A 3.0 kg ball moving at 8 m/s to the right collides with a 1.0 kilogram ball at rest. After the collision, the 3
kg ball moves at 5 m/s to the right. What is the velocity of the 1 kilogram ball?

Answers

Answer 1

Let m₁ = 3.0 kg and v₁ = + 8 m/s (so right is positive), and m₂ = 1.0 kg and v₂ = 0. The total momentum of the two balls before and after collision is conserved, so

m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'

where v₁' = + 5 m/s and v₂' are the velocities of the two balls after colliding, so

(3.0 kg) (8 m/s) = (3.0 kg) (5 m/s) + (1.0 kg) v₂'

Solve for v₂' :

24 kg•m/s = 15 kg•m/s + (1.0 kg) v₂'

(1.0 kg) v₂' = 9 kg•m/s

v₂' = (9 kg•m/s) / (1.0 kg)

v₂' = + 9 m/s

which is to say, the second ball is given a speed of 9 m/s to the right after colliding with the first ball.


Related Questions

Gravity Rocks!
Three friends were talking about gravity. One friend
held up a rock and asked his friends whether the gravi-
tational force on the rock depended on where the rock
was located. Each friend had a different idea about a
place where the gravitational force on the rock would
be the greatest. This is what they said:
Lorenzo: "I think if you put the rock on the top of a very tall mountain, the gravita-
tional force on the rock will be greatest."
Eliza: "I think the gravitational force will be greatest when the rock is resting on
the ground near sea level."
Flo: "I think you have to go really high up. If you drop the rock out of a high-
flying plane, the gravitational force will be greatest."
Explain why you agree with
Which friend do you most agree with?
that friend.

Answers

Answer:

Eliza’s suggestion is the most promising

Explanation:

Newton’s law of universal gravitation is \(F = G\frac{m_1m_2}{r^2}\) where G is a constant and both masses are constant in this experiment as well. So it only depends on r, the distance between the center of mass of both objects.

Bringing it high in the sky, as Flo suggests, is definitely not a good idea because it only increases the distance from the center of the Earth mass.

A mountain contains significant mass, so the center of the Earth mass is somewhat shifted to regions with the largest mountains. However, standing on top of a mountain, as Lorenzo suggests, doesn’t help since the shift of the center of mass, if any, is far smaller than the height of the mountain.

Standing near sea level, as Eliza suggests, is a good way to minimize the distance to the center of the Earth mass.

group of students is making model cars that will be propelled by model rocket engines. These engines provide a nearly constant thrust force. The cars are light—most of the weight comes from the rocket engine—and friction and drag are very small. As the engine fires, it uses fuel, so it is much lighter at the end of the run than at the start. A student ignites the engine in a car, and the car accelerates. As the fuel burns and the car continues to speed up, the magnitude of the acceleration will

Answers

Answer:

increase.

Explanation:

According to the newton’s second law of motion force is expressed as product of mass and acceleration.

F = m a

If the force acting is constant, then.

m∝ \(\frac{1}{a}\)

That is if the mass of object increases the acceleration decreases and vice versa. The above equation is used when the force acting on the body is constant.

As the thrust force from the rocket engine is constant throughout there will be a variation in the mass or acceleration.

Thus, it won't stay the same.

As the weight of the car is maximum at the start because of the fuel present in the rocket engine and minimum at the end as the fuel burns throughout the journey of the car. Weight will be minimum at the end and hence acceleration is maximum at the end.

Thus, it won't decrease.

As the acceleration is going from minimum at the start to maximum at the end, therefore it is continuously increases throughout its journey.

Thus, it will increase.  

An astronaut and equipment has a total mass of 182.8 kg. While initially at rest inspace, the astronaut fires a 144.4 newton rocket for 1.190 seconds. What is theaverage speed of the astronaut (in km/h)?

Answers

Given data:

* The total mass of an astronaut and equipment is,

\(m=182.8\text{ kg}\)

* The force is given as,

\(F=144.4\text{ N}\)

* The time taken is,

\(t=1.19\text{ s}\)

Solution:

According to the Newton's second law,

\(F=ma\)

where a is the acceleration of the body,

Substituting the known values,

\(\begin{gathered} 144.4=182.8\times a \\ a=\frac{144.4}{182.8} \\ a=0.7899ms^{-2} \end{gathered}\)

By the kinematic equations,

\(v-u=at\)

where u is the initial velocity and v is the final velocity,

Substituting the known values,

\(\begin{gathered} v-0=0.7899\times1.19 \\ v=0.94ms^{-1} \end{gathered}\)

The average speed of the astronaut is,

\(\begin{gathered} s_{average}=\frac{v+u}{2} \\ =\frac{0.94+0}{2} \\ =0.47ms^{-1} \end{gathered}\)

The average speed of the astronaut in Km/h is,

\(\begin{gathered} s_{average}=0.47\times\frac{10^{-3}^{}^{}}{\frac{1}{60\times60}} \\ s_{average}=0.47\times60\times60\times10^{-3} \\ s_{average}=1.692kmh^{-1} \end{gathered}\)

Thus, the average speed of the astronaut is 1.692 km/h.

when the direction of acceleration is opposite to the direction of velocity

Answers

Answer:

If acceleration points in the same direction as the velocity, the object will be speeding up. And if the acceleration points in the opposite direction of the velocity, the object will be slowing down.

In the study of personality, what model includes different traits that underlie one’s basic tendencies

Answers

In the study of personality, the Five-factor model includes different traits that underlie one’s basic tendencies.

What is the Five-factor model?

The Five-factor model is a scientific theory that states traits of the personality of an individual are due to its biology and therefore they respond to adaptations, which are central in the biology field.

In conclusion, in the study of personality, the Five-factor model includes different traits that underlie one’s basic tendencies.

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you choose a bowling ball with a smaller mass because you can roll it down the lane

which law is this?

(newtons laws 1,2 and 3)

Answers

Answer:

based on my research i found that it was newtons law # 1

Explanation:

Answer: newton's 2nd law revolves around mass {credits to Britannica} A lesson proving immovable objects and unstoppable forces are one and the same. Newton's second law is a quantitative description of the changes that a force can produce on the motion of a body.

a stationary object experiences two forces as shown in the diagram below

a stationary object experiences two forces as shown in the diagram below

Answers

Answer: the answer is B

Explanation: 80 is not the same as 150 so it will go the way 150 units of force is pulling.

I chose A. is it right?


If a particular cell is known to be round and incapable of producing its own food, which one of these organelles would you assume the cell must have?(1 point)


CENTRAL VACUOL

plasma membrane

cell wall

chloroplast

Answers

Answer:

nice try but it's plasma membrane

The cell that is known to produce their own food should have a central vacuole. The correct option is A.

What is a vacuole?

A vacuole is a cell organelle that is membrane-bound. Vacuoles are generally small in animal cells and help to sequester waste products.

Vacuoles in plant cells help to retain water balance. A solo vacuole can sometimes take up the maximum of the interior space of a plant cell.

Plant cells have much larger vacuoles than animal cells. When a plant cell stops growing, it usually has one very large vacuole.

That vacuole can sometimes take up more than half of the cell's volume. The vacuole can hold a lot of water or food.

The given cell is known to be round and incapable of producing its own food, so it must be having a central vacuole.

The correct option is A.

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lol
idk what this is​

Answers

Answer:

I know

Explanation:

Physics= hard

lol‍♀️‍♀️‍♀️‍♀️‍♀️‍♀️‍♀️‍♀️‍♀️‍♀️‍♀️‍♀️‍♀️‍♀️‍♀️‍♀️‍♀️‍♀️‍♀️‍♀️‍♀️‍♀️

A cell of a constant e. m.f is connected in series with a parallel arrangement of 8ohms coil and a uniform wire of length (Lcm). The total external resistance in the circuit is found to be 6ohms. calculate the resistance of the wire and its length. Resistivity of the wire material = 6.0×10^-5 ohm/meter, cross-sectional area of the wire = 6.0×10^-3cm².​

Answers

The resistance of the wire will be 24ohm and the length of the wire will be 24×10⁴cm.

As given in the question,

Rₜₒₜₐₗ = 6ohm

Resistivity = 6×10⁻⁵ohm/m = 6×10⁻⁵/100ohm/cm

Area(A)= 6×10⁻³cm²

Let R = resistance of the wire, therefore;

Rₜₒₜₐₗ = R×8 / R+8

6 = R×8 / R+8

6R + 48 = 8R

48 = 2R

R = 24ohm

R = 24ohm

we know that resistance (R)=rho×l/A

Therefore,

rho×l/A = 24

6×10⁻⁵/100 × l/6×10⁻³ = 24

10⁻⁴ × l = 24

l = 24×10⁴cm

So, the resistance of the wire will be R=24ohm and the length of the wire will be 24×10⁴cm.

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If a = (3, 2) and b = (-5, 3), what is a + b ?
(8,-1)
(2,5)
(-2,5)
(8,5)

Answers

Answer: a + b = (-2,5)

Explanation: I'm assuming that these are 1-dimensional matrices or vectors.

So,

a + b = [ a(x) + b(x), a(y) + b(y) ]

        = [ (3) + (-5) , (2) + (3) ]

        = [ (-2) , (5) ]

a +b = (-2,5)

¿Cuál es la frecuencia de rotación en la tierra?

Answers

Answer:

frequency is approximately 11.5 µHz, or more exactly, 11.5740740e-6 Hz

Explanation:

La Tierra gira más y más lento
Movimientos de la Tierra Características
Periodo de rotación sideral 365,256 96 días
Período de rotación (día sideral) 0,997 258 días, o 23,93419 h
Velocidad de rotación (en el ecuador) 1 674,364 km/h
Periodo de precesión 25 765 anos
4 more

HELP URGENT- will give brainliest if correct

HELP URGENT- will give brainliest if correct

Answers

Answer:

6 km is the right answer

hope it helps you

Explanation:

please mark me as brainliest

A boy throws an arrow at an original velocity of 2m / s, aiming to create an angle 0, referring to the balloon at a distance of 3m from the point of departure. Calculate the angle 0 and the height of the arrow.

Answers

Answer:

s=0.204m

Explanation:

Assuming that the arrow is thrown horizontally and there is no air resistance, we can use the following formula to calculate the launch angle 0:

tan(0) = opposite/adjacent = height/distance

where opposite is the height that the arrow reaches and adjacent is the distance to the balloon.

Rearranging the formula, we get:

0 = arctan(height/distance)

0 = arctan(height/3)

Taking the tangent of both sides, we get:

tan(0) = tan(arctan(height/3))

tan(0) = height/3

Now, we need to find the height of the arrow. Using the kinematic equation:

v^2 = u^2 + 2as

where v is the final velocity (0m/s, at maximum height), u is the initial velocity (2m/s), a is acceleration (-9.8m/s^2, due to gravity) and s is the distance travelled vertically until the arrow reaches maximum height.

At maximum height, the final velocity is 0m/s. Therefore, we have:

0 = (2m/s)^2 + 2(-9.8m/s^2)s

Solving for s, we get:

s = 0.204m

Therefore, the height of the arrow is approximately 0.204m.

Which type of land usage would increase as the population increases?

Answers

Answer:

If the population were to INCREASE land use would also INCREASE, if the human population DECREASED so would land use because there wouldn’t be as many people to using it. hope i helped

Answer:

D. Urban use

Explanation:

It shows here on this graph that overtime urban use is rising as the population is increasing! The other answers that are on this graph does not show it increasing!

Which type of land usage would increase as the population increases?

Find the density of seawater at a depth where
the pressure is 188 atm if the density at the
surface is 1050 kg/m3
. Seawater has a bulk
modulus of 2.3 × 109 N/m2
.
Answer in units of kg/m3.

Answers

The density of seawater at that depth is  1058.73 kg/m³

What is  bulk modulus ?

A substance's bulk modulus is a gauge of how resilient it is to compression. It is described as the ratio of the ensuing relative volume drop to the infinitesimal pressure rise.

Mathematically Bulk modulus can be defined as:

K = ρ dP/dρ

Hence, integrate and get:

ρ = ρ₀e^(p/K)

The density at the surface is 1050 kg/m³.

The bulk modulus = 2.3 × 10⁹ N/m²

Now put the values and get:

the density of seawater at that depth  = 1050 × e^(188×101325 ÷ 2.3 × 10⁹)

= 1058.73 kg/m³

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The density of seawater at a depth of where the pressure is 188 atm with a surface density of 1050 Kg/m³ is 1058.5 kg/m³.

What is density ?

The density of a substance is the measure of its mass per unit volume. It depends on the pressure, temperature and bond type of the substance.

The relation between the density at a depth in water to the surface density, pressure and bulk modulus is given by:

ρ = ρ0 (1+ ΔP/B)

Given ρ0 = 1050 kg/m³

pressure at depth = 188 atm

surface pressure = 1 atm

bulk modulus B = 2.3 × 10⁹ N/m²

Then,

ρ = 1050 kg/m³ (1 + (188- 1 atm) × 10⁵/2.3 × 10⁹ N/m²)

  =  1058.5  kg/m³.

Therefore, the density of sea water at the given depth is 1058.5  kg/m³.

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PLEASE HELP ME WITH THIS ONE QUESTION
What is the rest energy of a proton? (c = 2.9979 x 10^9 m/s, mp = 1.6726 x 10^-27)

Answers

Answer:

Energy =  1.5032*10^(-10) Joules

Explanation:

By Einstein's relativistic energy equation, we know that the energy of a given particle is given by:

Energy = rest energy + kinetic energy.

            = m*c^2  + (γ - 1)*mc^2

Where γ depends on the velocity of the particle.

But if the proton is at rest, then the kinetic energy is zero, and γ = 1

Then the energy is just given by:

Energy = m*c^2

Where we know that:

mass of a proton = 1.67*10^(-27) kg

speed of light = c = 2.9979*10^(8) m/s

Replacing these in the energy equation, we get:

Energy = ( 1.6726*10^(-27) kg)*( 2.9979*10^(8) m/s)^2

Energy = 1.5032*10^(-10) kg*m^2/s^2

Energy =  1.5032*10^(-10) J

Explain/Describe how atoms in domains determine whether a material is magnetic or not. (Please help this is due today)

Answers

Answer:

In a material, the magnetic behavior depends on the alignment of magnetic moments of the atoms. Magnetic moments are generated by the motion of the electrons in the atoms. When the magnetic moments of atoms in a material are aligned in a specific pattern, it creates a magnetic field which results in the material being magnetic.

In many materials, the magnetic behavior arises due to the alignment of magnetic domains, which are regions of atoms with magnetic moments aligned in the same direction. When many domains with aligned magnetic moments are present in a material, the material becomes magnetic.

The magnetic behavior of a material depends on the number of electrons and the arrangement of those electrons in the atoms. In particular, for an atom to have a magnetic moment, it must have unpaired electrons, meaning electrons that are not paired with another electron with the opposite spin. When these unpaired electrons in the atoms are aligned, they generate a magnetic moment. If all electrons are paired, there will not be a net magnetic moment, so the material will not be magnetic.

So, in summary, the magnetic behavior of a material is determined by the alignment of magnetic moments of atoms. When the magnetic moments of many atoms in a material align in the same direction, it creates a magnetic field, leading to a material being magnetic. This alignment is usually present in magnetic domains consisting of atoms with unpaired electrons.

Two identical loudspeakers 2.30 m apart are emitting sound waves into a room where the speed of sound is 340 m/s. Abby is standing 5.00 m in front of one of the speakers, perpendicular to the line joining the speakers, and hears a maximum in the intensity of the sound. Part A What is the lowest possible frequency of sound for which this is possible

Answers

Answer:

By the Pythagorean Theorem the distances from the speakers os

5 and 5.5 (rounding) meters   - let y be the wavelength in the solution

n y = 5      n is number of wavelengths from speaker

(n + m) y = 5.5      m must be integral for constructive interference

m y = .5       subtracting equations

m = 2      and y = ,25   for the above conditions

(n + 2) y = 5.5     substituting for m

n = 5.5 / .25 - 2 = 20

f = v / y     using frequency of sound

f = 340 / .25 = 1360 / sec    for lowest frequency

Check: D1 = y n  = ,25 * 20 = 5

and D2 = .25 * 22 = 5.5     for the distances traveled

Select the correct answer from each drop-down menu. Danica observes a collision between two vehicles. She sees a large truck driving down the road. It strikes a small car parked at the side of the road. Complete the passage summarizing the collision. On colliding, the truck applies a force on the stationary car, and the stationary car applies and opposite force on the truck. The front of the truck is designed to crumple in order to , which protects the well-being of the passengers.

Answers

The front of the truck is designed to crumple during a collision to absorb the impact energy, slow down the collision, and protect the well-being of the passengers. This design feature helps increase the collision time, reduce the forces acting on the passengers, and minimize the risk of severe injuries.

Danica observes a collision between two vehicles. She sees a large truck driving down the road. It strikes a small car parked at the side of the road. On colliding, the truck applies a force on the stationary car, and the stationary car applies an opposite force on the truck. The front of the truck is designed to crumple in order to absorb the impact energy and slow down the collision , which protects the well-being of the passengers.

During a collision, the principle of Newton's third law of motion comes into play. According to this law, for every action, there is an equal and opposite reaction. In the case of the collision between the truck and the car, the truck exerts a force on the car, pushing it forward, while simultaneously experiencing an equal and opposite force from the car.

The purpose of designing the front of the truck to crumple is to increase the collision time and absorb the kinetic energy. When the truck collides with the stationary car, the front of the truck deforms, crumples, and absorbs a significant amount of the impact energy. This process increases the time over which the collision occurs, reducing the forces acting on the passengers and minimizing the risk of severe injuries.

By allowing the truck to crumple, the kinetic energy of the collision is transformed into other forms, such as deformation energy and heat. This energy transformation helps protect the passengers by reducing the deceleration forces acting on them. It also helps prevent the transfer of excessive forces to the car's occupants and reduces the likelihood of severe injuries.

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Compute the speed of sound waves in air at room temperature (T=200C) and find the range of wavelengths in air to which the human ear (which can hear frequencies in the range of 20 – 20,000Hz) is sensitive. The mean molar mass of air (a mixture of principally nitrogen and oxygen) is 28.8 x 10-3kg/mol and the ratio of heat capacity is ϒ = 1.40.

Answers

The speed of sound waves in air at room temperature T=20° is 344.035 m/s.

The range of wavelength in air to which the human ear (which can hear frequencies in the range of 20 – 20,000Hz) is sensitive is  17.20 m to  0.0172 m.

What is wavelength?

The wavelength is the distance between the adjacent crest or trough of the sinusoidal wave. The wavelength is the reciprocal of the frequency of the wave.

Wavelength λ = c/f

where c is the speed of sound wave.

Given the room temperature T = 20 +273 = 293K

The velocity of sound wave is given by

v = √(γRT/m)

​where γ =1.4 , m = 28.8×10⁻³ kg/mol  R = 8.31 J/K.mol

Substituting the values, we get

v = 344.035 m/s

Thus, the speed of sound wave is 344.035 m/s

The human ear can hear frequencies in the range of 20 – 20,000Hz.

The wavelength corresponding to 20Hz is

λ = c/f

λ =  344.035 /20

λ  = 17.20 m

The wavelength corresponding to 20,000Hz is

λ =  344.035 /20000

λ  = 0.0172 m

Thus, the range of wavelength is 17.20 m to  0.0172 m sensitive to human ear.

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A wave has an amplitude of 0.0800 m
and is moving 7.33 m/s. One oscillator
in the wave takes 0.230 s to go from
one crest to the next crest. Find the
wavelength of the wave.
(Unit = m)

Answers

If a wave has an amplitude of 0.0800 m and is moving 7.33 m/s. The

wavelength of the wave is 1.69m.

What is the wavelength?

The wavelength of a wave can be determined using the equation:

Wavelength = velocity / frequency

To determine the frequency we need to calculate the reciprocal of the time it takes for one complete oscillation.

frequency = 1 / time

frequency = 1 / 0.230

frequency ≈ 4.35 Hz

Substitute the values into the wavelength equation:

wavelength = velocity / frequency

wavelength = 7.33 / 4.35

wavelength ≈ 1.69m

Therefore the wavelength of the wave is approximately 1.69 meters.

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6th grade measuring wavelengths!
PLEASE HELP!

6th grade measuring wavelengths!PLEASE HELP!

Answers

Wavelength of the given wave is 8 cm and frequency is  37.5 *\(10^{8}\) Hz.

What is frequency?

The number of vibrations counted per second is called frequency. A wave is a group of vibrations that are referred to as energy. The bottom node is known as the crest, and the top node is known as the trough.

The frequency of an alternating current is the number of full cycles per second. The hertz, also known as Hz, is the accepted unit of frequency. The frequency of a current is 1 Hz if one cycle is completed per second; 60 cycles per second equals 60 Hz.

There are 8 waves so assume one wave is 1 cm so wavelength is 8 cm and frequency of wave = speed of light/ wavelength

frequency = \(3*10 ^{8} / .08\)

Frequency = 37.5 *\(10^{8}\) Hz

Wavelength of the given wave is 8 cm and frequency is  37.5 *\(10^{8}\) Hz.

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Need help asap

A scientist has invented a robot to work on the seabed. According to his calculation, the armour of the robot can withstand a maximum pressure of 10⁵ Pa exerted by the sea water. If the density of the sea water is 1025 kg/m3, what is the maximum depth of the seabed that this robot can work? [Given g = 9.81 m/s2 and rho water = 1000 kg/m3] ​

Answers

Answer:

Explanation:

Well which is it ? ρ = 1000 kg/m³ or ρ = 1025 kg/m³?

Obviously the sea is salt water so we can ignore  ρ = 1000 kg/m³

1025 kg/m³(d  m)(9.81 N/kg) = 1 x 10⁵ N/m² = Pa

d = 9.9450535...

d = 10 meters

That's if we only account for the pressure due to the water. On top of that pressure would be atmospheric pressure which is about 101000 Pa

so the robot would be a hair above its pressure limit before it even got in the water.

A rope pulls a Tesla out of mud. The guy pulls a force F⊥ of 300N, and theta = 4.2°. The tension force T is ___ Newton.

A rope pulls a Tesla out of mud. The guy pulls a force F of 300N, and theta = 4.2. The tension force

Answers

A rope pulls a Tesla out of mud. The guy pulls a force F⊥ of 300N, and theta = 4.2°. The tension force T is 298.44__ Newton.

The problem describes a Tesla that is stuck in the mud and needs to be pulled out using a rope. the guy pulls a force F⊥ of 300N and that the angle between the rope and the horizontal plane is θ = 4.2°. The goal is to find the tension force T exerted by the rope.To solve for T, we'll need to use trigonometry. We can break the force vector into its horizontal and vertical components as follows:

Fx = F⊥ cosθ and Fy = F⊥ sinθ.

Since the rope is pulling the Tesla horizontally, the horizontal component of the force will be the tension force T. So we have:

T = Fx = F⊥ cosθ = (300 N) cos(4.2°) ≈ 298.44 N

Taking the cosine of the angle is necessary since it's the adjacent side that we're interested in, which is the horizontal component of the force. Therefore, the tension force exerted by the rope is approximately 298.44 N.

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4. Answer the following questions in terms of a wave's frequency, wavelength, amplitude, and
energy.
a. Describe the characteristics of a high pitch wave.
b. Describe the characteristics of a high-volume wave.

Answers

a. A high-pitch wave is characterized by a high frequency and a short wavelength. The frequency determines the pitch of the sound, with higher frequencies corresponding to higher pitches.

The wavelength is the distance between two consecutive peaks or troughs of the wave and is inversely proportional to the frequency. Therefore, a high-pitch wave has a shorter wavelength.

The amplitude of the wave, which is the height of the peak or the depth of the trough, is not directly related to the pitch of the sound, but it does determine the volume or intensity of the sound.

b. A high-volume wave is characterized by a high amplitude and a relatively long wavelength. The amplitude determines the volume or intensity of the sound, with higher amplitudes corresponding to louder sounds.

The wavelength of the wave does not directly affect the volume of the sound, but it can affect how the sound is perceived in different environments.

In general, longer wavelengths are more effective at traveling through obstacles such as walls and are better at penetrating long distances, whereas shorter wavelengths are more easily scattered and attenuated in the atmosphere.

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What causes rain?
a.air becomes filled with water vapor
b.water vapor condenses on dust particles
c. dust particles can no longer support water droplets

Answers

Answer:

the awnser is A

Explanation:

Brainliest Please

Answer:

A

Explanation

Within a cloud, water droplets condense onto one another so its causing so its causing the droplets to grow when they have grown to heavy the fall causing rain.

which object has a weight of about 22.5 n the book the rock the box the fish

Answers

Answer: The rock

Explanation:

rrent autempt in ptogress two horizontal, infinite, parallel plates are spaced a distance b apart. a viscous liquid is contained between the plates. the bo xed, and the upper plate moves parallel to the bottom plate with a velocity u. because of the no-slip boundary condition (se the liquid motion is caused by the liquid being dragged along by the moving boundary. there is no pressure gradient in the dir note that this is a so-called simple couette flow discussed in section 6.9.2. (a) start with the navier-stokes equations and datermine the velocity distribution between the plates
(b) Determine an expression for the flowrate passing between the plates (for a unit width). Express your answer in terms of b and U.

Answers

(a) The velocity distribution is, u = (U/b)y.

(b) The flow rate per unit width is \($\frac{1}{2}Ub$\).

We can start by writing down the Navier-Stokes equations for an incompressible fluid:

\(\rho (\dfrac{\partial{u}}{\partial{t}} + \vec{u}.\nabla{u}}) = -\nabla{p} + \mu\nabla^2{u} +f\)

where \($\rho$\) is the fluid density, \($\mathbf{u}$\) is the velocity vector, p is the pressure, \($\mu$\) is the dynamic viscosity, and \($\mathbf{f}$\) is any external forces. Since the flow is steady and there are no external forces, we can simplify the equation to:

\(\mu \dfrac{\partial^2{u}}{\partial{y}^2} = 0\)

where u is the velocity in the x direction and y is the distance from the bottom plate. Integrating this equation twice, we get:

u = (U/b)y

where U is the velocity of the top plate and we have used the no-slip boundary condition at the bottom plate (u=0 at y=0) and the top plate (u=U at y=b).

(b) The flow rate per unit width is given by:

\(Q = \int_0^bu(y)dy\)

Substituting the velocity distribution from part (a), we get:

\(Q = \int_0^b\dfrac{U}{b}(y)dy\\=\dfrac{1}{2}\dfrac{U}{b} b^2\)

Therefore, the flow rate per unit width is \($\frac{1}{2}Ub$\).

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Liz rushes down onto a subway platform to find her train already departing. She stops and watches the cars go by. Each car is 8.60 m long. The first moves past her in 1.80 s and the second in 1.61 s. Find the constant acceleration of the train.

Answers

The constant acceleration of the train is 0.33 m/s.

The average velocity can be calculated by using the formula:

velocity = distance/time

For the 1st car, the velocity is calculated as:

v₁ = 8.60 m / 1.80 s = 4.78 m / s

For the second car, velocity can be calculated as:

v₂ = 8.60 m / 1.66 s = 5.34 m / s

Now we can solve for the acceleration using the formula:

v₂² = v₁² + 2 a d

Rewriting in terms of a, we get

a = (v₂² – v₁²) / 2 d

a = (5.34)² – (4.78)² / (2 × 8.6)

a = 0.33 m/s

Therefore, the constant acceleration of the train is 0.33m/s.

what is acceleration explain?

acceleration, fee at which speed modifications with time, in terms of each pace and course. A factor or an object shifting in a directly line is improved if it hastens or slows down. motion on a circle is improved even if the velocity is steady, due to the fact the route is constantly converting

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