A model rocket rises with constant acceleration to a height of 4.2 m, at which point its speed is 27.0 m/s. How much time does it take for the rocket to reach this height? What was the magnitude of the rocket's acceleration? Find the height of the rocket 0.20 s after launch. Find the speed of the rocket 0.20 s after launch.

Answer:

Explanation:

Given:

Length of each side of the cube, [tex]L=10\ cm[/tex]

The Elecric flux through one of the side of the cube is, [tex]\phi =-1 kNm^2/C.[/tex]

The net flux through a closed surface is defined as the total charge that lie inside the closed surface divided by [tex]\epsilon_0[/tex]

Since Flux is a scalar quantity. It can added to get total flux through the surface.

[tex]\phi_{total}=\dfrac{Q_{in}}{\epsilon_0}\\6\times {-1}\times 10^3=\dfrac{Q_{in}}{\epsilon_0}\\\\Q_{in}=-6}\times 10^3\epsilon_0\\Q_{in}=-6}\times 10^3\times8.85\times 10^{-12}\\Q_{in}=-53.1\times10^{-9}\ C[/tex]

So the the charge at the centre is calculated.

To determine the magnitude of acceleration, use the formula (final velocity - initial velocity) / time. To calculate the distance traveled during the braking period, use the formula (initial velocity + final velocity) / 2 * time.

The magnitude of acceleration can be calculated using the formula:

acceleration = (final velocity - initial velocity) / time

acceleration = (50 mi/h * 1.46667 ft/s - 74 mi/h * 1.46667 ft/s) / 3 s

The distance traveled during the braking period can be calculated using the formula:

distance = (initial velocity + final velocity) / 2 * time

distance = (74 mi/h * 1.46667 ft/s + 50 mi/h * 1.46667 ft/s) / 2 * 3 s

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Answer:

The final velocity of the car is 30 m/s.

Explanation:

Given that,

Initial speed of the car, u = 0

Acceleration of the car, [tex]a=5\ m/s^2[/tex]

Time taken, t = 6 s

Let v is the final velocity of the car. It can be calculated using first equation of kinematics as :

[tex]v=u+at[/tex]

[tex]v=at[/tex]

[tex]v=5\ m/s^2\times 6\ s[/tex]

v = 30 m/s

So, the final velocity of the car is 30 m/s. Hence, this is the required solution.

Answer:

Decreases.

Explanation:

Electric potential energy is the potential energy which is associated with the configuration of points charge in a system and it is the result of conservative coulomb force.

When the negatively charge ion is at the position of the negative probe than its potential energy is positive when it is move towards the positive probe it's potential energy becomes negative due to the negative ion.

Therefore, potential energy is decreases when negative charge ion moves through the water from negative probe to positive probe.

Answer:

percent abundance of the heaviest isotope is 78 %

Explanation:

given data

atomic weight = 48.68 amu

mass 1 = 47 amu

mass 2 = 48 amu

mass 3 = 49 amu

natural abundance = 10 %

to find out

percent abundance of the heaviest isotope

solution

we consider here percent abundance of the heaviest isotope is x

so here lightest isotope = 47 amu of 10 %   ..........1

and heaviest isotope = 49 amu of x       ................2

and middle isotope = 48 amu of 100 - 10 - x      ........3

so

average mass = add equation 1 + 2 + 3

average mass = 10% ( 47) + x% ( 49) + (90 - x) % (48)

48.68 = 4.7 + 0.49 x + 43.2 - 0.48 x

x = 0.78

so percent abundance of the heaviest isotope is 78 %

The largest force constant of the spring can be found by balancing the kinetic energy of the crate at the top of the ramp with the elastic potential energy of the compressed spring at the bottom of the ramp and taking into consideration the static friction.

To calculate the largest force constant of the spring at the bottom of the ramp, we would use Hooke's law which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position. This force can be represented by -kx, where k is the force constant and x is the displacement. The displacement in our scenario is the movement of the crate down the ramp. We know that at the base of the ramp, kinetic energy of the crate will be transformed into elastic potential energy as it compresses the spring.

The kinetic energy of the crate at the top of the ramp will be 1/2*m*v^2 (mass * velocity squared) and at the bottom it will be converted into the potential energy of the compressed spring represented by 1/2*k*x^2. Here, given mass of the crate as 1890/9.81 kg, its velocity as 1.8 m/s, and it travels 5m along the ramp.

Setting these two energies equal, we can find the value of spring constant k.

Also, based on the problem, the static friction must be overcome at the bottom of the ramp to avoid the crate rebound. This scenario involves the interplay of several fundamental concepts in physics including kinetic and potential energy, the work-energy principle, and concepts of kinetic and static friction. Different parts of the given information and reference text refer to these aspects of physics.

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Final answer:

The time it takes for the car to fall is 0.606 s and the horizontal velocity of the car is 0.497 m/s.

Explanation:

To find the time it takes for the toy car to fall, we can use the kinematic equation:

h = (1/2)gt^2

Where h is the height, g is the acceleration due to gravity, and t is the time. Rearranging the equation, we can solve for t:

t = sqrt(2h / g)

Plugging in the values, we have:

t = sqrt(2 * 1.807 / 9.8) = 0.606 s

To find the horizontal velocity of the car, we can use the equation:

v = d / t

Where v is the velocity, d is the horizontal distance, and t is the time. Plugging in the values, we have:

v = 0.3012 / 0.606 = 0.497 m/s

Answer:[tex]\theta =49.76^{\circ}[/tex] North of east

Explanation:

Given

Research station is 9.6 km away in [tex]42^{\circ}[/tex]North of east

after travelling 3.1 km [tex]25^{\circ}[/tex] north of east

Position vector of safari after 3.1 km is

[tex]r_2=3.1cos25\hat{i}+3.1sin25\hat{j}[/tex]

Position vector if had traveled correctly is

[tex]r_0=9.6cos42\hat{i}+9.6sin42\hat{j}[/tex]

Now applying triangle law  of vector addition we can get the required vector[tex](r_1)[/tex]

[tex]r_1+r_2=r_0[/tex]

[tex]r_1=(9.6cos42-3.1cos25)\hat{i}+(9.6sin42-3.1sin25)\hat{j}[/tex]

[tex]r_1=4.325\hat{i}+5.112\hat{j}[/tex]

Direction is given by

[tex]tan\theta =\frac{y}{x}=\frac{5.112}{4.325}[/tex]

[tex]\theta =49.76^{\circ}[/tex]

Answer:

Average velocity

[tex]v=\frac{d}{t}\\ v=\frac{10m}{70s}\\v=.1428 \frac{m}{s}[/tex]

Average speed,

[tex]S=\frac{D}{t}\\ S=\frac{90}{70}\\ S=1.29\frac{m}{s}[/tex]

Explanation:

(a)Average velocity

We have to find the average velocity. We know that velocity is defined as the rate of change of displacement with respect to time.

To find the average velocity we have to find the total displacement.

since displacement along east direction is 50m

and displacement along west=40m

so total displacement,

[tex]d=50m-40m\\d=10m[/tex]

total time,

[tex]t=28 s+42 s\\t=70 s[/tex]

therefore, average velocity

[tex]v=\frac{d}{t}\\ v=\frac{10m}{70s}\\v=.1428 \frac{m}{s}[/tex]

(b)Average Speed:

Average speed is defined as the ratio of total distance to the total time

it means

Average speed= total distance/total time

here total distance,

[tex]D= 50m+40m\\D=90m[/tex]

and total time,

[tex]t= 28s+40s\\t=70s[/tex]

therefore,

Average speed,

[tex]S=\frac{D}{t}\\ S=\frac{90}{70}\\ S=1.29\frac{m}{s}[/tex]

Answer:

The net Electric field at the mid point is 289.19 N/C

Given:

Q = + 71 nC = [tex]71\times 10^{- 9} C[/tex]

Q' = + 42 nC = [tex]42\times 10^{- 9} C[/tex]

Separation distance, d = 1.9 m

Solution:

To find the magnitude of electric field at the mid point,

Electric field at the mid-point due to charge Q is given by:

[tex]\vec{E} = \frac{Q}{4\pi\epsilon_{o}(\frac{d}{2})^{2}}[/tex]

[tex]\vec{E} = \frac{71\times 10^{- 9}}{4\pi\8.85\times 10^{- 12}(\frac{1.9}{2})^{2}}[/tex]

[tex]\vec{E} = 708.03 N/C[/tex]

Now,

Electric field at the mid-point due to charge Q' is given by:

[tex]\vec{E'} = \frac{Q'}{4\pi\epsilon_{o}(\frac{d}{2})^{2}}[/tex]

[tex]\vec{E'} = \frac{42\times 10^{- 9}}{4\pi\8.85\times 10^{- 12}(\frac{1.9}{2})^{2}}[/tex]

[tex]\vec{E'} = 418.84 N/C[/tex]

Now,

The net Electric field is given by:

[tex]\vec{E_{net}} = \vec{E} - \vec{E'}[/tex]

[tex]\vec{E_{net}} = 708.03 - 418.84 = 289.19 N/C[/tex]

Explanation:

a) Dark matter: a kind of matter we can't directly observe but that we can imply its presence in various observations including gravitational effects which can't be explained by accepting theories of gravity unless more matter is present. This is the reason why dark matter is thought to account for around 80% of the matter in the universe.

b)21cm Radiation: also called hydrogen line, is a spectral line emitted by neutral hydrogen, it has a frequency of 1420megahertz and 21 cm wavelength. In astronomy, this line is used to study the amount and velocity of hydrogen in the galaxy.

Milky way: it's a barred spiral galaxy with more than 200 billion stars, approximately 100000 light-years in diameter and the sun is located about 28000light years from the center.

From the outside its structure has the following characteristics:

Two fundamentals parameters of the milky Way are [tex]R_{0}[/tex] (the radial distance from de sun to the galactic center) and [tex]Θ_{0}[/tex], the galactic rotational velocity at [tex]R_{0}[/tex]

Einstein's Theory of General Relativity: general relativity is a metric theory of gravitation, that defies gravity as a geometric property of space and time, this means there's no gravitational force deflecting objects from their natural straight paths, but a change in properties of space and time that changes this straight path into a curve.

At weak gravitational fields and slow speed, this theory overlaps with Newton's.

Pulsars: they are rotating neutron stars that emit a focused beam of electromagnetic radiation its formation happens when a medium mass star dies and it maintains its angular momentum emitting a powerful blast of radiation along its magnetic field lines. They are useful to search for gravitational waves, and even to find extrasolar planets.

I hope you find this information interesting and useful! Good luck!

The total charge on a cloud when breakdown of the surrounding air begins is calculated using Gauss's Law. The breakdown field strength, radius of the cloud and permittivity of free space are needed. The number of excess electrons in the cloud is then found by dividing the total charge by the charge of an electron.

The charge q on a spherically symmetric object, such as our cloud, when an electric field E is induced on its surface can be calculated using Gauss's Law, which states that the total charge enclosed by a Gaussian surface is equal to the electric field times the surface area of the Gaussian surface divided by the permittivity of free space (ε0). In our case, E = Eb (the breakdown field strength), the radius of the sphere, r = 0.5km = 500m (half the diameter), and ε0 = 8.85 x 10^-12 C2/N·m2. Therefore, q = (4πr2Eb)ε0.

For question 2: To calculate the number of excess electrons in the cloud, we should recall that the charge of an electron is -1.602 x 10^-19 C. Therefore, the number of excess electrons, N, can be calculated using N = q / Charge of an electron.

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Final answer:

The race car driver is approximately 7.644 km from where she started.

Explanation:

To find the distance from where the race car driver started, we can use the Pythagorean theorem. We can consider the north-south movement as one leg of a right triangle, and the east-west movement as the other leg. The distance from the starting point is equal to the square root of the sum of the squares of the two legs. In this case, the north-south leg is 6.71 km and the east-west leg is 3.67 km. Using the Pythagorean theorem, the distance from the starting point is:

d = √((6.71 km)² + (3.67 km)²)

d = √(44.9041 km² + 13.4689 km²)

d = √(58.3730 km²)

d = 7.644 km

Therefore, the race car driver is approximately 7.644 km from where she started.

Answer:

a) 14×10⁹ years

b) 4.4×10¹⁷ seconds

Explanation:

1 billion years = 1000000000 years

1000000000 years = 10⁹ years

14 billion years

= 14×1000000000 years

= 14000000000 years

= 14×10⁹ years

∴ 14 billion years = 14×10⁹ years

b) 1 year = 365.25×24×60×60 seconds

14×10⁹ years = 14×10⁹×365.25×24×60×60

= 441806400×10⁹ seconds

Rounding off,  we get

= 4.4×10⁸×10⁹

= 4.4×10¹⁷ seconds

∴ 14 billion years = 4.4×10¹⁷ seconds

The basketball's velocity just before hitting the floor is approximately -6.26 m/s (downward), while just after it leaves the floor, it reaches around 5.42 m/s (upward). During the brief 0.02 seconds it's in contact with the floor, its average acceleration is enormous, about 584 m/s², and directed upward.

This question involves the physics concept of velocity and acceleration related to a bouncing basketball. Let's dig into the details one by one:

Using Physics, the velocity of an object just before it hits the ground can be calculated using the equation for motion that involves falling from a height namely v² = u² + 2gh, where u is the initial velocity, g is acceleration due to gravity, v is the final velocity and h is the height. Since the ball was released, the initial velocity (u) is 0, g is approximately 9.8 m/s² (negative because the ball is falling downwards), and h is -2.0 m (negative because it is below the release point). Solving for v, the equation transforms to v = sqrt(u² + 2gh) = sqrt(0 + 2*(-9.8)*(-2)) = sqrt(39.2) which is approximately 6.26 m/s (negative, indicating downward).

Assuming the ball reaches the height of 1.5 m with uniform acceleration, we can use the same equation, but this time treating it as a ground-to-air motion with initial velocity 0, g = 9.8 m/s² (positive because the motion is upward), and h = 1.5 m. Solving for v, we get v = sqrt(u² + 2gh) = sqrt(0 + 2*9.8*1.5) = sqrt(29.4) which is approximately 5.42 m/s (positive, indicating upward).

Acceleration can be calculated using the formula a = (v_final - v_initial) / t, where v_final is the final velocity, v_initial is the initial velocity, and t is the time. The change in velocity here is the difference between the velocity just after the ball leaves the floor and the velocity just before it hits the floor, i.e., (5.42 m/s - -6.26 m/s) = 11.68 m/s. Given that the ball is in contact with the floor for 0.02 seconds, the average acceleration is therefore a = (11.68 m/s) / 0.02 s = 584 m/s². This is considerably higher than g because while in contact with the floor, the ball is being rapidly decelerated and then accelerated in the opposite direction due to the impact force. The direction is upward, same as the final velocity.

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Answer:

A. [tex]H=\frac{v_{0}^{2}Sin^{2}\theta }{2g}[/tex]

B. 5556.1 m

Explanation:

A.

Launch speed, vo

Angle of projection = θ

The value of vertical component of velocity at maximum height is zero. Let the maximum height is H.

Use third equation of motion in vertical direction

[tex]v_{y}^{2}=u_{y}^{2}+2a_{y}H[/tex]

[tex]0^{2}=\left (v_{0}Sin\theta  \right )^{2}-2gH[/tex]

[tex]H=\frac{v_{0}^{2}Sin^{2}\theta }{2g}[/tex]

B.

u = 330 m/s

Let it goes upto height H.

V = 0 at maximum height

Use third equation of motion in vertical direction

[tex]v^{2}=u^{2}+2as[/tex]

[tex]0^{2}=330^{2}-2\times 9.8\times H[/tex]

H = 5556.1 m

Answer:

The frequency of motion is 5.8 Hz.

Explanation:

frequency of motion of any object is defined as the number of times the object repeats it's motion in 1 second.

mathematically frequency equals [tex]f=\frac{1}{T}[/tex]

where,

'T' is the time it takes for the object to complete one revolution. Since it is given that the ball completes 5.8 revolutions in 1 seconds thus the time it takes for 1 revolution equals [tex]\frac{1}{5.8}s[/tex]

Hence[tex]T=\frac{1}{5.8}s[/tex]

thus the frequency equals

[tex]\frac{1}{\frac{1}{5.8}}s^{-1}\\\\f=5.8s^{-1}=5.8Hz[/tex]

Answer:

5.8 Hz.

Explanation:

Given:

The frequency of the motion of a rotating object is defined the total number of revolutions the object makes in unit time. It is measured in units of Hertz (Hz) or per second.

It is given that the ball is making 5.8 revolutions in one second, therefore, its frequency of motion would be the same, i.e., 5.8 Hz.

The relativistic factor y (gamma) quantifies the relativistic effects based on the speed of an object. In your given case with v = 0.932c, gamma would be approximately 2.61, indicating significant relativistic effects. The provided options do not include this value, suggesting some error.

The dimensionless parameter used in relativity is denoted as y (gamma), and it is referred to as the relativistic factor. It is associated with the relative speed of an object and is defined by the equation y = 1/√(1 − (v²/c²)), where v is the object's velocity and c is the speed of light.

For your case where v = 0.932c, we'll substitute this into the formula and solve for y. This results in y being approximately equal to 2.61. This isn't available in the provided options, which would indicate an error in the question or provided choices.

Without a doubt, as y approaches and surpasses 1, the relativistic effects become more noticeable in an object's behavior. Significant relativistic effects mean that the classical interpretation, where we neglect these effects, becomes increasingly inaccurate.

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Answer:

The emission spectrum is always the same and can be used to identify the element and part of the Bohr model proposed that electrons in the hydrogen are located in particular orbits around the nucleos are True.

Explanation:

The Niels Bohr and quantic mecanic theorys are both based on the study of atomics spectrums. The atomic spectrum is a characteristic pattern of a light wavelenght emited wich is unique to each element.

For example, if we put some low pressure hydrogen in a glass tube and in the tp of the glass we apply a voltage big enough to produce a electric current in the hydrogen gas, the tube its going to emit light wich have a color dependig of the gas element in the interior. If we observe this light with a spectrometer we are going to see shining lines and each one of this lines have a wavelenght and diferent colors. This lines are called emission spectrum and the wavelength of that spectrum are unique to eache element.

Summering up, we can identify elements using the emission spectrum because any element produces the same spectrum than other element.

 According to Niels Bhor theory  the electron only can be in especific discret ratios to the nucleus. Where this electron moves himself in circukar orbits under the influence of the Coulomb attraction force.

Answer:

Explanation:

Total volume of the shell on which charge resides

= 4/3 π ( R₁³ - R₂³ )

= 4/3 X 3.14 ( 33³ - 20³) X 10⁻⁶ m³

= 117 x 10⁻³ m³

Charge inside the shell

-117 x 10⁻³ x 1.3 x 10⁻⁶

= -152.1 x 10⁻⁹ C

Charge at the center

= - 60 x 10⁻⁹ C

Total charge inside the shell

= - (152 .1 + 60 ) x 10⁻⁹ C

212.1 X 10⁻⁹C

Force between - ve charge and proton

F = k qQ / R²

k = 9 x 10⁹ .

q = 1.6 x 10⁻¹⁹ ( charge on proton )

Q = 212.1 X 10⁻⁹ ( charge on shell )

R = 33 X 10⁻² m ( outer radius )

F = [tex]\frac{9\times10^9\times1.6\times10^{-19}\times212.1\times 10^{-9}}{(33\times10^{-2})^2}[/tex]

F = 2.8 X 10⁻¹⁵ N

This force provides centripetal force for rotating proton

mv² / R = 2.8 X 10⁻¹⁵

V² = R X 2.8 X 10⁻¹⁵ / m

= 33 x 10⁻² x 2.8 x 10⁻¹⁵ /(  1.67 x 10⁻²⁷ )

[ mass of proton = 1.67 x 10⁻²⁷ kg)

= 55.33 x 10¹⁰

V = 7.44 X 10⁵ m/s

Answer:

(A). The rabbit travel the distance 138 m.

(B). The average speed of the hiker for the entire trip is 7.2 km/h.

Explanation:

Given that,

Speed = 12.0 m

Time = 11.5 second

(A). We need to calculate the distance

Using formula of distance

[tex]d=v\times t[/tex]

[tex]d =12.0\times11.5[/tex]

[tex]d=138\ m[/tex]

The rabbit travel the distance 138 m.

(B). Given that,

Distance = 5.10 km

Time = 1 hours

Distance 16.5 km

Time = 2 hours

We need to calculate the average speed of the hiker for the entire trip

Using formula of average speed

[tex]v=\dfrac{D}{T}[/tex]

Where, D = Total distance

T = Total time

Put the value into formula

[tex]v=\dfrac{5.10+16.5}{1+2}[/tex]

[tex]v=7.2\ km/h[/tex]

The average speed of the hiker for the entire trip is 7.2 km/h.

Hence, This is the required solution.

Answer:

The yearly accumulation for the current year is 130

Explanation:

Accumulation is defined as

input - output = accumulation

The accumulation rate is accumulation per unit of time (in this case a year)

The accumulation rate will then be the amount of births, plus the amount of immigrants minus the amount of deaths.

ar = 500*0.2 + 55 - 0.05*500

ar = 100 + 55 - 25

ar = 130

Answer:

Explanation:

a )  V = 3 cos(0.5t)

differentiating with respect to t

dv /dt = -3 x .5 sin0.5t

= -1.5 sin0.5t.

acceleration = - 1.5 sin 0.5t

when t = 3 s

acceleration = - 1.5 sin 1.5

= - 1.496 ms⁻²

v = 3 cos.5t

b )  dx/dt = 3 cos 0.5 t

dx = 3 cos 0.5 t dt

integrating on both sides

x = 3 sin .5t / .5

x = 6 sin0.5t

At t = 2 s

x = 6 sin 1

x = 5.05 m

Answer:

X(t) = 9.8 *t - 4.9 * t^2

Explanation:

We set a frame of reference with origin at the hand of the girl the moment she releases the ball. We assume her hand will be in the same position when she catches it again. The positive X axis point upwards.The ball will be subject to a constant gravitational acceleration of -9.81 m/s^2.

We use the equation for position under constant acceleration:

X(t) = X0 + V0 * t + 1/2 * a *t^2

X0 = 0 because it is at the origin of the coordinate system.

We know that at t = 2, the position will be zero.

X(2) = 0 = V0 * 2 + 1/2 * -9.81 * 2^2

0 = 2 * V0 - 4.9 * 4

2 * V0 = 19.6

V0 = 9.8 m/s

Then the position of the ball as a function of time is:

X(t) = 9.8 *t - 4.9 * t^2

Answer:

The acceleration of the bullet is 212.12 m/s²

Explanation:

Given that,

Force = 1.4 N

Mass = 6.6 g

We need to calculate the acceleration

Using newton's second law

[tex]F=ma[/tex]

[tex]a=\dfrac{F}{m}[/tex]

Where, F = force

m = mass

Put the value into the formula

[tex]a=\dfrac{1.4 }{6.6\times10^{-3}}[/tex]

[tex]a=212.12\ m/s^2[/tex]

Hence, The acceleration of the bullet is 212.12 m/s²

Answer with Explanation:

The person stating that the scientific law cannot be changed is not correct in his claim.

A scientific law can be defined as a statement that is deemed to explain or predict a natural process and is validated by repeated experiments.

In the light of above statement we may conclude that if the law is validated by experiments it should not be subjected to change but this is not the case as an experiment may be done in the future that invalidates the law.

A classical example of this case is the whole of Newtonian law of gravitation. Classically if we analyse this law it is perfect to describe the motion of solar system , planets ,satellites found in nature hence we should find it absolutely correct and since rockets are designed on the basis of this law we can safely assume that it is correct but it is not the case as the gravity is described radically differently by Einstein by his general theory of relativity thus invalidating the newton's law of gravity.

But we still use the Newton's law of gravity as the error's that are involved in the results of the newton's law are not significant to influence any radical departure from the design philosophy of objects such as rocket's or satellites. It always boils down to the accuracy that we need but theoretically we can say that newton's law of gravity was invalidated by Einstein's general theoty of relativity.  

Answer:

Energy density will be 14.73 [tex]J/m^3[/tex]

Explanation:

We have given capacitance [tex]C=225\mu F=225\times 10^{-6}F[/tex]

Potential difference between the plates = 365 V

Plate separation d = 0.200 mm [tex]0.2\times 10^{-3}m[/tex]

We know that there is relation between electric field and potential

[tex]E=\frac{V}{d}[/tex], here E is electric field, V is potential and d is separation between the plates

So [tex]E=\frac{V}{d}=\frac{365}{0.2\times 10^{-3}}=1825000N/C[/tex]

Energy density is given by [tex]E=\frac{1}{2}\varepsilon _0E^2=\frac{1}{2}\times 8.85\times 10^{-12}\times (1.825\times 10^6)^2=14.73J/m^3[/tex]

Answer:

1.004 × 10⁴ kPa

Explanation:

Given data

[tex]\frac{1.024g}{cm^{3}}.\frac{1kg}{10^{3}g} .\frac{10^{6}cm^{3}}{1m^{3} } =1.024 \times 10^{3} kg/m^{3}[/tex]

In order to prevent water from entering, the air pressure must be equal to the pressure exerted by the seawater at the bottom. We can find that pressure (P) using the following expression.

P = ρ × g × h

P = (1.024 × 10³ kg/m³) × (9.806 m/s²) × 1000 m

P = 1.004 × 10⁷ Pa

P = 1.004 × 10⁷ Pa × (1 kPa/ 10³ Pa)

P = 1.004 × 10⁴ kPa

Answer:

[tex]A. 8.29\times 10^{-18}\ J[/tex]

Explanation:

Given that:

p = magnitude of charge on a proton = [tex]1.6\times 10^{-19}\ C[/tex]

k = Boltzmann constant = [tex]9\times 10^{9}\ Nm^2/C^2[/tex]

r = distance between the two carbon nuclei = 1.00 nm = [tex]1.00\times 10^{-9}\ m[/tex]

Since a carbon nucleus contains 6 protons.

So, charge on a carbon nucleus is [tex]q = 6p=6\times 1.6\times 10^{-19}\ C=9.6\times 10^{-19}\ C[/tex]

We know that the electric potential energy between two charges q and Q separated by a distance r is given by:

[tex]U = \dfrac{kQq}{r}[/tex]

So, the potential energy between the two nuclei of carbon is as below:

[tex]U= \dfrac{kqq}{r}\\\Rightarrow U = \dfrac{kq^2}{r}\\\Rightarrow U = \dfrac{9\times10^9\times (9.6\times 10^{-19})^2}{1.0\times 10^{-9}}\\\Rightarrow U =8.29\times 10^{-18}\ J[/tex]

Hence, the energy stored between two nuclei of carbon is [tex]8.29\times 10^{-18}\ J[/tex].

Answer:

(a) [tex]v_{1}=0+a_{1}t_{1}   = a_{1}t_{1}[/tex].

(b) [tex]v_{final}=v_{initial}+at\\ v_{2}=v_{1}+a_{2}  t_{2}[/tex]

(c) [tex]219807.5m[/tex]  

Explanation:

To find an expression for the rocket's speed [tex]v_{1}[/tex] at time [tex]t_{1}[/tex], we use the constant acceleration model, which relates these variables with the expression:[tex]v_{final} =v_{intial}+at[/tex]. In this case, the initial velocity is null, because accelerates from rest. So, we take all values of the first interval, and we replace it to find the expression:

[tex]v_{1}=0+a_{1}t_{1}   = a_{1}t_{1}[/tex]. (expression for the first interval).

Then, we do the same process to find the expression of the second interval, we just replace the variables given:

[tex]v_{final}=v_{initial}+at\\ v_{2}=v_{1}+a_{2}  t_{2}[/tex]

In this case, you can notice that the initial velocity used is the one we obtain from the first interval, because the end of the first period is the beginning of the second period.

To calculate the total distance we have to sum the distance covered during the two intervals, that it's translated as: [tex]d_{total} = d_{1} + d_{2}[/tex].

Then, we use this equation to replace in each distance: [tex]v_{final}^{2} = v_{initial}^{2}  +2ad[/tex].

Isolating d we have:

[tex]d=\frac{v_{final}^{2}-v_{initial}^{2}}{2a}[/tex].

Now, we apply the equation to each interval to obtain [tex]d_{1}[/tex] and [tex]d_{2}[/tex]:

[tex]d_{1}=\frac{v_{1}^{2}-0}{2a_{1}}[/tex].

[tex]d_{2}=\frac{v_{2}^{2}-v_{1}^{2}}{2a_{2}}[/tex].

Before calculating the total distance, we need to know the magnitude of each speed.

[tex]v_{1}=a_{1}t_{1}[/tex]

[tex]v_{1}=(67)(39)=[tex]v_{2}=v_{1}+a_{2}  t_{2}= 2613\frac{m}{s^{2}}+34\frac{m}{s^{2}}(49sec)=4279\frac{m}{s}[/tex][/tex]

At last, we use all values known to calculate the total distance:

[tex]d_{total} = d_{1} + d_{2}[/tex]

[tex]d_{total} =\frac{v_{1}^{2}-0}{2a_{1}} + \frac{v_{2}^{2}-v_{1}^{2}}{2a_{2}}[/tex].

[tex]d_{total} =\frac{(2613)^{2} }{2(67)} +\frac{(4279)^{2}-(2613)^{2}  }{2(34)}\\ d_{total}=50953.5+168854=219807.5m[/tex]  

Therefore, the total distance traveled until the ends of the second period is [tex]219807.5m[/tex]. The rocket is in the Thermosphere.