17. A skateboarder is going 10 m/s the instant it is launched vertically off a ramp. If the mass of the skateboarder is 50 kg, how high above the ramp can he possibly go? If the mass of the skateboarder is 100 kg, how high above the ramp can he possibly go? If the speed of the skateboard is 20 m/s when it is launched how high above the ramp can he possibly go? (5.1m, 5.1m, 20.4m)​

According to the given hint, solar panels generate an average  about 200 Watt/m2.

1. The annual USA energy consumption is 103,108,904,000,000,000,000J.

2. The average power required for the USA over one year is 3.2 trillion watt.

3. The total area needed to provide this power is 32.6 billion [tex]m^{2}[/tex].

4. The surface area of the USA is 9.834*[tex]10^{12}[/tex] [tex]m^{2}[/tex].

Solar energy originates from the sun. Solar panels (also called "PV panels") are used to convert light from the sun, which consists of energetic particles called "photons", into electricity that can be used to power electrical loads increase.

Solar panels can be used in a variety of applications including remote power systems for cabins, telecommunications equipment, remote sensing and, of course, power generation for residential and commercial photovoltaic systems.

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The answer to the question is that the acceleration equals 4.9 m/s² and the cord tension is 58.8 N.

The force produced when ever a load is attached at one or both of the end of such a material in such a direction away from the material's cross-section is known as the tension force. It's frequently referred to a tension force as a "pushing" force.

(a) Let's use Newton's Second Law for Movement to our example:

[tex]$$\begin{gathered}T-m_1 g=m_1 a, \\T-m_2 g=-m_2 a .\end{gathered}$$[/tex]

Eliminating [tex]$T$[/tex], we get:

[tex]$$\begin{gathered}\left(m_2-m_1\right) g=\left(m_1+m_2\right) a, \\a=\frac{\left(m_2-m_1\right) g}{m_1+m_2}, \\a=\frac{(12 \mathrm{~kg}-4 \mathrm{~kg}) \cdot 9.8 \frac{\mathrm{m}}{\mathrm{s}^2}}{4 \mathrm{~kg}+12 \mathrm{~kg}}=4.9 \frac{\mathrm{m}}{\mathrm{s}^2} .\end{gathered}$$[/tex]

(b) By adding "a" to the first equation, we can get the cord's tension:

[tex]$$T=m_1(a+g)=4 \mathrm{~kg} \cdot\left(4.9 \frac{\mathrm{m}}{\mathrm{s}^2}+9.8 \frac{\mathrm{m}}{\mathrm{s}^2}\right)=58.8 \mathrm{~N}$$[/tex]

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The time period and frequency of the glider are found to be 3.7 second and 0.27 Hz respectively.

The air glider is oscillating between the 3.00 cm marl and 59.0 cm mark.

It is given that the air glider completes 10 oscillations in 37.0 seconds.

So, in order to find the time period of the oscillation, we can write,

Time taken by glider to complete 10 oscillations = 37 seconds.

Time taken by glider to complete 1 oscillation = 37/10 seconds.

Time taken by glider to complete 1 oscillation = 3.7 seconds.

So, the time period of oscillation of the glider is 3.7 seconds.

Now, the frequency of the air glider will be,

f = 1/T

Where,

T is the time period,

So, putting values,

f = 1/3.7 Hertz

f = 0.27 Hz.

So, the frequency of the air glider is 0.27 Hz.

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Complete question - an air-track glider attached to a spring oscillates between the 3.00 cm mark and the 59.0 cm mark on the track. the glider completes 10.0 oscillations in 37.0 s. Find the a. Time period b. Frequency.

It is true that the hydrologic cycle is powered by heat from the sun, which is used to energize the water to evaporate from the planet's surface's many water sources.

The water balance is crucial because it determines how water gets to people, plants, and other species. In addition to supplying water for people, animals, and plants, it also transports nutrients, diseases, and sediment to and from aquatic habitats.

The hydrologic cycle, another name for the water cycle, describes where and how water is kept on Earth. In the sky, on the surface of the land, and underground, water is kept in reserve. It can be either a liquid or a solid.

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When a loop repeats until a variable has a specific value, that value is often referred to as the "terminating condition" or the "loop condition."

It is the value that determines when the loop will stop executing and control will be passed to the next line of code. In programming languages, loops are used to execute a block of code repeatedly until a certain condition is met. There are different types of loops, such as for loops, while loops, and do-while loops, that can be used to accomplish this.

In a for loop, the loop condition is typically specified as part of the loop header, along with the initialization and increment/decrement of the loop variable. For example:

for (int i = 0; i < 10; i++) {

// code to be executed

}

In this example, the loop will repeat until the value of the variable "i" is equal to 10. At that point, the loop will terminate and control will be passed to the next line of code.

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When  two lamps with one thick filament and one with a thin filament of the same material, are connected in parallel to a power supply. Then the  current is greater in the lamp with a thick filament.

Ohm's Law can be used to calculate the relationship between voltage, current, and resistance in an electrical circuit.

Ohm's law can be written as follows:,

V = I x R

When written out, the formula is as follows: voltage = current x resistance, or

Volt = Amp x Ω.

Because theory is connected in parallel and the potential difference across each filament is the same, we can conclude that a material's resistance is [tex]R = \rho*lA[/tex]

[tex]\rho[/tex] is the resistivity if the material for the two filaments is the same and the length 'l' is also the same

The area of cross section of a thick filament is greater than that of a thin filament. The resistance is less than the thin filament current. [tex]I = \frac{V}{R}[/tex]

since V is same

If R is smaller, current is greater, and thus current is greater in thick filament.

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Option B;  Natural levees formed Suspended load is deposited when the river covers the floodplain.

Usually, earth is used to construct levees. Sediment is forced to the side by the natural flow of a body of water, forming a natural levee. Frequently, a river's banks rise up from the river bed just a little bit . Sediment, silt, and other materials pushed aside by the rushing water are accumulated along the banks to form levees. A natural levee may be the intersection of the flood plain and the channel (a broad, low ridge of built along the side of a channel by debris- laden floodwater). When floodwater that is clogged with debris overflows a channel and goes into a floodplain, a levee is formed.

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When air enters the diffuser of a ramjet engine decelerates to negligible velocity then nozzel exit velocity is 1320.725 m/s.

A nozzle (from nose, meaning 'small spout') is a tube of varying cross-sectional area (usually axisymmetric) aiming at increasing the speed of an outflow, and controlling its direction and shape. Nozzle flow always generates forces associated to the change in flow momentum.

In the simplest case of a rocket nozzle, relative motion is created by ejecting mass from a chamber backwards through the nozzle, with the reaction forces acting mainly on the opposite chamber wall, with a small contribution from nozzle walls.

The flow in a nozzle is very rapid (and thus adiabatic to a first approximation), and with very little frictional loses (because the flow is nearly one-dimensional, with a favourable pressure gradient except if shock waves form, and nozzles are relatively short), so that the isentropic model all along the nozzle is good enough for preliminary design.

Applying steady flow energy equation,

h1+v1^2/2000 = h2+v2^2/2000

680.556^2/2000 = Cp(T2-T1)

230.42 = T2-T1

T2=460.425 K

and P2=227 Kpa

h2+q=h3

q=Cp(T3-T2)

T3=1734.05K

Now by sfee equation

V4=1320.725 m/s

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if all volcanic activity were to stop tomorrow, there would be a reduction in carbon flux into the atmosphere. is 99%

A carbon flux is the volume of carbon that is transferred across carbon stocks during a certain period of time. 1. To put it simply, it is the transfer of carbon from the land to the seas, the atmosphere, and living things. For instance, the atmosphere receives inflows from decomposition (CO2 emitted by the breakdown of organic matter), forest fires, and the burning of fossil fuels, while the atmosphere also receives outflows from plant growth and ocean absorption. The ocean operates as a net sink of 1.7 GtCyr, which is where the highest natural flow occurs between the atmosphere and the ocean. A significantly smaller net sink exists in the terrestrial ecosystem.

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The wave frequency, speed, and wavelength of two strings with the same thickness but differing lengths will be the same in both strings.

A string will vibrate at a varied frequency depending on its length. Higher frequency and higher pitch are produced by shorter strings. The  frequency and wavelength are inversely proportional. Shorter frequency corresponds to a longer wavelength. The relationship between these two characteristics is explained by the fact that the speed of a wave is equal to the product of its frequency and wavelength. A wave's speed increases with increased string tension, which raises its frequency (for a given length). The wave frequency, speed, and wavelength of two strings with the same thickness but differing lengths will be the same in both strings.

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Option B;A coin and a ring roll down an incline starting at the same time. The coin will be the one to descend first.

Its rotational inertia will be higher. Because of this, it accelerates more slowly than a coin. First to the bottom, the coin makes it. Any item that can be turned possesses rotational inertia. It is a scalar value that indicates how challenging it is to modify the object's rotational velocity around a specific rotational axis and time. Similar to how mass functions in linear mechanics, rotational inertia plays a similar purpose. According to the equation rotational inertia = mass x radius2, rotational inertia is not a vector but a scalar that depends on the radius of rotation.

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The period of oscillation of the Taipei 101 building is 13 seconds .

In the question ,

it is given that ,

the length of the cables(L) is = 42 m

the mass of the mass damper is = 660000 Kg ,

the amplitude is = 75 cm = 0.75 m

we know that the acceleration due to gravity(g) is = 9.8 .

the formula for the Time Period (T) is

T = 2π√(L/g)

Substituting the values ,

we get ,

T = 2π√(42/9.8)

Simplifying further ,

we get ,

T = 13.00079 seconds

T ≈ 13 seconds .

Therefore , the period of oscillation is = 13 seconds .

The given question is incomplete , the complete question is

Taipei 101 (a 101-story building in Taiwan) is sited in an area that is prone to earthquakes and typhoons, both of which can lead to dangerous oscillations of the building. to reduce the maximum amplitude, the building has a tuned mass damper, a 660,000 kg mass suspended from 42-m-long cables that oscillates at the same natural frequency as the building . when the building sways, the pendulum swings, reaching an amplitude of 75 cm in strong winds or tremors. damping the motion of the mass reduces the maximum amplitude of oscillation of the building .

What is the period of oscillation of the building?

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Yes, for floating objects, the buoyant force equals the weight of the objects. since each object has the same weight, they must have the same buoyant force to counteract that weight and make them float.

The object can stay suspended at its current depth if the buoyant force is equal to its weight. Regardless of whether an item floating, descends, or is immersed in a liquid, the buoyant force is constantly at work. Any item in any fluid will experience an upward push called the buoyant force.

The total upward force acting on any item in any fluid is known as buoyant force. The object will ascend to the surface as well as float if the buoyant force is higher than its weight. The object will sink if the buoyant force is lower than its weight.

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The maximum acceleration which the truck can have without causing the normal reaction at a to be zero is  77.3 ft/sec²

Calculation :

Sum of vertical forces,

By - W = (W/g) ay

By - 180 = (180/32.2) x 0

Vertical reaction, By = 180 lb

Horizontal forces,

Bx = m ax

Bx = (W/g) ax = (180/32.2) x 7.3

Horizontal reaction, Bx = 432 lb

Now taking moment about B,

W x 10 x (12/13) = m ax x 10 x (5/13)

180 x 10 x 12/13 = (180 /32.2) ax x 10 x 5/13

Acceleration, the rate of change of velocity over time for both velocity and direction. A point or object moving in a straight line accelerates as it accelerates or decelerates. Circumferential motion is accelerated because it always changes direction even at constant velocity.

Acceleration, ax = 77.3 ft/sec^2

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The amount of heat energy that must be transferred for conversion is 632730 J.

Mass of ice = m = 210 g

Temperature change = t = 100 - 0 = 100

Latent heat of fusion = L = 334 KJ/ Kg

Latent heat of vaporisation = L' = 2.26 X 10³ KJ/Kg

Specific heat of water = c = 4.19 KJ/Kg

Heat required to convert ice to water = mL

Heat required to raise the temperature of water to boiling point = m X c X t

Heat required to convert water to steam = mL'

Thus, total heat energy required = q =

= q = mL + mL' + (m X c X t)

= q = (210 X 334) + (210 X 2.26 X 10³) + (210 X 4.19 X 100)

= q = 70140 X 474600 + 87990

= q = 632730 J

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In order to find the actual distance of the shark from the wall, we need to use the lens equation. This equation is used to calculate the distance of an object from a lens, given the distance of the image from the lens, the focal length of the lens, and the refractive index of the material between the lens and the object. In this case, we can assume that the tunnel wall acts as a lens, and the water between the shark and the wall acts as the medium through which the light travels.

We can use the lens equation to find the actual distance of the shark from the wall by setting the distance of the image from the lens (3.0 m) equal to the focal length of the lens (R) divided by the refractive index of the medium (1.33), minus the actual distance of the shark from the wall (d):

3.0 m = (4.0 m)/1.33 - d

Solving for d, we find that the actual distance of the shark from the wall is 1.5 m. Therefore, the shark is actually 1.5 m away from the tunnel wall, not 3.0 m as it appears in the tunnel.

This calculation assumes that the shark is a flat object, which is not necessarily true. In reality, the shark may be closer to or further from the wall than the calculation indicates, depending on its shape and orientation. Additionally, the refractive index of water can vary depending on factors such as temperature, salinity, and pressure, so the value used in this calculation may not be entirely accurate.

The shark 's actual distance from the wall is 4 m.

The ratio of light's speed in a vacuum to that in a particular medium is known as the refractive index.

Refraction index and index of refraction are other names for the term "refractive index." The characteristics of the medium affect the speed of light in that medium. The optical density of the medium affects the speed of electromagnetic waves.

When the object is in denser medium and  observer is in rarer medium; refractive index of the medium can be written as:

μ = actual distance/apparent distance

actual distance = μ × apparent distance

= 1.33 × 3.0 m

= 3.99 m

= 4 m. (approx.)

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If a person's strength test standard score is 0.0, assuming a normal distribution, that person is stronger than 50% of the population.

The most prevalent continuous probability distribution is the Normal (or Gaussian) distribution. As the curve becomes closer to zero on either side of the mean, the function calculates the likelihood that a given event will fall between any two real number limits. A normal curve's undercut area is always equal to one.

Approximately 68 percent of the observations (or 68 percent of the area under the curve) will always fall within two standard deviations (one above and one below) of the mean, regardless of how a normal distribution appears or how large or small the standard deviation is.

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Thus, the statement 'the buoyant force on the block exerted by the water is equal to the weight of the volume of water displaced by the block' is correct.

In the figure, (FB)block is buoyant force on block, (FB)steel is buoyant force on steel object, Wsteel is weight of the steel object, Wblock is weight of the steel block, and 7 is tension in the string. is

Weight of an object acts always in downwards.

Buoyant force on an object which is placed in a fluid is always upward direction. When the buoyant force is equal to the weight of the object, then the object floats in the fluid.

From the Archimedes principle, the buoyant force exerted by a fluid on an object which is placed in it is equal to the weight of the fluid displaced by the object.

Thus, the statement 'the buoyant force on the block exerted by the water is equal to the weight of the volume of water displaced by the block' is correct.

When the block is floating, the buoyance force supported by the water is equal to the total weight of the block and steel object. Thus, the statement the buoyant force on the block is equal to its weight is not correct.

As the steel object is at rest in the water, then the net force acting on it is zero.

(F ret )steel  =0

T+(F B ) steel -W steel =0 W steel =T+(F B ) steel

Therefore,

T<W steel

Thus, the statement tension in the string is less than weight of the steel object is correct.

If the weight of the steel object is equal to the buoyant force, then the tension in the string should be zero. But the steel object is hanging with the string, so tension never is zero.

Thus, the statement 'the buoyant force on the steel object is equal to its weight' is not correct.

If the tension in the string is equal to the weight of the steel object, then the buoyant force on the steel object should be zero. But any object in a fluid should experiences the buoyant force.

Thus, the statement 'the tension in the string is equal to the weight of the steel object' is not correct.

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At each point in its course, the satellite's velocity would be perpendicular to the circle. The satellite would accelerate in the direction of the circle's centre, or the body around which it is orbiting. Thus, option A is correct.

Because the satellite orbits the earth, the gravitational pull of the planet on the satellite supplies the necessary centrifugal force. In a circular orbit, the gravitational force is constant, hence the satellite's velocity is also constant.

Therefore, A satellite in a circular orbit around the earth moves at a constant speed and maintains the same height above the planet.

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Over the last 600,000 years, the highest pre-industrial concentration of carbon dioxide in the atmosphere was approximately 300 ppm.

One carbon atom is covalently doubly linked to two oxygen atoms in every carbon dioxide molecule, giving it the chemical formula CO2. At room temperature, it exists. in. the gaseous. state. Carbon dioxide functions as a greenhouse gas in the atmosphere by being transparent to visible light while absorbing infrared radiation. As of May 2022, it was a trace gas in the Earth's atmosphere, rising from pre-industrial levels of 280 ppm to 421 ppm (or around 0.04%) by volume. [9] [10] These elevated carbon dioxide concentrations and climate change are mostly brought about by the burning of fossil fuels. [11] Groundwater, lakes, ice caps, and ocean all contain carbon dioxide because it is soluble in water. Upon dissolving in water, carbon dioxide

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At touchdown, the flaps' lift coefficient reaches its maximum of 1.8. Upon touchdown, there is a 279-meter zero lift drag.

Vt = 1.8 Vtotal = 1.8 [tex]\sqrt{2w/PSc}[/tex]

Pg = 1.225 kg/m³

1.8 [tex]\sqrt{2* 105000/1.225*50*3}[/tex] = 61.02

V = 0,7 Vt = 0.7 *61.02 = 42.714

After touch down L = 0,

Drag = 1/2 *1.225 *30 *30 *50*0.05 = 1448

Sl = 1.69 * 105000² / 9.81 * 61.02*50*3[1448 + 0.02*105000]

Sl = 279m

The zero-lift drag coefficient and the lift-induced drag coefficient factor, respectively, are denoted by CD0 and k. Under a particular aircraft aerodynamic configuration, the values of both parameters are taken to be constants. Flight can be accomplished without drag. However, without removing air, it is impossible to completely eliminate drag during flight. Although it is not entirely necessary for flight, an airplane that achieves lift will always experience some form of drag because air is required to produce lift. Increasing the zero-lift drag coefficient Cd0 has the effect of raising (TR)min while lowering the velocity at which it occurs. When the drag-due-to-lift factor K is raised, the result is an increase in (TR)min and an increase in the velocity at.

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82 K is the change in temperature of the gas during this expansion.

Monatomic gases are those that are composed of molecules with just one atom in them. Monatomic gases include gases like helium or sodium vapor. They may be recognized from diatomic or polyatomic gases relatively simply.

A single atom makes up a monoatomic gas. Examples include the gases helium and neon. Since there is just one atom in monoatomic gas, N has the value and K has an independent interaction with the other particles (again because it is composed of only one atom).

Given that,

no. of moles (n) = 8.8 moles

work (W) = 9000 J

For adiabatic process, Q = 0

=> ΔU = - W

For ideal mono-atomic gas, ΔU = 3nRΔT/2

So, ΔT = -2W/3nR

or, ΔT = - (2 × 9000) / (3 × 8.8 × 8.314)

or, ΔT = - 82 K

So, 82 K is the change in temperature of the gas during this expansion.

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The ocean water contains different types of ions.

The increase in the salt concentration results in the higher density of the ocean water. This salt concentration in the ocean is the result of different ions present in it.

The water is mostly present in the oceans and in some parts it is in the form of running water in the rivers. The oceans are salty due to the presence of the dissolved ions.

The salty nature of the oceans is also due to the ions carried by the rain water and other form of running water on the surface of the Earth. The amount of salt present in the ocean water in a particular region varies as compared to the other.

This variation in the concentration of the salt in the water leads to the variation in the density of the ocean water because if the concentration of the salt is low, then less amount salt is present in unit volume and therefore it has less density whereas if the concentration of the salt is more, it will lead to the higher density of the ocean water.

Therefore, the correct statement about ocean is that it contains different ions that are responsible for its salinity.

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The specific heat of a metal is 54.89J/kg.K

What does "specific heat" mean?

Specific heat is the amount of energy needed to raise a substance's temperature by one degree Celsius per gram. Typically, the units of specific heat are calories or joules per gram per degree Celsius.

Given: The bottle weighs 3.6 kg and holds 13.5 kg of water.

The weight of the metal is 1.8 kg, and its initial temperature is 175 C.

From 16 to 18 degrees Celsius, the temperature rises.

The container and water both received the same amount of heat from the metal object.

Qp = Qw +Qc

​(mp)cΔT= (mw)(cw)ΔT + (mc)cΔT

where, respectively, p, w, and c stand for a metal object, a liquid, and a container.

c = [(mw)(cw)ΔT] / [(mp)cΔT -  (mc)cΔT]

  =[ 13.5*4187*(18-16) ] / [1.8*(175-16) - 3.6* (18-16)]

  =  54.89J/kg.K

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Volume of water is  17.2N,

The rock displace volume of water whose weight is 37.6 - 20.4 = 17.2N

The mass of this water is 17.2/9.80 =1.755 kg and its volume equal to the rock volume is 1.755/1000 =  1.755 × [tex]10^{-3}[/tex]

The form of the container where the water is contained affects the amount of water inside. You must know the vessel's length, width, and depth in order to calculate the volume of a square or rectangular vessel. The volume equation is V=L W D, where L stands for length, W for width, and D for depth. The formula for the rectangular tank's filled volume is provided as V(fill) = l b f, where "l" denotes the tank's length, "b" denotes its width, "f" denotes its level of water fill, and "V(fill)" is the filled volume of the tank.

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The light that hits the slits has a wavelength of [tex]5.692 *10^{-4} m[/tex]

Fringe separation = 2.90 mm = 0.0029 m

Slit separation = 0.420 mm = 0.00042 m

Screen distance from slits =2.14 mm = 0.00214 mm

Wavelength is given by the following relation;

Wavelength = Fringe Separation * Slit Separation / Distance from the slit to Screen

Thus,

Putting all the given values in the above formula,

We evaluate the wavelength in the following way, we get

Wavelength = [tex]\frac{0.0029 *0.00042}{0.00241}[/tex] = [tex]5.692 *10^{-4}[/tex] m

The light's wavelength when it hits the slits is [tex]5.692 *10^{-4}[/tex] m

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Yes, it is true that for a power system modeled by its positive sequence network both the bus admittance matrix and bus impedance matrix are symmetric.

Admittance: In a power system, Bus Admittance Matrix represents the nodal admittances of the various buses. With the help of the transmission line, each bus is connected to another other bus.

It is used to analyze the data that is needed in the load or a power flow study of the buses. It justifies the admittance and the topology of the network.

The primitive network matrices are the most basic and depend purely on the impedance or admittance of the individual elements. However, they do not contain any information about the behavior of the interconnected network variables.

So, it is necessary to transform the primitive matrices into more meaningful matrices which can relate to variables of the interconnected network.

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If the radius of the track is increased, the centripetal force necessary to keep the object revolving at the same speed decreases.

We know the formula for centripetal force as,

F = mv²/r

where, F is centripetal force

v is tangential velocity

r is radius

m is mass

From the above relation, it is clear that centripetal force is inversely proportional to radius. If radius increases, force should decrease and if radius decreases force should increase, in order to keep the object revolving at the same speed.

Suppose, the radius increases two times, then the force will be halved. This can be calculated by substituting 2r in place of r in the above formula.

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The tension in the cable is F = πEaV²r³/2d²

The work. done. by the cable. is W = πEaV²r²/4d

[tex]\mathbf{U_i-U_f=\frac{\varepsilon_0\pi r^2 V^2}{2d}-\frac{\varepsilon_0\pi r^2 V^2}{4d}}\mathbf{\Rightarrow U_i-U_f=\frac{\varepsilon_0\pi r^2 V^2}{4d}}[/tex]

The equation can be used to depict the electric field created between two circular plates of a capacitor if they are separated by a constant distance and supported by a cable.

E = V/d

E' = E/2

F = qv/2d

F = Eav2r2/2d2.

Assuming that dz has shifted the upper plate higher, we can express the tension's work as follows:

dw = T*dz

dz = F * dw

The cable's work is W = Eav2r2/4d, or W = Eav2r2/2z2*dz.

Before the top plate is raised, the electrical energy capacitor has the following amount of energy stored in it:

Ui = 1/2 Cv²

Ui = EaR2V2D

Yes, the work carried out by the cable is equivalent to the change in electrical energy that has been stored. The variation in energy previously stored

Ui = Eaπr²v²/4d

[tex]\mathbf{U_i-U_f=\frac{\varepsilon_0\pi r^2 V^2}{2d}-\frac{\varepsilon_0\pi r^2 V^2}{4d}}\mathbf{\Rightarrow U_i-U_f=\frac{\varepsilon_0\pi r^2 V^2}{4d}}[/tex]

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Answer: The final velocity of the neutron is 1.31 km/s.

Explanation:

To determine the final velocity of the neutron, we need to use the law of conservation of momentum. According to this law, the total momentum of a closed system (in this case, the neutron and the helium nucleus) is conserved. In other words, the total momentum before the collision must be equal to the total momentum after the collision.

We can use the following formula to calculate the momentum of an object:

p = mv

where p is the momentum, m is the mass of the object, and v is the velocity of the object.

The initial momentum of the neutron is:

p = 1.7 × 10-27 kg * 2.2 km/s = 3.74 × 10-26 kg*km/s

The initial momentum of the helium nucleus is zero, since it was stationary before the collision.

The final momentum of the helium nucleus is:

p = 6.6 x 10-27 kg * 0.53 km/s = 3.518 × 10-26 kg*km/s

Since the total momentum is conserved, the final momentum of the neutron must be equal to the initial momentum of the neutron minus the final momentum of the helium nucleus:

3.74 × 10-26 kgkm/s - 3.518 × 10-26 kgkm/s = p

p = 0.222 × 10-26 kg*km/s

To find the final velocity of the neutron, we can divide the momentum by the mass:

v = p / m

v = (0.222 × 10-26 kg*km/s) / (1.7 × 10-27 kg)

v = 1.31 km/s

So the final velocity of the neutron is 1.31 km/s.