the position of a wind-up toy is given by: over the domain of {0 s < < 1 s}, where is in m, and is in s. what is the maximum speed of the toy?

Answers

Answer 1

The maximum speed of the wind-up toy is 9.33 m/s.

To find the maximum speed of the toy, we need to find the first derivative of the position function and then find the maximum value of that derivative. The first derivative of x(t) is:

dx/dt = 2t(1 + 7t - 12t^2 + 5t^3) + t^2(7 - 24t + 15t^2)

Next, we need to find the maximum value of this derivative function over the given domain. To do this, we can set the derivative equal to zero and solve for t, then check the values of the derivative at those points to see if they correspond to a maximum or minimum.

Setting the derivative equal to zero:

0 = 2t(1 + 7t - 12t^2 + 5t^3) + t^2(7 - 24t + 15t^2)

Solving for t, we find that t = 0 and t = 1/3. These two values correspond to the minimum and maximum speeds of the toy, respectively.

Finally, we can evaluate the derivative at t = 1/3 to find the maximum speed:

dx/dt = 2(1/3)(1 + 7(1/3) - 12(1/3)^2 + 5(1/3)^3) + (1/3)^2(7 - 24(1/3) + 15(1/3)^2)

Evaluating the expression, we get:

dx/dt = 2(1/3)(1 + 7(1/3) - 12(1/3)^2 + 5(1/3)^3) + (1/3)^2(7 - 24(1/3) + 15(1/3)^2)

= 2(1/3)(1 + 7(1/3) - 12(1/3)^2 + 5(1/3)^3) + (1/3)^2(7 - 8 + 5)

= 2(1/3)(1 + 7/3 - 4 + 5/3) + (1/3)^2(12)

= 2(1/3)(12/3) + (1/3)^2(12)

= 24/3 + 4/3

= 28/3

The maximum speed of the wind-up toy is approximately 3.72 m/s.

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The complete question is:

The position of a wind-up toy is given by: x(t)= t^2(1+7t-12t^2+5t^3) over the domain of {0s < t < 1s}, where x is in m, and t is in s. what is the maximum speed of the toy?

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Related Questions

as the sun angle , the amount of energy reaching the surface . question 16 options: increases; decreases increases or decreases; remains constant increases; increases decreases; increases

Answers

As the sun angle decreases, the amount of energy reaching the surface decreases.

The sun angle refers to the angle between the sun and the horizontal surface. The higher the sun angle, the more direct the sun's rays are reaching the surface, which results in a higher amount of energy.

On the other hand, when the sun angle is lower, the sun's rays are more spread out and less direct, leading to a decrease in the amount of energy reaching the surface.

Additionally, the sun angle changes throughout the day as the earth rotates and also changes seasonally as the earth orbits the sun. Understanding the relationship between the sun angle and the amount of energy reaching the surface is important for various applications, including solar energy generation and building design to optimize energy use.

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Your question seems incomplete, but I suppose the question was:

"as the sun angle _______, the amount of energy reaching the surface ______.

question options: increases; decreases increases or decreases; remains constant increases; increases decreases; increases."

A vector is represented by a(n)………?

Answers

Answer:

An Alphabet with an arrow on top

Explanation:

Vectors are denoted by alphabets in boldface or alphabets with arrows above them

A marble is rolling at a velocity 100cm/sec with a momentum of 10,000 g-cm/sec. What is it’s mass?

Answers

Answer:

100g

Explanation:

Use the formula,

momentum = mass* velocity

Now substitute the respective values,

10,000g - cm/s = m * 100 cm/s

m = 10⁴ g-cm/s / 100 cm/s

m = 100g

And we are done!

a 1500kg ferry boat has a momentum of 25000 kg-m/a. What is the speed of the ferry boat

Answers

The speed of the ferry boat is 16.67 meters per second.

The Pythagorean theorem is what?

At a velocity of 10.0 m/s, the boat crossed the calm sea. Un = 2.00 m/s, river water speed Let v represent the ferry's effective river crossing speed, allowing it to travel directly to the location on the opposite side. We can then express their velocities as shown below.

What made Pythagoras well-known?

Greek philosopher Pythagoras made significant contributions to mathematics, astronomy, and music theory. Although the Babylonians were aware of the theorem 1000 years before Pythagoras, he may be the first to use it.

We can use the formula for momentum:

p = mv

where p is momentum, m is mass, and v is velocity or speed.

Rearranging this formula to solve for velocity, we get:

v = p/m

Substituting the given values, we get:

v = 25000 kg-m/s / 1500 kg

v = 16.67 m/s

Therefore, the speed of the ferry boat is 16.67 meters per second.

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Activity 3 A driver parked his car in the open on a hot day because he wanted to go for lunch in a small town A man in the tow. advised the driver to park the car under a tree shade but the driver refused. Task: Prepare a comprehensive message with reasons that would convince the driver to pack the car under the shade.​

Answers

Answer:

Dear driver,

I hope this message finds you well. I am writing to you today because I noticed that you have parked your car in the open on this hot day. I understand that you are planning to go for lunch in the town, but I would like to respectfully offer you some advice.

I strongly recommend that you park your car under the shade of a tree. There are several reasons for this that I would like to share with you. Firstly, parking your car in direct sunlight can cause the interior to become extremely hot and uncomfortable, which can make it difficult to get back into your vehicle after lunch. This can also cause the steering wheel and other interior surfaces to become too hot to touch, which can be dangerous.

Furthermore, parking your car in direct sunlight can also have a negative impact on the health of your car. The intense heat can cause the dashboard, upholstery, and other materials to fade and deteriorate over time. It can also increase the risk of interior damage from sun exposure and make the car look older than it actually is.

Finally, parking under the shade of a tree will help to keep your car cooler, which can make it more comfortable for you to get back into and drive when you are ready to leave. This can also help to extend the life of your car and maintain its appearance.

I hope that these reasons have convinced you to park your car under the shade of a tree during your time in the town. If you have any further questions or concerns, please don't hesitate to reach out to me.

Thank you for your time and consideration.

Explanation:

what is the volume of an aluminum ball at 10°c if its volume at 160°c is 300cm3?

Answers

The volume of the aluminum ball is 297 cm³.

What is the volume of the aluminum ball?

The volume of an object changes with temperature, according to the law of linear thermal expansion.

The volume of the aluminum ball is calculated as follows;

V = V₀ ( 1 + 3αΔθ )

where;

V₀  is the initial volume of the aluminumα is the coefficient of linear expansion of aluminum

V = 300 cm³ ( 1 +   3 x 23 x 10⁻⁶ x  (-150 ) )

V = 297 cm³

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determine the moment of each of the three forces about point b MF1(B)=? MF2(B)=? MF3(B)=?

Answers

MF1(B)= 149.52 N - m, MF2(B)= 600 N - m, MF3(B)= ON - m.

Explain about force?

Force is a vector quantity that is defined as the rate of change of momentum of an object with respect to time. It is measured in Newtons (N) and is the product of mass and acceleration, according to Newton's second law of motion. Force can be applied by pushing, pulling, or twisting an object and can be used to create motion, stop motion, or change the direction of motion. Force can also influence the shape of an object through compression, tension, and shear.

(MF₁) B = F₁ cos 30° (3) – F₁ sin 30° (4)

           = 250 cos 30° (3) — 250 sin 30° (4)

           = 649.52 - 500

           = 149.52 N - m

(MF₂) B = F₂ cos 60° (4) – F₂ sin 60° (0)

            = 300 cos 60° (4) — 300 sin 60° (0)

            = 600 - 0

            = 600 N - m

As the force F3 passes through point B, moment of the force F3 about point B is zero.

(MF3)B = ON - m

Therefore, MF1(B)= 149.52 N - m, MF2(B)= 600 N - m, MF3(B)= ON - m is the answer.

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an object in shm oscillates with a period of 4.0 s and an amplitude of 10 cm. how long does the object take to move x

Answers

An object in SHM oscillates with a period of 4.0 s and an amplitude of 10 cm. The object takes to move is 0.409s.

The time it takes for an object in simple harmonic motion (SHM) to move a certain distance can be calculated using the formula:

x = A sin ωt

where,

t is the time to move a distance x, time period T = 4 s

A is the amplitude of the oscillation

ω is Angular frequency = 2π/T= 1.57 rad/s

Then,

x = A sin ωt

6 = 10 sin(1.57t)

sin(1.57t) = 0.6

1.57 t = 0.6435

t= 0.409s.

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how does a simple cell work

Answers

Answer:

A simple cell can be made by connecting two different metals in contact with an electrolyte

A simple cell consists of two solid electrodes placed in an electrolyte connected together by an electrical conductor such as wire. The two electrodes must be two different metals. The electrolyte can be acid solution, alkaline solution, salt solution or even a fruit such as orange or lemon.

B. An object with a mass of 500,000 Kg and an object with a mas of 700.00 k have a force df grantsionalateshor between them that measures 00045N. How far apart are the two objects?

Answers

The two objects are approximately 22,201.86 meters apart.

 

The formula we use to determine the gravitational force between objects is;

F = G * (m1 * m2) / r^2

where;

F is the force of gravity, G is the gravitational constant (6.67430 × 10^-11 m^3 kg^-1 s^-2)m1 and m2 refer to the masses of the objects,r refers to the distance between the objects' centers.

Rearrange this formula to solve for the distance between the objects, we get;

r = sqrt((G * m1 * m2) / F)Substituting the given values, we get:r = sqrt((6.67430 × 10^-11 m^3 kg^-1 s^-2 * 500000 kg * 700.00 kg) / 0.00045 N)r = 22201860 meters

The two objects are roughly 22,201.86 meters apart, according to the calculation.

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Which phase of matter is made up of particles that are packed closely together, with both a definite shape and a definite volume?
A. Gas
B. Liquid
C. Plasma
D. Solid

Answers

The correct option is D. Solid phase of matter is made up of particles that are packed closely together, with both a definite shape and a definite volume.

In physics, a Solid is a state of matter characterized by its ability to maintain a fixed shape and volume when subjected to external forces. The particles in a solid are tightly packed together and have a fixed position relative to each other, giving the solid its rigidity.

Solids have a definite shape because their particles cannot move past one another, and they have a definite volume because the particles are tightly packed together. The properties of solids, such as density, thermal conductivity, and electrical conductivity, depending on the arrangement of their particles and the forces between them.

Solids can exist in different crystal structures, depending on the arrangement of their atoms or molecules. Examples of solids include metals, minerals, and rocks, as well as everyday objects such as tables, chairs, and buildings. Solids are important in many areas of physics, including materials science, condensed matter physics, and solid-state electronics.

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suppose that 2 j of work are needed to stretch a spring from its natural length of 30 cm to a length of 42 cm. how much work (in j) is needed to stretch it from 35 cm to 40 cm?

Answers

The work needed to stretch the spring from 35 cm to 40 cm is 0.35 Joule. The result is obtained by using the formula for potential energy of a spring.

How to count the potential energy of a spring?

The potential energy can be expressed as

P.E = ½kx²

Where

k = spring constantx = spring displacement

Suppose that 2 J of work are needed to stretch a spring from its natural length of 30 cm to a length of 42 cm. Find work (in Joule) is needed to stretch it from 35 cm to 40 cm!

We have P.E₁ = 2 J when

x₁ = (42 - 30) cm

x₁ = 12 cm

x₁ = 0.12 m

The spring constant is

P.E₁ = ½kx₁²

2 = ½k(0.12)²

4 = 0.0144k

k = 277.77

k ≈ 278 N/m²

When it stretches for

x₂ = (40 - 35) cm

x₂ = 5 cm

x₂ = 0.05 m

The work needed will be

P.E₂ = ½kx₂²

P.E₂ = ½(278)(0.05)²

P.E₂ = 139(0.0025)

P.E₂ = 0.35 Joule

Hence, to stretch it from 35 cm to 40 cm, the work needed is 0.35 Joule.

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2. a solid conducting sphere (or any shaped conductor), charged either positively or negatively, has no electric field inside it. how is this so?

Answers

It has a consistent distribution of the charges in a solid conducting sphere (or any shaped conductor), charged either positively or negatively, has no electric field inside it.

When retained in an electric or magnetic field, the basic physical characteristic of matter, electric charge, produces a force. A moving electric charge creates a magnetic field, and an electric charge is related with an electric field. Magnetic and electric fields combine to form the electromagnetic field. The interaction of the charges results in the electromagnetic force, which is the fundamental force in physics. Tell us about electric charges, their varieties, and their characteristics throughout this session. A scalar quantity is an electric charge. In addition to having a magnitude and direction, a quantity must also abide by the laws of vector addition, such as the parallelogram law of vector addition and the triangle law of vector addition. The quantity is only referred to as a vector quantity after vector addition.

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Similarities and differences between thermionic emission and liquid evaporation

Answers

There are both similarities and differences between thermionic emission and liquid evaporation elaborated below.

Vapourization is the process by which the liquid state transforms into the vapour state, and thermonic emission is the thermally induced inflow of charge carriers.

The thermally convinced ingress of charge carriers from a face or over an implicit-energy barrier is known as thermionic emission. This happens because, as we are aware, the thermal energy applied to the carrier overrides the material's ability to perform its intended function.

The process through which a liquid transforms into a gas is known as vaporisation. The molecules' kinetic energy increases along with the temperature. The force of attraction between the molecules weakens as a result of this increase in kinetic energy, allowing them to escape into the environment as vapours.

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a block weighing 55 lb is being pushed by a 13 lb force on a smooth surface. determine the acceleration of the block rounded to three significant figures.

Answers

On a flat surface, a 55 kg block is being dragged by something like a 13 lb force. The block accelerates at a rate of 7.64 feet per second.

What are example and force?

As a response, the body's motion, shape, height, etc., could also alter. An alternative would be to firmly push or shove a door. Force is a vector quantity, hence it has a magnitude and direction. According to Newton's second law, pressure is the "service offering of a body's normal and acceleration."

What characteristics does force have?

Therefore, the characteristics of columns of force are just that they begin at a positively charged ions and end at a negative charge, never cross, are proportionate to charge, and cannot pass through a conductor.

W = 55lb

m = w/g

g = 32.18 ft/s2

= 55/ 32.18

= 1.70 lbm

F = 13 lb

F = ma

13 = 1.70 * a

a = 7.64 ft/s2

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reflects from the mirror, and reaches point b. how far below the top edge does the ray strike the mirror?

Answers

The distance below the top edge at which the ray strikes the mirror depends on the angle of incidence.

What is ray strikes?

Ray tracing is a computer graphics rendering technique for generating an image by tracing the path of light as it interacts with an object or scene. Ray tracing is capable of producing a very high degree of visual realism, including effects like reflections, refractions, and shadows.

The distance below the top edge at which the ray strikes the mirror depends on the angle of incidence. The angle of incidence is the angle between the incident ray and the normal to the mirror surface. The distance below the top edge can be found using the law of reflection which states that the angle of incidence is equal to the angle of reflection. If we denote the angle of incidence as θ and the distance below the top edge as h, then we can calculate h using the tangent of θ.

h = tan(θ) * distance from point a to the top edge of the mirror

Therefore, the distance below the top edge at which the ray strikes the mirror depends on the angle of incidence.

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why might the unemploymeht rate cometimes increase when the pace of job creation exceeds the increase in population

Answers

The unemployment rate is a measure of the percentage of the labor force that is currently unemployed and actively seeking employment. When the pace of job creation exceeds the increase in population, it would be expected that the unemployment rate should decrease, as there are more job opportunities available for job seekers.

It's important to note that unemployment rates are often subject to seasonal fluctuations, with certain times of the year seeing more job losses than others. For example, there may be a decrease in employment in certain industries during the winter months, or during the summer months when school is out. These seasonal fluctuations can lead to temporary increases in unemployment rates, even if job creation is occurring.

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A rhinoceros is at the origin of coordinates at time t1=0. For the time interval from t1 to t2= 10.0s, the rhino's average velocity has x-component -3.20 m/s and y-component 5.40 m/s.
*At time t2=10.0s what is the x-coordinate of the rhino?
*At time t1=10.0s what is the y-coordinate of the rhino?
*How far is the rhino from the origin?

Answers

At t2=10.0s, the x-coordinate of the rhino is -32 and at time t1=10, the y-coordinate of the rhino is 64.8m. The rhino is 72.27 m.

Given:

x-component of avg. velocity is 3.20 m/s.

x-component of avg. velocity 5.40 m/s.

initial position of rhino, (x1,y1)= (0,0)

initial time, t1=0s

final time, t2=12s

a) As we know that average velocity is total displacement per unit time.

Position of x-coordinate of the rhino:

Vx= x2/t2

-3.20= x2/10

x2= -32m

Position of y-coordinate of the rhino:

Vy= y2/t2

5.40= y2/12

y2= 64.8 m

Now the distance from the origin:

s=[tex]\sqrt{x2^{2} +y2^{2} }[/tex]

s=[tex]\sqrt{(-32)^{2} } + (64.8)^{2} \\[/tex]

s=[tex]\sqrt{1024}+ 4199.04[/tex]

s=72.27 m

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If a nearsighted person has a far point df that is 3. 50m from the eye, what is the focal length f1 of the contact lenses that the person would need to see an object at infinity clearly? Express your answer in meters. If a farsighted person has a near point that is 0. 600m from the eye, what is the focal length f2 of the contact lenses that the person would need to be able to read a book held at 0. 350m from the person's eyes? Express your answer in meters

Answers

(-3.5 m) (-0.22man) The focal length f1 of the lenses contacts infinity clearly if a nearsighted person has a distant point df that is 3. 50 m from the eye.

What is focal distance vs focal length?

The focal length of a lens, when focussed at infinity, is the distance between its rear nodal point and the focusing plane (where the camera's sensor is located). This is a characteristic of the lens that controls both the angle of vision and the perspective.

The focal length is the distance from the principal focus to the concave lens' optical centre.

The magnification at which a lens pictures far-off objects depends on its focal length. It is equivalent to the separation between the image plane and a pinhole that can capture distant objects that are the same size as the target lens.

Therefore, The sign convention dictates that the focal length of a concave lens always is negative.

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what is the angular momentum of a thin loop of radius 2m and mass 1 kg, rotating at a velocity of 4 rad/s?

Answers

The angular momentum of a thin loop of radius 2m and mass 1 kg, rotating at a velocity of 4 rad/s is 8 kg·rad/s

What is angular momentum?

The rotational equivalent of linear momentum is angular momentum, often known as moment of momentum or rotational momentum. It is a conserved quantity, meaning that the total angular momentum of a closed system stays constant, making it a significant physical quantity. Both the direction and the amplitude of the angular momentum are always conserved. The functional characteristics of motorbikes, frisbees, bullets, and gyroscopes are due to the conservation of angular momentum.Angular momentum conservation also explains why storms occur.

Given :  m=1 kg       w=4 rad/s        r=2 mm

So, angular momentum   L=mwr

⟹ L=1×4×2

= 8 kg rad /s

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describe how you would use an uncalibrated force probe and the springs in question 1 to develop a quantitative

Answers

By using two known mass pans or objects, we can create the calibrated force probe using the uncalibrated force probe and springs that are already provided.

What occurs when an object is subjected to force from both sides?

Newton's third law states that if object A exerts a force on object B, then object B must exert a force of equal size and in the opposite direction on object A. This law serves as an example of how forces always exist in pairs in nature and how no body can exert a force without also experiencing one.

What distinguishes a balanced force from an imbalanced force?

When forces are balanced, they cancel one another out, causing the item they are acting on to remain in motion. conflicting forces don't cancel out each other and cause the thing they are acting on to modify its motion.

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what is the diffraction limit of a 130-meter radio telescope observing radio waves with a wavelength of 21 centimeters?

Answers

The diffraction limit of the 130-meter radio telescope observing radio waves with a wavelength of 21 centimeters is 0.0022 meters.

The diffraction limit of a radio telescope is defined as the minimum size of the telescope's aperture that is necessary to produce a diffraction-limited image of an incoming wave. It is given by the formula:

d = 1.22 * λ / D

where d is the diffraction limit, λ is the wavelength of the incoming wave, and D is the diameter of the telescope's aperture.

In this case, the wavelength of the incoming wave is 21 centimeters, or 0.21 meters, and the diameter of the telescope's aperture is 130 meters. Plugging these values into the formula, we get:

d = 1.22 * 0.21 / 130 = 0.0022 m

So, the diffraction limit of the 130-meter radio telescope observing radio waves with a wavelength of 21 centimeters is 0.0022 meters.

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g if you changed the source wavelength to a longer wavelength, e.g. 600nm, how would the distance between the zero order maximum and the third order maximum change?

Answers

There would be an increase in the maximum order.

How will the wavelength change?

If you change the source wavelength to a longer wavelength, for example, from 500 nm to 600 nm, the distance between the zero order maximum and the third order maximum would increase.

The distance between the diffraction peaks in a diffraction grating is proportional to the wavelength of the light. As the wavelength increases, the distance between the diffraction peaks also increases. The diffraction peaks are also proportional to the order of the diffraction. Therefore, as the wavelength increases, the distance between the zero order maximum and the third order maximum also increases.

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A weight hangs motionless from a spring, with a spring constant of 75 N/m. The spring stretched from its original length by 0.333 meters. How much weight hangs from the spring?

Group of answer choices

15 N

45 N

35 N

25 N

Answers

Answer:

25 N

Explanation:

You can just observe the units of the numbers given to know that

75 N/m * .333 m = 25 N

can the internal forces within a soccer ball produce an impulse on the soccer ball to change its momentum why or why not

Answers

The internal forces within a soccer ball can produce an impulse on the soccer ball to change its momentum. When the ball is struck by a player's foot, the internal forces within the ball cause it to compress and rebound.

What is the compress ?

Compression is the process of reducing the size of a file or data set by encoding information using fewer bits. It is used to reduce the amount of data sent over a network or stored on a hard drive. Compression is generally done by compressing data into smaller data sets, which are then decompressed when needed. Compression can also be used to reduce the size of images, allowing them to be stored or transmitted more quickly. Compression algorithms such as lossless and loss can also be used to reduce the amount of data loss when transmitting or storing data.

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in parallel association, should the equivalent resistance be smaller or bigger than any individual resistor in the circuit? justify your answer.

Answers

The equivalent resistance is always less than the smallest resistor in the parallel network.

Then the inverse of the equivalent resistance of two or more resistors connected in parallel is the algebraic sum of the inverses of the individual resistances.

If the two resistances or impedances in parallel are equal and of the same value, then the total or equivalent resistance, [tex]R_t[/tex] is equal to half the value of one resistor. That is equal to R/2 and for three equal resistors in parallel, R/3, etc.

Note that the equivalent resistance is always less than the smallest resistor in the parallel network so the total resistance, [tex]R_t[/tex] will always decrease as additional parallel resistors are added.

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20 points !! An ultraviolet wave from the Sun traveling at the speed of light has a wavelength of 3 × 10−8m. Calculate the frequency of this wave.

Answers

Answer:

[tex]1.0 \times 10 {}^{16} per \: second[/tex]

or simply

1.0×10¹⁶/s

Explanation:

Greetings !!

Given values :-

speed of light= 3×10⁸

wavelength= 3×10-⁸

required value :-

frequency= ?

solution:-

Firstly, recall the velocity-wavelenght equation

V=f λ

Substitute known variables into the equation

(3×10⁸) = f(3×10-⁸)

Solve for frequency

f= 1.0×10¹⁶/s.

If you have any questions or unclear ideas tag on comment box

Hope it helps!!!

I’m only answering so that you can give him brainliest because he deserves it

At Absolute Zero Temperature (0 Kelvin), state how much thermal energy an object has. At Absolute Zero Temperature, state the pressure that a fluid exerts on its system container.

Answers

At absolute zero temperature, the pressure of a fluid will approach zero.

What is absolute zero?

Absolute zero is the lowest temperature that can be reached in the universe and is defined as 0 Kelvin (K) on the Kelvin scale. It is equivalent to -273.15°C on the Celsius scale and -459.67°F on the Fahrenheit scale.

At absolute zero temperature (0 Kelvin), an object has zero thermal energy. This is because the definition of absolute zero temperature is the point at which an object has the minimum possible amount of thermal energy. At this temperature, all matter is in its lowest energy state and all random thermal motion has stopped.

Regarding the pressure of a fluid at absolute zero temperature, it is important to note that absolute zero temperature does not necessarily mean that the fluid is at a pressure of zero. The pressure of a fluid is determined by its temperature and its volume, not by its absolute temperature alone. The pressure of a fluid in a container is related to the average kinetic energy of the molecules in the fluid and their number density.

So, At absolute zero temperature, the pressure of a fluid will approach zero, but it will not be exactly zero because even at this temperature, the fluid molecules still have a non-zero kinetic energy due to their quantum mechanical motion.

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compare this to the diffraction limit of the hubble space telescope for visible light. why, to be useful, radio telescopes must be much larger than optical telescopes?

Answers

Radio telescopes must be larger than optical telescopes because of the longer wavelengths of radio waves, which result in a lower diffraction limit.

The diffraction limit of a telescope is determined by its aperture size, or the diameter of its collecting area. For the Hubble Space Telescope, the diffraction limit for visible light is approximately 0.05 arcseconds. This means that the telescope can resolve structures or details that are separated by at least 0.05 arcseconds of an angle.

On the other hand, radio telescopes are much larger than optical telescopes because radio waves have longer wavelengths than visible light. The diffraction limit of a radio telescope is proportional to the wavelength of the radiation it observes. Because radio wavelengths are much longer than those of visible light, radio telescopes must be much larger in order to achieve the same level of resolution as optical telescopes.

In addition, radio telescopes can detect emissions from much larger structures in space, such as galaxies and clusters of galaxies. These emissions are typically very weak and difficult to detect, so radio telescopes must have a large collecting area in order to detect them.

To sum up, radio telescopes must be larger than optical telescopes because of the longer wavelengths of radio waves, which result in a lower diffraction limit, and the need to detect weak radio emissions from large structures in space.

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A steel wrecking ball is moving with 30,000 J of kinetic energy. The ball collides witha spring and comes to a complete stop. If the spring has a k = 50,000 N/m how much is the spring compressed?

Answers

Answer:

1.02 m

Explanation:

We are here given that ,

Kinetic energy= 30,000 J spring constant= 50,000N/m

We need to find out the compression in the spring. As we know that,

[tex]\longrightarrow E = \dfrac{1}{2}kx^2 \\[/tex]

where [tex]x[/tex] is the compression in the spring. So that,

[tex]\longrightarrow 30,000 J = \dfrac{1}{2}\times 50,000 \times x^2 \\[/tex]

[tex]\longrightarrow x^2=\dfrac{60,000}{50,000} \\[/tex]

[tex]\longrightarrow x^2=\dfrac{6}{5}= 1.2m^2\\[/tex]

[tex]\longrightarrow x=\sqrt{1.2} m \\[/tex]

[tex]\longrightarrow \underline{\underline{ x \approx 1.02 \ m }} \\[/tex]

and we are done!

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