A tennis ball is thrown upward from the top of a 680 foot high building at a speed of 56 feet per second. The tennis ball's height above ground can be modeled by the equation . When does the tennis ball hit the ground?

Answer:

(a) h = 500 - 4.9t²

(b) 98.99 m/s

(c) h = 500 - Vot - 4.9t²

    14.14 m/s

Explanation:

(a) You can use the equation of linear motion s = vi.t + 0.5gt²

(b) [tex]v_{f} ^{2} = v_{i} ^{2} +2ax\\v = \sqrt{0^{2} + 2*9.8*500 } = 98.99 m/s[/tex]

(c) [tex]v_{f} ^{2} = v_{i} ^{2} + 2ax\\v_{i} = \sqrt{100^{2} -2*9.8*500}=14.14 m/s[/tex]

The initial velocity mucg be greater than 14.14 m/s to break the cannister

Answer:

Explanation:

This generator is called Vande Graff generator.

It collects the charge from the belts and accumulate on a large sphere.

It is used to accelerate the charge particles and based on the principle of corona discharge and charge resides on the outer surface.

Answer:

fumaroles or smokers

Explanation:

Fumaroles: they are gaseous emissions from lavas in craters at more or less elevated temperatures. Its composition varies according to the temperature of the lavas, in such a way that it changes since the fumaroles appear until their extinction.

Water flows in the form of steam continuously through the cracks of a volcano or volcanic surface because its temperature exceeds 100 °C.

Groups of fumaroles

- Dry fumaroles: They are those that come off the melting lava, in the vicinity of the crater. Its temperature is higher than 500oC. They are mainly composed of sodium, potassium and sulfur dioxide and carbon dioxide.

- Acid fumaroles: with temperatures between 300oC and 400oC, they are constituted by a large amount of water vapor, with hydrochloric acid and sulphurous anhydride.

- Alkaline fumaroles: Temperature close to 100oC, contain water vapor with hydrogen sulfide and ammonium chloride.

Answer:

ρ = 1061 kg/m³

Explanation:

The pressure at the top pf the box is clearly different from the pressure at the bottom of of the  box due to the depth. So the problem can be solve the following way:

Difference in pressure =  density * acceleration due to gravity * height

ΔP = ρgΔh

112 000 Pa - 109 400 Pa = ρ * 9.8 m/s² * 0.25 m

                                     ρ = 1061 kg/m³

The density of the fluid can be calculated using the formula P=hρg, where P is the pressure, h is the height or depth, ρ is the density, and g is the acceleration due to gravity. The pressure difference is due to the fluid itself and can be used to find the density when the height and acceleration due to gravity are given.

The student's question is about finding the density of a fluid given the pressure at the top and bottom of the cube. The key to finding this is using the formula that relates pressure, depth, and density in a fluid, which is P=hρg where P is the pressure, h is the height or depth, ρ is the density, and g is the acceleration due to gravity.

Given that the difference in pressure between the bottom and top of the cube is 112.00 kPa - 109.40 kPa = 2.60 kPa, this represents the change in hydrostatic pressure due to the fluid itself. Now, convert this pressure difference from kPa to Pa (since 1 kPa = 1000 Pa), we get 2.60 kPa * 1000 = 2600 Pa.

The height of the cube is given as 25.0 cm which needs to be converted to meters (since 1m = 100 cm), giving us a height of 0.25 m. We can calculate the density of the fluid using the rearranged formula ρ = P/gh. Substituting known values: ρ = 2600 Pa / (9.81 m/s² * 0.25 m). The answer will then give us the density of the fluid.

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Answer:

592.92 x 10³ Pa

Explanation:

Mole of ammonia required = 10 g / 17 =0 .588 moles

We shall have to find pressure of .588 moles of ammonia at 30 degree having volume of 2.5 x 10⁻³ m³. We can calculate it as follows .

From the relation

PV = nRT

P x 2.5 x 10⁻³ =  .588 x 8.32 x ( 273 + 30 )

P = 592.92 x 10³ Pa

Answer: c is true

Explanation: the boy choirstars sang the soprano and alto. Although Palestrina choir is made up of six voice part of soprano, alto, tenor, baritone and bass and the choir sings without instruments.

In the case of Giovanni Pierluigi da Palestrina’s Pope Marcellus Mass, the correct statement is that all the parts were originally sung by men and boys. It was not written in Italian, does not represent Protestant music tactics and was not banned by the Council of Trent.

Out of the provided options, the statement that is true of Giovanni Pierluigi da Palestrina’s Pope Marcellus Mass is that all the parts were originally sung by men and boys (option c). The work is a significant one in the history of polyphonic choral music and it marked a departure from the complex style of the early Renaissance period. Instead of Italian, the mass is actually written in Latin, which was the language conventionally used in the liturgy of the Catholic Church (thus discrediting option b). Unlike Protestant music of the time (which negates option a), it does not emphasize congregational singing but instead focuses on the choir. It was also never banned by the Council of Trent. (disproving option d)

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Answer:

speed 2.997 10⁸, 2,254 10⁸, 1,999 10⁸ m / s

[tex]\lambda_{n}[/tex]  727.7, 547, 485 nm

Explanation:

The index of refraction is defined as the relationship between the speed of light in a vacuum and in a material medium

      n = c / v

Let's calculate the speed of light in the media

Air

The refractive index is very close to that of the vacuum n = 1,00029

In most experiments they are considered equal

     v = c/ n

     v = 2,998 10⁸ / 1,00029

     v = 2,997 10⁸ m / s

Water

n = 1.33

     v = 2.998 10⁸ / 1.33

     v = 2,254 10⁸ m / s

Glass

n = 1.50

     v = 2,998 10⁸ / 1,50

     v = 1,999 10⁸ m / s

Frequency and wavelength are related by the equation

      c = λ f

When a beam with a given frequency hits excites the electrons of the material and induces forced oscillations, which has the same frequency of the incident, so the frequency of the beam does not change when passing from one medium to the other.

As speed changes the only way that equality is maintained is that the wavelength changes

      [tex]\lambda_{n}[/tex] = λ₀ / n

Air

      [tex]\lambda_{n}[/tex] =727.7 nm

Water

       [tex]\lambda_{n}[/tex] = 727.7 / 1.33  

      [tex]\lambda_{n}[/tex] = 547.14 nm

Glass

     [tex]\lambda_{n}[/tex] = 727.7 / 1.50

    [tex]\lambda_{n}[/tex] = 485.13 nm

Answer:(1) Pre-solar nebula

(2). Planet formation

Explanation:

Nebular hypothesis says that the Solar System formed from the gravitational collapse of a fragment of a giant molecular cloud.

One of the collapsing fragments called the pre-solar nebula formed what became the Solar System.

The planet can also be formed by accretion. Accretion is a process in which planets began as dust grains in orbit around the central protostar.

When the terrestrial planets were forming, they remained immersed in a disk of gas and dust.

Answer:

Part a)

[tex]V' = 7.77 Volts[/tex]

Part b)

[tex]k' = 6.27 [/tex]

Explanation:

As we know that capacitor plate is connected across 2.1 V and after charging it is disconnected from the battery

So here we can say that charge on the plates will remain conserved

So we will have

[tex]Q = kC(2.1)[/tex]

now dielectric is removed between the plates of capacitor

so new potential difference between the plates

[tex]V' = \frac{Q}{C'}[/tex]

[tex]V' = \frac{kC(2.1)}{C}[/tex]

[tex]V' = 3.7 \times 2.1 [/tex]

[tex]V' = 7.77 Volts[/tex]

Part b)

Now the capacitor plates are again isolated and unknown dielectric is inserted between the plates

So again charge is same so potential difference is given as

[tex]V" = \frac{Q}{k'C}[/tex]

[tex]0.59 V = \frac{kCV}{k'C}[/tex]

[tex]0.59 = \frac{3.7}{k'}[/tex]

[tex]k' = 6.27 [/tex]

Final answer:

The resulting potential difference of the capacitor after the paper is withdrawn is 7.77V. The dielectric constant of the unknown substance, where the potential decreased to 0.59 times the original, is approximately 6.27.

Explanation:

The potential difference across a capacitor is inversely proportional to the dielectric constant of the material between the plates. When a paper dielectric with a constant of 3.7 is removed from a charged capacitor, the potential difference increases because the dielectric constant of air is nearly 1.

Find the resulting potential difference of the capacitor

The initial potential difference (V1) with paper is 2.1V, and the dielectric constant for paper (k1) is 3.7. When the paper is removed, the dielectric constant becomes that of air, which is approximately 1 (k2). For an isolated capacitor, the charge (Q) remains constant, so we can use the relation that the product of the potential difference (V) and the dielectric constant (κ) is a constant (Q=CV and C=κC0). Therefore, V1k1 = V2k2. By substituting the known values: 2.1V * 3.7 = V2 * 1, we find that V2 = 2.1V * 3.7 = 7.77V.

Find the dielectric constant of the inserted unknown substance

If the potential difference with the new substance is 0.59 times the initial potential (when paper filled the capacitor), then V3 = 0.59 * 2.1V. The dielectric constant of the new substance (k3) can be found using the same principle where V1k1 = V3k3. With V3 = 0.59 * 2.1 = 1.239V, we get 2.1V * 3.7 = 1.239V * k3, leading to k3 = (2.1V * 3.7) / 1.239V ≈ 6.27.

Answer:34 cm

Explanation:

Given

mass of meter stick m=80 gm

stick is balanced when support is placed at 51 cm mark

Let us take 5 gm tack is placed at x cm on meter stick so that balancing occurs at x=50 cm mark

balancing torque

[tex]80\times 10^{-3}(51-50)=5\times 10^{-3}(50-x)[/tex]

[tex]80=5(50-x)[/tex]

[tex]80=250-5x[/tex]

[tex]5x=170[/tex]

[tex]x=\frac{170}{5}[/tex]

[tex]x=34 cm[/tex]

To balance the nonuniform meterstick, the 5.00-g tack should be placed at approximately 50.4 cm from the pivot point.

To find the location on the meterstick where the 5.00-g tack should be placed so that the stick will balance at the 50.0 cm mark, we can use the principle of torque balance.

The torque balance equation is given by:

Torque(counter-clockwise) = Torque(clockwise).

In this case, the torque is equal to the force multiplied by the distance from the pivot point. The force exerted by the 5.00-g tack can be calculated using the formula:

Force = mass * acceleration due to gravity.

By substituting the known values into the equation and solving for the distance, we can determine where the tack should be placed on the meterstick.

In this case, the tack should be placed at approximately 50.4 cm from the pivot point.

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The maximum possible emf induced in the antenna due to the motion of the automobile can be calculated using Faraday's law of electromagnetic induction. Plugging in the given values, the maximum possible emf is calculated as 2.4 x 10^-8 V.

The maximum possible emf induced in the antenna due to the motion of the automobile can be calculated using Faraday's law of electromagnetic induction. The equation for calculating the emf is given by μoθlvB, where μo is the permeability of free space, l is the length of the antenna, v is the velocity of the automobile, and B is the magnetic field strength. Plugging in the given values, we have:

μo = 4π x 10^-7 Tm/A

l = 1.0 m

v = 100.0 km/h = 27.78 m/s

B = 5.5 x 10^-5 T

Using these values, we can calculate the maximum possible emf induced in the antenna as:

emf = (μoθlvB) = (4π x 10^-7 Tm/A)(1.0 m)(27.78 m/s)(5.5 x 10^-5 T) = 2.4 x 10^-8 V

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The maximum possible emf induced in the 1.0 m long antenna moving at 100.0 km/h in a 5.5×10⁻⁵ T magnetic field is approximately 1.53 mV. The calculation involves using the motional emf formula: emf = vBL. Converting the velocity to meters per second and plugging in the values gives the result.

Motional EMF Calculation

The question is about finding the electromotive force (emf) induced in a radio antenna moving through the Earth's magnetic field. This situation involves motional emf, which can be determined using the formula:

emf = vBL

where:

Now, substituting these values into the formula:

emf = 27.78 m/s × 5.5 × 10⁻⁵ T × 1.0 m

emf ≈ 1.53 × 10⁻³ V

Therefore, the maximum possible induced emf in the antenna due to its motion is approximately 1.53 mV.

Answer:

The velocity as a fraction of c is 0.986 c m/s

Solution:

As per the question:

Time measured by the astronaut, t = 15 yrs

Time measured in the frame of mission control, t' = 130 yrs

Now,

Using the formula of time dilation:

[tex]t' = \frac{t}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}[/tex]

Substituting appropriate values in the above eqn:

[tex]130 = \frac{15}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}[/tex]

[tex]\sqrt{1 - \frac{v^{2}}{c^{2}}}= \frac{15}{130}[/tex]

Squaring both the sides we get:

[tex]1 - \frac{v^{2}}{c^{2}}= (\frac{15}{130})^{2}[/tex]

[tex]\frac{v^{2}}{c^{2}} = 1 - (\frac{15}{130})^{2}[/tex]

v = 0.986 c m/s

The rocket must travel at about 99.45% of the speed of light for the astronauts aboard to age 15 years while those on Earth age 130 years, according to the theory of special relativity and the phenomenon called time dilation.

The question asks about the speed a rocket needs to travel as a fraction of the speed of light (c) for the astronaut aboard to age 15 years while those back on Earth age 130 years - an application of time dilation in special relativity. The solution to this is in the theory of relativity proposed by Albert Einstein, which states that time passes at different speeds for people depending on their relative motion.

The time dilation formula is given by Δt = γΔτ, where Δτ is the 'proper time' experienced by the moving astronaut, Δt is the time experienced by the stationary observers on Earth, and γ is the Lorentz factor, defined as γ = 1 / sqrt(1 - (v^2/c^2)).

Here, Δt is 130 years, Δτ is 15 years, and we are asked to solve for v/c. Plugging in the given values and solving for v/c, we find that v/c = sqrt(1 - (15/130)^2), approximately equals to 0.9945 or 99.45% of the speed of light. Therefore, the rocket must travel at about 99.45% of the speed of light for the astronaut to age 15 years while those on Earth age 130 years.

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Answer:

a) rotate counterclockwise as viewed from above.

Explanation:

The text tells us it is spinning counterclockwise.

Answer:

C. undulating displacement of air molecules caused by pressure changes.

Explanation:

Sound is a mechanical wave arising from the movement back and forth of the media objects through which the sound wave travels.If a sound wave moves through air from left to right, then particles of air will move both to the right and to the left as the sound wave's energy passes through it.

The sound wave is formed by air molecules that are displaced due to pressure changes.

Therefore the answer is C.

Sound waves are caused by the undulating displacement of air molecules due to pressure changes. Hence, option(c) is correct.

1. When an object like a speaker cone vibrates, it alternately compresses and expands the air around it.

2. The regions where air molecules are pushed together are called compressions, and the regions where they are spread apart are called rarefactions.

3. Sound waves travel through the air as longitudinal waves, consisting of alternating high-pressure (compression) and low-pressure (rarefaction) regions.

4. These pressure changes propagate at a speed of approximately 340 m/s in air, creating the disturbance known as a sound wave.

Answer:

T = 812.8414 N

Explanation:

Using the law of newton we found the vertical(y) and horizontal(x) forces as:

∑[tex]F_x[/tex] = T - [tex]F_k[/tex] = ma

Where T is the tension, [tex]F_k[/tex] is the friction force, m is the mass of the stuntman and a is the aceleration of the stuntman.

but a is equal to 0 because he is moving at a constant velocity, so:

T - [tex]F_k[/tex] = 0

T = [tex]F_k[/tex]

Also,

[tex]F_k[/tex] = [tex]U_kN[/tex]

where [tex]U_k[/tex] is the coefficient of kinetic friction and N is the normal force.

For find N we use:

∑[tex]F_y =[/tex] N - mg = 0

N = mg

N = (119)(9.8)

N = 1166.2

Finally we solve for T as:

T = [tex]U_kN[/tex]

T = (0.697)(1166.2)

T = 812.8414 N

Answer:

Impulse, J = 250.4 kgm/s,  Avg Force F=3091.4 N

Explanation:

Since we know that impulse is the change in momentum i.e. Δp and   Δp[tex]=mv[/tex], therefore, to calculate the velocity we perform:

As the person has fallen by a 0.50m height, its potential energy changes into kinetic energy, therefore,

K.E.=P.E.

[tex]\frac{1}2}mv^{2}[/tex]=[tex]mgh[/tex]

[tex]v=\sqrt{2gh}[/tex]

[tex]v=\sqrt{2*9.8*0.50}[/tex]

[tex]v=3.13ms^{-1}[/tex]

(a) Impulse [tex]J[/tex] = Δp[tex]=mv[/tex]

[tex]J= 80*3.13[/tex]

[tex]J = 250.4 kgms^{-1}[/tex]

(b)  Avg Force F = Δp/Δt

[tex]F=\frac{250.4}{0.081}[/tex]

[tex]F=3091.4[/tex] N

After defining variables and initial conditions, analyzing the block's motion before collision, and applying the conservation of momentum principle, we found that the block had been falling for approximately 0.198 seconds before colliding with the bullet.

1. Defining Variables and Initial Conditions:

m: Mass of the bullet (0.026 kg)

v_b: Velocity of the bullet before collision (750 m/s)

M: Mass of the block (5 kg)

v_f: Final velocity of the block before collision (unknown)

t: Time the block falls before collision (unknown)

V: Final velocity of the combined bullet-block system after collision (unknown)

2. Analyzing Block's Motion before Collision:

The block is initially dropped from rest, so its initial velocity (v_o) is 0 m/s.

The block experiences acceleration due to gravity (g) in the downward direction, represented by a negative sign (-g).

We want to find the final velocity (v_f) of the block just before the collision using the kinematic equation:

v_f = v_o + at

Since v_o = 0 and a = -g, we get:

v_f = -gt

3. Applying Conservation of Momentum:

During the collision, momentum is conserved, meaning the total momentum before the collision equals the total momentum after.

Before the collision, the momentum is the sum of the bullet's momentum (mv_b) and the block's momentum (Mv_f).

After the collision, the combined bullet-block system moves together with a final velocity (V).

We can express the conservation of momentum equation as:

mv_b + Mv_f = (m + M)V

4. Solving for Time (t):

Substitute the expressions for v_f and V from previous steps:

(0.026)(750) + (5)(-gt) = (0.026 + 5)(gt)

Simplify and solve for t:

19.5 - 49t = 49.2548t

98.7548t = 19.5

t = 0.198 seconds

Therefore, the block had been falling for 0.198 seconds before the collision with the bullet.

Answer:

λ=589nm

Explanation:

The wavelength of the sodium light can be calculated using the next equation:

[tex] \lambda = \frac{\Lambda D}{L} [/tex]  

where Λ: is the distance between the adjacent bright regions, λ: is the wavelength of the sodium light, L: is the distance between slits and screen, and D: is the distance between slits.  

[tex] \lambda = \frac{7.32mm \cdot 0.12mm}{1490mm} = 5.89\cdot 10^{-4}mm = 589nm [/tex]

Therefore, the λ of the sodium light is 589 nm.  

I hope it helps you!

Answer:

Option (e).

Explanation:

The Compton's equation is:

[tex] \lambda^{'} = \frac{h}{m_{e} c} \cdot (1 - Cos(\theta)) + \lambda = \lambda_{c} (1 - Cos(\theta)) + \lambda [/tex] (1)

where λ': is the wavelength scattered, λ: is the initial wavelength, h: is Planck's  constant, [tex] m_{e} [/tex]: is the electron rest mass, c: speed of light, Θ: scattering angle (between λ and λ'), and [tex] \lambda_{c} [/tex]: is a constant known as the Compton wavelength of the electron = 0.00243 nm.          

From equation (1), the scattered radiation is directly proportional to the scattering angle, having the maximum value when Θ=90°:

[tex] \theta = 90 ^{ \circ} \rightarrow \lambda^{'} = \lambda_{c} (1-Cos(90)) + \lambda = \lambda_{c} + \lambda [/tex]

And the minimum value when Θ=0°:

[tex] \theta = 0 ^{ \circ} \rightarrow \lambda^{'} = \lambda_{c} (1-Cos(0)) + \lambda = \lambda [/tex]

Hence, the options (a) and (b) are incorrect.

Similarly, we can see from equation (1) that the scattered radiation depends also on the wavelength of the primary beam and no wavelength other than that (since [tex] \lambda_{c} [/tex] is a constant), so the correct option is (e).  

Have a nice day!

Answer:

Explanation:

Given

Mechanical Energy of Spring-Block system is 1 J

Maximum Amplitude is [tex]A=10 cm[/tex]

maximum speed [tex]v_{max}=1.2 m/s[/tex]

Suppose [tex]x=A\sin \omega t [/tex]be general equation of motion of spring-mass system

where A=max amplitude

[tex]\omega [/tex]=Natural frequency of oscillation

t=time

[tex]v_{max}=A\omega =1.2[/tex]

[tex]0.1\cdot \omega =1.2[/tex]

[tex]\omega =12 rad/s[/tex]

maximum kinetic Energy must be equal to total Mechanical Energy when spring is un deformed i.e. at starting Position

[tex]\frac{1}{2}mv_{max}^2=1[/tex]

[tex]m=\frac{2}{1.2^2}=\frac{2}{1.44}=1.38 kg[/tex]

Also [tex]\omega [/tex]is also given by

[tex]\omega =\sqrt{\frac{k}{m}}[/tex]

[tex]k=\omega ^2\cdot m[/tex]

where k= spring constant

[tex]k=12^2\cdot 1.38 [/tex]

[tex]k=200 N/m[/tex]

Answer:

0.0971

Explanation:

we know that

[tex]f max = kn[/tex]

that fmax is maximum of static friction , k is coefficient of friction and n is surface reaction force

so we know that from newtons second law

mg=n

so

kmg = 102

k = 102/mg = 102/(10*105) = 0.0971

Final answer:

The coefficient of static friction (μs) between the sofa and carpet is calculated by dividing the force required to start the sofa moving by the normal force, yielding μs = 102 N / 1050 N.

Explanation:

The coefficient of static friction μs is the ratio of the force of static friction Fs to the normal force N. It can be calculated using the equation μs = Fs / N, where Fs is the force required to start moving the object and N is the weight of the object acting perpendicular to the surface. Here, the normal force is equivalent to the weight of the sofa, which is the mass of the sofa multiplied by the acceleration due to gravity (g). With a mass of 105 kg and g approximated as -10 m/s2, the normal force is N = 105 kg × 10 m/s2 = 1050 N. The provided force to start the sofa moving is 102 N, so the coefficient of static friction is μs = 102 N / 1050 N.

Answer:

5 N

Explanation:

The bucket is moving at a constant speed of 2m/s Therefore F=ma is 0 N for this to be correct the magnitude of the force exerted by the rope must be equal to the weight of the bucket which is 5 N

Answer:

Magnitude of force on the rope=5N

Explanation:

The bucket is lowered by a constant speed,therefore the tension on the rope must be equal to the weight of the bucket.

Answer:

v₂ = 7.6 x 10⁴ m/s

Explanation:

given,

speed of comet(v₁) = 1.6 x 10⁴ m/s

distance (d₁)= 2.7 x 10¹¹ m

to find the speed when he is at distance of(d₂) 4.8 × 10¹⁰ m

v₂ = ?

speed of planet can be determine using conservation of energy

K.E₁ + P.E₁ = K.E₂ + P.E₂

[tex]\dfrac{1}{2}mv_1^2-\dfrac{GMm}{r_1} = \dfrac{1}{2}mv_2^2-\dfrac{GMm}{r_2}[/tex]

[tex]\dfrac{1}{2}v_1^2-\dfrac{GM}{r_1} = \dfrac{1}{2}v_2^2-\dfrac{GM}{r_2}[/tex]

[tex]v_2^2= v_1^2 + \dfrac{2GM}{r_2}-\dfrac{2GM}{r_1}[/tex]

[tex]v_2= \sqrt{v_1^2 +2GM(\dfrac{1}{r_2}-\dfrac{1}{r_1})}[/tex]

[tex]v_2= \sqrt{(1.6\times 10^4)^2 +2\times 6.67 \times 10^{-11}\times 1.99 \times 10^{30}(\dfrac{1}{4.8\times 10^{10}}-\dfrac{1}{2.7\times 10^{11}})}[/tex]

v₂ = 7.6 x 10⁴ m/s

The speed when at a distance of [tex]4.8*10^{10} m[/tex] is mathematically given as

vf = 6.92 * 10^(4) m/s

Generally, the equation for the conservation of energy is mathematically given as

E = (1/2)mv^2 - GmM/r

Where

E_i = E_f

Hence

(1/2)mv_i^2 - [tex]\frac{GmM}{(r_i)}[/tex] = (1/2)mv_f^2 - [tex]\frac{GmM}{(r_f)}[/tex]

[tex]v_f = \sqrt{[(v_i)^2 + 2MG((1/r_f) - (1/r_i))]}[/tex]

Therefore

[tex]v_f = \sqrt{(2.1*10^4)^2 + 2(1.9891 * 10^{31})*(6.67 * 10^{-11})(\frac{1}{4.9} * 10^{10}) - (\frac{1}{2.5} * 10^{11}))} *20.408 *10^{12}[/tex]

[tex]v_f = \sqrt{(441000000) + 435.38 * 10^{7}}[/tex]

vf = 6.92 * 10^(4) m/s

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When a region of rarefaction from one sound wave overlaps with a similar region in another wave, they cause constructive interference. The result is an increased amplitude, which makes the sound louder.

When a region of rarefaction of one sound wave overlaps with a region of rarefaction in another sound wave, it results in constructive interference. This is because both the waves are essentially 'in sync', and they amplify each other. The amplitude of the resulting wave increases, and in terms of sound, this means that the sound becomes louder, because amplitude is directly related to the volume or loudness of the sound. Hence, the correct answer is: Constructive interference; the sound becomes louder because the amplitude increases.

For instance, if you're playing two sounds of the same frequency and amplitude together, and their waves align such that their areas of rarefaction meet, the combined sound would be louder than the individual sounds. This is a direct application of the physics concept of wave interference.

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Answer:

The free end must be attached at a distance of 27.5 cm

Solution:

Mass, m = 141 kg

Length of the rods, L= 55 cm

Now,

As clear from fig. 1:

The free end of the rod 2 must be attached at:

F = 2 W

[tex]WL = W(55 - L)[/tex]

2L = 55

L = 27.5 cm

Final answer:

The question is about the angles of maxima and minima in a double-slit interference pattern for two identical loudspeakers placed 1.00 m apart.

Explanation:

The distance between two identical loudspeakers placed 1.00 m apart is given as 'd'.

In the given situation, the listener stands 4.00 m from the wall directly in front of one of the speakers. This distance can be considered as 'L'.

The formula to calculate the distance between adjacent maxima and minima in a double-slit interference pattern is:

d*sin(theta) = m*lambda

- Where 'd' is the distance between the speakers
- 'theta' is the angle at which the maxima or minima occur
- 'm' is the order of the maxima or minima
- 'lambda' is the wavelength of the sound

Applying this formula, we can calculate the angles at which the maxima and minima occur for the given situation.

The phase difference between the waves reaching the observer is approximately 0.66 radians. The frequency closest to 300 Hz for minimal sound due to destructive interference is approximately 286 Hz.

To solve the problem, we need to find the phase difference and the frequency closest to 300 Hz for minimal sound.

a.) The speed of sound, v, is typically about 343 m/s in air. Using the formula for wavelength, λ = v/f, we get:

For the listener standing 4.00 m from one speaker and 4.12 m from the second speaker, the difference in the path length, ΔL, is:

The phase difference, φ, is given by:

b.) For destructive interference, the path difference should be half-integer multiples of the wavelength:

Simplifying, we find the frequency:

Solving for f when n = 0 (closest to 300 Hz):

Thus, the frequency closest to 300 Hz for minimal sound is approximately 286 Hz.

complete question:

Two identical loudspeakers are placed on a wall 1.00 m apart. A listener stands 4.00 m from the wall directly in front of one of the speakers. A single oscillator is driving the speakers at a frequency of 300 Hz.

(a) What is the phase difference in radians between the waves from the speakers when they reach the observer? (Your answer should be between 0 and 2?.)

rad

(b) What is the frequency closest to 300 Hz to which the oscillator may be adjusted such that the observer hears minimal sound?in Hz

Answer:

See attachment

Explanation:

Answer:

vf = 12.51 m/s

Explanation:

Newton's second law to the grocery cart:

∑F = m*a Formula (1)

∑F : algebraic sum of the forces in Newton (N)

m : mass s (kg)

a : acceleration  (m/s²)

We define the x-axis in the direction parallel to the movement of the grocery cart  and the y-axis in the direction perpendicular to it.

Forces acting on the grocery cart

W: Weight of the block : In vertical direction  downward

N : Normal force : In vertical direction  upward

F : horizontal force

Calculated of the mas of the grocery cart (m)

W = m*g

m = W/g

W = 94.0 N  , g = 9.81 m/s²

m = 94/9.81

m = 9.58 Kg

Calculated of the acceleration of the grocery cart (a)

∑F = m*a

F = m*a

42.6 = (9.58)*a

a = (42.6) / (9.58)

a = 4.45 m/s²

Kinematics Equation of the grocery cart

Because the grocery cart moves with uniformly accelerated movement we apply the following formula to calculate its final speed :

vf²=v₀²+2*a*d Formula (2)

Where:  

d:displacement  (m)

v₀: initial speed  (m/s)

vf: final speed   (m/s)

a: acceleration (m/s²)

Data:

v₀ = 0

a = 4.45 m/s²

d = 17.6 m

We replace data in the formula (2) :

vf²=v₀²+2*a*d

vf² = 0+2*(4.45)*(17.6)

vf² = 156.64

[tex]v_{f} = \sqrt{156.64}[/tex]

vf = 12.51 m/s

Info:

weight: 96.1 kg

Length: 6 m

moved: 3.66 m

Answer:

m L = m d + M d

m L − m d = M d

m (L − x) = M x

M = m (L − x) / x

M = 96.1 kg (6 m − 3.66 m) / 3.66 m

M =  61.44098361 kg

The boats mass.

A 96.1 kg of man sits on a stem of a 6-meter longboat. The boat ouches the pier and but is not tied. The man notices a mistake and walks to the prow of the boat he moves a distance of 3.66 meters away from the pier. Thus assuming the given information the bot offers no resistance.

The mass of the boat will be equal to 61.4 kg.

Learn more about the man sits on the stern.

brainly.com/question/14519050.

Answer:

upper motor neurons in the premotor cortex

Explanation:

Motor neurons are a type of nervous system cells that are located in the brain  and in the spinal cord. They have the function of producing the stimuli that cause the contraction of the different muscle groups of the organism. They are therefore essential for daily activities that require muscle contraction: walking, talking, moving hands and in general all body movements.