. It was not possible to be on the time of projectile flight. The value of time of flight is equal to the number of years you have left in your life. We'll get equal to 11.1 until 9.81 upon two and two signed 27.4, because he dies at 27.4. Two is 118.31 little per second. obstinacy is the right answer. I think that is Mhm. Correct answer is obstinacy It is necessary to explain this questio.

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The scenario in which there is not the conservation of momentum is when  the objects sticks together. Option C.

We know that momentum is a vector quantity. This implies that momentum would have both magnitude and direction. The fact that momentum has both magnitude and direction implies that we have to consider where the arrow of the velocity direction of the momentum is pointing.

By the law of the conservation of linear momentum, we know that the total momentum of a closed system is a constant. The meaning of this is that the total momentum before collision must be equal to the total momentum after collision.

If the objects do stick together after the collision, there would be a loss of the momentum of the objects thus there is no conservation of momentum in that case.

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The time taken by the truck to get to the required position 5 km away from the fire is 261.55 s.

Tone at which the truck approaches at = 470 hz

Tone at which the truck recedes = 420 hz

Distance = 5.0 Km away

Speed = constant

Speed of sound = v

Speed of air = V

Frequency of sound = f

Frequency when truck approaches = f₁ =

= f₁ = [( V + v) / V ] X f

Frequency when the truck recedes = f₂ =

= f₂ = [( V - v) / V ] X f

Thus, equating both equations =

= f₁ / f₂ = (V + v) / (V - v)

= 470/420 = (340.278 + v) / (340.278 - v )

= [ 470 X 340.278 ] - 470v = [ 420 X 340.278 ] + 420v

= 159930.66 - 470v = 142916.76 + 420v

= 17013.9 = 890v

= v = 19.117 m/s

The time taken = t =

= s = ut + (1/2)at²

= 5 X 10³ = 0 + (19.117 X t)

= t = 261.55 s

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The maximum coefficient of static friction between box and floor such that the person can push horizontally on the box and cause it to start moving is;  μ₂ = 4.2

A force that keeps an object at rest is called static friction. It is the friction experienced when we try to move a stationary object on a surface without actually triggering any relative motion between the body and  surface.

To move the box, force exerted by the person on the box must equal the force exerted by the box

F₁= F₂

m₁*g*μ₁ = m₂*g*μ₂

Given; m₁ = 600kg ; m₂= 100kg;  μ₁= 0.7

600 * 0.7 = 100 * μ₂

μ₂ = 4.2

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