A security review has flagged this architecture as vulnerable, and a Security Engineer has been asked to make this design more secure. The company has a short deadline and a second VPN connection to the Aurora account is not possible.
How can a Security Engineer securely set up the bastion host?
A. Move the bastion host to the VPC and VPN connectivity. Create a VPC peering relationship between the bastion host VPC and Aurora VPC.
B. Create a SSH port forwarding tunnel on the Developer's workstation to the bastion host to ensure that only authorized SSH clients can access the bastion host.
C. Move the bastion host to the VPC with VPN connectivity. Create a cross-account trust relationship between the bastion VPC and Aurora VPC, and update the Aurora security group for the relationship.
D. Create an AWS Direct Connect connection between the corporate network and the Aurora account, and adjust the Aurora security group for this connection.

Answer:Federal Law mandates that the steering or helm area of a power boat less than 20 feet in length must have Capacity Plate. The correct option is B.

Explanation: The capacity Plate indicates the maximum weight capacity and/or the maximum number of people that the boat can carry safely in good weather. Information on the capacity Plate includes the maximum number of adult persons, the maximum gross load, and the maximum size of engine, in horsepower,

Answer:

b. Capacity Plate.

Explanation:

According to the Federal Law, boats of less than 20 feet in length need to have a capacity plate that has to be in the steering area all the time. Also, this capacity plate has to show the maximum people capacity, weight and horsepower recommended. Because of this, the answer capacity plate.

Answer: Option (B) is the correct answer.

Explanation:

As we know that the temperature when the vapor pressure of liquid becomes equal to the atmospheric pressure surrounding the liquid. And, during this temperature liquid state of substance changes into vapor state.

But during this process of change in state of substance the temperature will cease to change for some time because unless and until all the liquid molecules do not convert into vapor state the temperature will not rise or change.

As the boiling point of water is [tex]100^{o}C[/tex] so the temperature ceases to change from [tex]98^{o}C[/tex] to [tex]102^{o}C[/tex].

Therefore, we can conclude that when heating water, during [tex]98^{o}C[/tex] to [tex]102^{o}C[/tex] temperature range the temperature will cease to change for some time.

Final answer:

Meteorology is the study of the atmosphere and weather patterns, aiming to predict weather in the short term. It is different from climatology, which deals with long-term climate trends, and is a part of the broader field of atmospheric science.

Explanation:

The term meteorology refers specifically to the study of the atmosphere and its various phenomena, including weather patterns. This scientific field encompasses the processes and forces that contribute to the weather and aims to predict weather in the short term, which is crucial for numerous aspects of daily life and safety. Despite some common misconceptions, meteorology does not equate to the study of meteors, and it should not be confused with climatology, which is the study of climate, or long-term weather patterns, over extended periods such as decades, centuries, and millennia.

Climatology and meteorology both fall under the broader umbrella of atmospheric science, which combines these and other disciplines that focus on the atmosphere.

Therefore, the correct answer to the student's question would be option B: Meteorology is the study of the atmosphere and its related weather systems.

Answer:

Venus, Earth, Mars, Mercury

Explanation:

The atmospheric pressure is determined by the gravitational attraction of the planet over the atmosphere.

Since the gravitational force is defined as:

[tex]F = G\frac{m1m2}{r^{2}}[/tex] (1)

Notice from equation 1, how the gravitational force depends on the masses of the two objects that are interacting and the distance to the square between them.

For this particular case, m1 is the mass of the planet and m2 is the mass of the gasses in the atmosphere. While the r is the distance between those two.

Venus has a more dense atmosphere and than the Earth, so it has a higher atmospheric pressure. The same case can be seen for the Earth and Mars.

Mercury is the one with the lower atmospheric pressure since it has a thin atmosphere as a consequence of his small size.

The Atmospheric pressure on terrestrial planets, highest to lowest, are generally Venus, Earth, Mars, and Mercury. These rankings can change based on the specific positioning of the planets in the provided images.

The terrestrial planets in our solar system, from Mercury through Mars, have significant differences in atmospheric pressure due to several factors like their distance from the sun, their composition, size, and presence of a magnetic field. Based on the data we have:

Venus has the highest atmospheric pressure among terrestrial planets, which is about 92 times the pressure of Earth's atmosphere at sea level.

Earth comes next. Its atmospheric pressure, also known as barometric pressure, varies depending on altitude but averages about 1 bar at sea level.

Mars has a very thin atmosphere with a surface pressure less than 1% of Earth's.

Mercury, being the smallest and closest to the Sun, has virtually no atmosphere and thus has the lowest surface atmospheric pressure among the terrestrial planets.

Please note that the ranking could change if the images in question show the planets placed differently from the order mentioned.

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Displacement is the difference between two co-ordinates so the origin doesn't matter.

Explanation:

       Instantaneous velocity = d/dt (position vector)

      d = vt + 1/2 at² is the displacement acceleration equation.

      d = u + at is the velocity displacement equation.

Displacement always has continuity with velocity and Acceleration.The average velocity is 0 if the displacement is 0.

Answer:

x = t³ − 12t² + 45t

Explanation:

Position is the integral of velocity.

x = ∫ v dt

x = ∫ (3t² − 24t + 45) dt

x = t³ − 12t² + 45t + C

The particle is originally at the origin, so at t = 0, x = 0.

0 = (0)³ − 12(0)² + 45(0) + C

0 = C

x = t³ − 12t² + 45t

Answer:

The major transition occurred as a consequence of this change in the universe at this time is that  b)The universe became transparent to light for the first time.

Explanation:

For the first 380,000 years or so, the universe was essentially too hot for light to shine. The heat of creation smashed atoms together with enough force to break them up into a dense plasma, an opaque soup of protons, neutrons and electrons that scattered light like fog. Then 380,000 years after the Big Bang, matter cooled enough for atoms to form during the era of recombination, resulting in a transparent, electrically neutral gas.

This set loose the initial flash of light created during the Big Bang, which is detectable today as cosmic microwave background radiation. However, after this point, the universe was plunged into darkness, since no stars or any other bright objects had formed yet.

Answer:

horizontal structural member that supports a floor. Beams are typically wood, cold formed metal framing or steel.

Joists

Horizontal timbers, beams or bars supporting a floor.

Answer:

1.Reduced pedal travel

2.  Firmer pedal feel

Explanation:

A power brake booster is defined as  a device that reduces the amount of force that it takes to apply hydraulic brakes.  Power brake boosters harness manifold vacuum to accomplish this. Brake booster multiply force on the pedal to the master cylinder

Vacuum booster works by pulling the air out of the booster chamber with a pump creating a low pressure system inside. As soon as  the driver steps on the brake pedal, atmospheric pressure is pushed into the booster by the input rod booster.

The advantage of cargos hydraulic brake booster over conventional vacuum booster is reduced pedal travel and firmer pedal feel

Final answer:

The 2020 NV Cargo's hydraulic brake booster offers increased braking power, improved response time, and reduced pedal effort compared to a conventional vacuum booster.

Explanation:

The benefits of the 2020 NV Cargo's hydraulic brake booster over a conventional vacuum booster include increased braking power, improved response time, and reduced pedal effort.

The hydraulic brake booster uses hydraulic pressure generated by a motorized pump to amplify the force applied to the brake pedal, resulting in more effective stopping power.

Unlike a vacuum booster, which relies on engine vacuum, the hydraulic brake booster is independent of engine conditions, providing consistent braking performance even under challenging operating conditions.

Answer:

b) 6

Explanation:

Given

v(t)=3t²+6t

X(0) = 2

X(1) = ?

Knowing that

v(t)=3t²+6t = dX/dt

⇒ ∫dX = ∫(3t²+6t)dt

⇒ X - X₀ = t³ + 3t²

⇒ X(t) = X₀ + t³ + 3t²

If  X(0) = 2

⇒  X(0) = X₀ + (0)³ + 3(0)² = 2

⇒  X₀ = 2

then we have

X(t) = t³ + 3t² + 2

when

t = 1

X(1) = (1)³ + 3(1)² + 2

X(1) = 6

After a time, t =1, the position of the particle has been 6. Thus, the correct option is b.

The velocity of the particle moving along the x-axis has been given by:

[tex]\rm v(t)\;=\;3t^2\;+\;6t[/tex]

The differentiation of v(t) in terms of x will be:

[tex]\rm \dfrac{dx}{dt}\;=\;3t^2\;+\;6t[/tex]

[tex]\rm \int dx\;=\;\int (3t^2\;+\;6t)\;dt[/tex]

differentiation with the limits if X be x and [tex]\rm x_0[/tex]:

x -  [tex]\rm x_0[/tex] = [tex]\rm t^3\;+\;3t^2[/tex]

In the given question, the value of  [tex]\rm x_0[/tex] = 2:

At time t = 0

x = [tex]\rm t^3\;+\;3t^2\;+\;x_0[/tex]

x = [tex]\rm (0)^3\;+\;3(0)^2\;+\;2[/tex]

x = 2.

To find the position of the particle at time =1, given, [tex]\rm x_0[/tex] = 2.

x = [tex]\rm (1)^3\;+\;3(1)^2\;+2[/tex]

x = 1 + 3 + 2

x = 6.

Thus, after time, t =1, the position of the particle has been 6. Thus, the correct option is b.

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Answer:PHARMING

Explanation:

Social engineering can be defined as an attempt to manage,change and regulate the future development and the behaviour of a society.

Common types of social engineering attack include; Watering hole, Pretexting, Phishing,Whaling attack, Baiting, PHARMING, and so on.

PHARMING is an attempt to redirect internet traffic from a legitimate site to a different identical-looking site. PHARMING is a spamming practice, a cyberattack and also, a type of phishing in which hackers use in stealing personal information from people on the internet.

PHARMING is done through the injection of malicious data or code into the victims' computer system. This injection is known as the DNS cache poisoning.

Explanation:

As the distance between a planet and the sun increase, the following quantities will decrease.

1. The gravitational force is given by :

[tex]F=G\dfrac{m_1m_2}{r^2}[/tex]

As the distance between a planet and the sun increase, the gravitational force decrease.

2. As the distance between a planet and the sun increase, it result in the decrease in its speed. Due to decrease in gravitational force, centripetal force acting on the planet should decrease. Since,

[tex]F_c=\dfrac{mv^2}{r}[/tex]

v is the tangential speed

So, the tangential speed must decrease.

3. The distance traveled in a day should decrease.

Hence, this is the required solution.

Answer:

the ratio F1/F2 = 1/2

the ratio a1/a2 = 1

Explanation:

The force that both satellites experience is:

F1 = G M_e m1 / r²       and

F2 = G M_e m2 / r²

where

Therefore,

F1/F2 = [G M_e m1 / r²] / [G M_e m2 / r²]

F1/F2 = [G M_e m1 / r²] × [r² / G M_e m2]

F1/F2 = m1/m2

F1/F2 = 1000/2000

F1/F2 = 1/2

The other force that the two satellites experience is the centripetal force. Therefore,

F1c = m1 v² / r    and

F2c = m2 v² / r

where

Thus,

a1 = v² / r ⇒ v² = r a1    and

a2 = v² / r ⇒ v² = r a2

Therefore,

F1c = m1 a1 r / r = m1 a1

F2c = m2 a2 r / r = m2 a2

In order for the satellites to stay in orbit, the gravitational force must equal the centripetal force. Thus,

F1 = F1c

G M_e m1 / r² = m1 a1

a1 = G M_e / r²

also

a2 = G M_e / r²

Thus,

a1/a2 = [G M_e / r²] / [G M_e / r²]

a1/a2 = 1

1. The ratio of the gravitational force on the first 1000 kg satellite to that on the second 2000 kg satellite is 1/2.

2. The ratio of the acceleration of the first 1000 kg satellite to that of the second 2000 kg satellite is also 1/2.

The gravitational force (F) between two objects is given by the equation:

F = G * (m1 * m2) / r²

Where:

- F is the gravitational force.

- G is the universal gravitational constant.

- m1 and m2 are the masses of the two objects.

- r is the distance between the centers of the two objects.

In this case, both satellites are in the same orbit around the Earth, so their distances from the center of the Earth (r) are the same.

Let's calculate the ratio F1/F2 for the first satellite (mass m1) and the second satellite (mass m2):

F1/F2 = (G * m1 * m_Earth) / r² / (G * m2 * m_Earth) / r²

F1/F2 = (m1 * m_Earth) / (m2 * m_Earth)

Now, we have m_Earth in both the numerator and denominator, so it cancels out:

F1/F2 = m1 / m2

So, the ratio of the gravitational force on the first satellite (F1) to that on the second satellite (F2) is simply the ratio of their masses, which is:

F1/F2 = 1000 kg / 2000 kg = 1/2

Now, let's calculate the ratio a1/a2 for the accelerations of the first satellite and the second satellite. The acceleration due to gravity is given by:

a = G * (m_Earth) / r²

Since both satellites are at the same distance (r) from the center of the Earth, the ratio a1/a2 is the same as the ratio of their masses:

a1/a2 = m1 / m2 = 1000 kg / 2000 kg = 1/2

So, the ratio of the acceleration of the first satellite (a1) to that of the second satellite (a2) is also 1/2.

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Each hin-ge exerts a horizontal force of 165 N on the door.

To find the horizontal components of the force exerted on the door by each hin-ge, we need to divide the weight of the door evenly between the two hing-es. The weight of the door is 330 N, so each hin-ge will support 330 N / 2 = 165 N.

Next, we need to determine the horizontal component of the force exerted by each hin-ge. Since the door's center of gravity is at its center and the hin-ge is 0.50 m from the top and 0.50 m from the bottom, the horizontal distance between the hin-ge and the center of gravity is the same for both hin-ges.

Using the formula for torque, τ = force × distance, we can calculate the torque exerted by the weight of the door about each hin-ge. Since the torque is equal to the force times the perpendicular distance from the axis of rotation to the line of action of the force, and the horizontal component of force is perpendicular to the distance, we can set up the following equation: torque = force × distance

Solving for the horizontal component of force, we have: force = torque / distance

By plugging in the torque value for each hin-ge and the distance value, we get:

force = 165 N × 0.50 m / 0.50 m = 165 N

Therefore, the horizontal components of force exerted on the door by each hin-ge are both 165 N.

Answer:

[tex]a_{c}= 4.44\frac{m}{s}[/tex]

Explanation:

When an object goes on a circular movement, it has a centripetal acceleration that always points toward the center of the circle, it is the responsible of the change of direction in the movement of the object. and that centripetal acceleration is related with the speed in the next way:

[tex]a_{c}=\frac{v^{2}}{r} [/tex], with v the speed, r the radius of the track that is half of the diameter (22.5 m)

[tex]a_{c}=\frac{10^{2}}{22.5} [/tex]

[tex]a_{c}= 4.44\frac{m}{s}[/tex]

Answer:

Cheek

Explanation:

Typically the scope is a bead on the gun's edge. Our eye must be in alignment with the muzzle, so that the proper placement of our head on the stock is crucial. The stock will fit snugly to our cheek as we put the pistol to our face with our head on other side just above gun's center line.

The correct answer is cheek.

Q. : How fast must a 3000 kg elephant move to have the same kinetic energy as a 65.0 kg sprinter running at 10m/s?

Answer:

The elephant must be 1.47 m/s fast to have the same kinetic energy with the sprinter

Explanation:

Kinetic Energy: This is the energy of a body in motion. It can be expressed mathematically as

Ek = 1/2mv²

Since the kinetic energy the elephant = the kinetic energy of the sprinter.

1/2m₁v₁² = 1/2m₂v₂².......................... Equation 1

Making v₁ the subject of the equation,

v₁ = √(m₂v₂²/m₁)................................. Equation 2

Where v₁ = speed of the elephant, m₁ = mass of the elephant, v₂ = speed of the sprinter, m₂ = mass of the sprinter.

Given: m₁ = 3000 kg, m₂ 65 kg, v₂ = 10 m/s

Substituting these values into equation 2,

v₁ =√(65×10²/3000)

v₁ = [tex]\sqrt{(6500)/3000[/tex]

v₁ =[tex]\sqrt{2.167}[/tex]

v = 1.47 m/s

Therefore The elephant must be 1.47 m/s fast to have the same kinetic energy with the sprinter

Answer:

200 feet

Explanation:

Most streets in US with bike lane, especially San Francisco, when entering a bicycle lane to make a right turn, you must enter 200 feet to the lane before making the turn.

Typically, when making a right turn, you should enter the bicycle lane no more than 200 feet before the turn. Always yield to cyclists before merging into the lane. These rules can vary by location.

Regarding the query about bicycle lanes and right turns, each city or state can have different regulations, but a common rule in many regions is that a driver intending to make a right turn must enter the bicycle lane no more than 200 feet before making the turn. This allows for a safe and orderly flow of both motorized and non-motorized traffic. It's important to check if this rule applies specifically to your region though, as variations can and do exist. Always make sure to yield to any cyclists in the bike lane before merging into it.

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Answer:

a) 80.0096 cm

Explanation:

This is an exercise of thermal expansion, we must calculate how much each material is dilated and the difference is the expansion of the measurement

The expression for linear dilation

            ΔL = α L₀ ΔT

Let's start with the steel

          ΔL / L₀ = 1.1 10⁻⁵ (40 -20)

          ΔL / L₀ = 22 10⁻⁵

Copper

          ΔL / L₀ = 1.7 10⁻⁵ (40-20)

          ΔL / L₀ = 34.0 10⁻⁵

What made the copper bar high is the differentiated being read

        ΔD =  ΔL / L₀_copper -  ΔL / L₀_Steel

The initial length of the steel balance is made equal to the length of the copper rod

        ΔL = (34 - 22) 10⁻⁵ / 80

        ΔL = 0.0096

For which the final length of the copper bar

        [tex]L_{f}[/tex] = L₀ +ΔL

         [tex]L_{f}[/tex] = 80 +0.0096

        [tex]L_{f}[/tex] = 80.0096 cm

The correct answer is a

Answer:

The projectile's speed as it passes the satellite is 1497.8 m/s.

Explanation:

Given that,

Radius of planet [tex]r=5.00\times10^{6}\ m[/tex]

Mass of planet [tex]m=3.95\times10^{23}\ kg[/tex]

Speed = 2000 m/s

Height = 1000 km

We need to calculate the projectile's speed as it passes the satellite

Using conservation of energy

[tex]E_{1}=E_{2}[/tex]

[tex]\dfrac{1}{2}mv_{1}^2+\dfrac{GmM}{r_{1}}=\dfrac{1}{2}mv_{2}^2+\dfrac{GmM}{R+h}[/tex]

[tex]\dfrac{v_{1}^2}{2}+\dfrac{GM}{r_{1}}=\dfrac{v_{2}^2}{2}+\dfrac{GM}{R+h}[/tex]

[tex]-\dfrac{v_{2}^2}{2}=-(\dfrac{GM}{R}-\dfrac{GM}{R+h}-\dfrac{v_{1}^2}{2})[/tex]

[tex]v_{2}^2=v_{1}^2+2GM(\dfrac{1}{R+h}-\dfrac{1}{R})[/tex]

[tex]v_{2}=\sqrt{v_{1}^2+2GM(\dfrac{1}{R+h}-\dfrac{1}{R})}[/tex]

Put the value into the formula

[tex]v_{2}=\sqrt{2000^2+2\times6.67\times10^{-11}\times3.95\times10^{23}(\dfrac{1}{5.00\times10^{6}+1000\times10^{3}}-\dfrac{1}{5.00\times10^{6}})}[/tex]

[tex]v_{2}=1497.8\ m/s[/tex]

Hence, The projectile's speed as it passes the satellite is 1497.8 m/s.

Answer:

17.7 mm

Explanation:

Poiseuille's law can be used to solve for the radius of the pipe

Volume per seconds flowing through the pipe = 7.3 / (51 × 60 s) = 0.0239 m³ / s

volume per seconds = π R^4 ( Pi - Po) / ( 8 ηL) where R is the radius of the pipe in mm, (Pi - Po) is the pressure difference in Pa, L is the length of the pipe in meters, and η is the viscosity in Pa.s

Pi - Po = ( 7.4 - 1.01) × 10^5 since 1 atm represent atmospheric pressure and it is equal to 1.01 × 10^5

Pi -Po = 6.39 × 10^5

substitute the values into the equation

0.00239 = 3.142 × (R^4) × 6.39 × 10^5 / ( 8 × 11 × 0.934)

cross multiply

0.00239 × 8 × 11 × 0.934 = (R^4) × ( 2.01 × 10^6)

make R subject of the formula

R^4 = (0.00239 × 8 × 11 × 0.934) / ( 2.01 × 10^6)

R = [tex]\fourthroot{9.77 * 10^-8}[/tex]  

R = 0.0177 m = 17.7 mm

Answer:

D) Anytime you change lanes

Explanation:

Correct way to execute a change of direction maneuver :

1 - The driver must warn by means of optical signals any maneuver that implies a lateral or backward displacement of his vehicle, as well as his intention to immobilize it or to slow down his gear in a considerable way. Such optical warnings will be made well in advance of the start of the maneuver, and, if they are bright, they will remain in operation until the end of the maneuver.

2 - Unless the road is conditioned or signposted to perform it in another way, it will be as close as possible to the right edge of the road, if the change of direction is to the right, and to the left edge, if it is to the left and the road is One way. If it is on the left, but the road through which it circulates is two-way traffic, it will adhere to the longitudinal mark of separation between the senses or, if it does not exist, to the axis of the road, without invading the area destined to the Wrong Way; when the road is two-way traffic and 3 lanes, separated by dashed longitudinal lines, should be placed in the center. In any case, the placement of the vehicle in the appropriate place will be carried out with the necessary advance and the maneuver in the least possible space and time.

3 - If the change of direction is on the left, it will leave the center of the intersection on the left, unless it is conditioned or marked to leave it on the right .

You must give a signal either by hand and arm or by a signal device anytime changing lanes. The correct option is (D).

Traffic lights, turn signals, horn blowing, and hand gestures are examples of signals used in the context of driving and transportation to express intentions and maintain order on the road.

Providing signals while driving is important for the safety of oneself and others. Signals are a safety measure to avoid accidents.

It is crucial to give other drivers advance notice of your intended lane change in order to safeguard their safety. Other drivers can anticipate your actions and modify their driving accordingly if you signal. It is a fundamental component of prudent and secure lane switching.

Hence, You must give a signal either by hand and arm or by a signal device anytime changing lanes. The correct option is (D).

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Answer:

He touts the benefits of e-programs by stressing that:

E-training are highly adjustable and flexible as well as employees can complete their training according to their ease.

Explanation:

The concept of E-training is becoming more and more popular now-a-days as it has the following advantages:

Due to these reasons, the manager wants the company to do the e-training programs.

Final answer:

a. C = A cos(φ), S = -A sin(φ).

b. A = √(C²+S²), φ = atan2(S, C).

Explanation:

Both expressions given for the general solution of a harmonic oscillator can be related to each other by using trigonometric identities.

The first expression, x(t)=Acos(ωt+φ), involves an amplitude A and a phase shift φ, whereas the second one, x(t) = Ccos(ωt) + Ssin(ωt), includes two parameters C and S for the coefficients of cosine and sine respectively.

To convert between the two forms, we use the cosine of a sum identity, which states that:

cos(a + b) = cos(a)cos(b) - sin(a)sin(b).

For part (A), expressing Acos(ωt+φ) in the form of Ccos(ωt) + Ssin(ωt), we get:
C = A cos(φ),
S = -A sin(φ).

For part (B), deriving A and φ in terms of C and S from the second equation, we use the Pythagorean identity and the definitions of cosine and sine to get:
A = √(C²+S²),
φ = atan2(S, C).

The constants C and S can be expressed in terms of A and ϕ as C = A cos(ϕ) and S = -A sin(ϕ). Conversely, A and ϕ can be expressed in terms of C and S as A = √(C² + S²) and ϕ = tan⁻¹(-S/C).

Explanation:

Part A: Expressing C and S in terms of A and ϕ

The given forms are:

We can use the trigonometric identity for the sum of angles to rewrite A cos(ωt + ϕ):

Comparing this with x(t) = C cos(ωt) + S sin(ωt), we identify:

Part B: Expressing A and ϕ in terms of C and S

From the relationships above:

Answer:

a)165,6 m

b)Directly over the target

Explanation:

a)To calculate the time that ball hits the ground after released, we will use the free fall formula below:

[tex]h=(1/2)*g*t^2[/tex]

h=65m

g=9,8m/s^2

[tex]65=0,5*9,8*t^2\\t^2=65/(0,5*9,8)\\t=3,6 sec[/tex]

Plane has the speed of 46m/s. Due to there is no air resistance weight remains the same speed while free falling. So the distance will be:

[tex]x=46*3,6=165,6 m[/tex]

b) Due to no air resistance plane and weight will be at the same speed on the air. Therefore, when the weight hits the ground plane will be directly over the target.

The pilot should drop the weight 165.6 m prior to the target, and the plane will have passed the target by the time the weight lands.

In Physics, we know that the motion of the dropped weight is governed by the equations of free fall, specifically that the time t for an object to fall from rest under gravity g, ignoring air resistance, from a height h is given by t = sqrt(2h/g). In this case, g = 9.81 m/s2 (earth's acceleration due to gravity), and h= 65 m. Therefore, if we put these values into the formula, we get t = sqrt(2*65/9.81) ≈ 3.6s.

For part A, the distance from the target where the pilot should drop the weight is the same as the distance the plane will travel in the time it takes for the weight to hit the ground, which is the product of the plane's speed (46m/s) and the time of flight t of the weight. Therefore, the distance is 46*3.6 = 165.6 m.

The answer for part B is that the plane will have passed the target when the weight hits the ground as it continues to move forward at 46 m/s.

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Answer:

25 times less than the Moon's mass

Explanation:

The asteroids are small, rocky objects that orbit the Sun. Although asteroids orbit the Sun like planets, they are much smaller than planets.

There are millions of boulder-size and larger rocks that orbit the Sun, most of them between the orbits of Mars and Jupiter.

The largest asteroid is Ceres with a diameter of 1000 kilometers. Pallas and Vesta have diameters of about 500 kilometers and about 15 others have diameters larger than 250 kilometers

Although  in the Solar System there are millions the asteroids, the combined mass of all of the asteroids is about 25 times less than the Moon's mass.

Then the answer for your question is:

25 times less than the Moon's mass

bibliographic source: www.astronomynotes.com

Answer:

If the canoe heads upstream the speed is zero. And directly across the river is  8.48 [km/h] towards southeast

Explanation:

When the canoe moves upstream, it is moving in the opposite direction of the normal river current. Since the velocities are vector (magnitude and direction) we can sum each vector:

Vr = velocity of the river = 6[km/h}

Vc = velocity of the canoe = -6 [km/h]

We take the direction of the river as positive, therefore other velocity in the opposite direction will be negative.

Vt = Vr + Vc = 6 - 6 = 0 [km/h]

For the second question, we need to make a sketch of the canoe and we are watching this movement at a high elevation. So let's say that the canoe is located in point 0 where it is located one of the river's borders.

So we are having one movement to the right (x-direction). And the movement of the river to the south ( - y-direction).

Since the velocities are vector we can sum each vector, so using the Pythagoras theorem we have:

[tex]Vt = \sqrt{(6)^{2} +(-6)^{2} } \\Vt=8.48[km/h][/tex]

When paddling upstream against a current of equal speed, the canoe remains stationary (0km/hr), as the man's paddling counteracts the downstream current. If the man were to paddle the canoe directly across the river, the speed of the canoe would be 6 km/hr, since the river's current doesn't directly impact the speed he can move perpendicular to the current.

This question deals with the concept of relative motion in Physics. When the man paddles the canoe upstream, he is going against the river current. Therefore, the effective speed of the canoe is the difference between his paddling speed and the river current speed, i.e., 6 km per hour (canoe speed) - 6 km per hour (current speed) = 0 km per hour.

When the man paddles the canoe directly across the river, the river's current doesn't directly affect his progress across the river. Thus, the speed of the canoe remains the speed with which the man paddles it, i.e., 6 km per hour. However, the path will not be straight because of the river's current. It is essential to understand these principles to solve similar problems involving relative motion.

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Answer:

Speed of Tarzan at the bottom of the swing is 12.5 m/s.

Explanation:

Given that,

Length of the vine, L = 31 m

The swing is inclined at an angle of 42 degrees with the vertical. We need to find the speed at the bottom of the swing if he pushes off with a speed of 6.00 m/s. using the conservation of mechanical energy as :

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

[tex]gh=\dfrac{1}{2}v^2[/tex]

h is the height of the height.

[tex]h=L-L\ cos\theta[/tex]

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

[tex]v=\sqrt{2gL(1-\ cos\theta)}[/tex]

[tex]v=\sqrt{2\times 9.8\times 31(1-\ cos(42))}[/tex]

v = 12.492 m/s

or

v = 12.5 m/s

So, his speed at the bottom of the swing if he pushes off with a speed of 6.00 m/s is 12.5 m/s. Hence, this is the required solution.

Option b.

By making use of the conservation of mechanical energy principle and using trigonometric relations, we find that Tarzan's final speed as he reaches the bottom of his swing is approximately 12.55 m/s, hence answer choice (B) 12.5 m/s is the closest.

To solve this problem, we need to recognize that this is a problem about the conservation of mechanical energy. Initially, Tarzan has both kinetic energy (because he pushes off with a speed of 6.00 m/s) and potential energy (because he is at a height above the lowest point of the swing). At the bottom of the swing, all of this energy will have been transformed into kinetic energy, as he is now at the lowest point of the swing, and hence has no potential energy.

The kinetic energy at the top of the swing is (1/2)*m*(6.00 m/s)^2 and the potential energy at the top of the swing is m*g*h. We can write the height 'h' in terms of the length of the vine (31.0 m) and the angle it makes with the vertical, theta (42.0°), as h = L*(1 - cos(theta)) = 31.0 m*(1 - cos(42.0°)).

As mechanical energy is conserved, the sum of kinetic and potential energy at the top of the swing will equal the kinetic energy at the bottom of the swing, which we can write as (1/2)*m*v_f^2. Equating and simplifying gives us a value of v_f = sqrt(2*g*L*(1 - cos(theta))(2*9.8 m/s^2*31.0 m*(1 - cos(42.0°)))).

Popping these numbers into a calculator gives an answer of approximately 12.55 m/s. Hence, the closest answer, and the one we should choose, is (B) 12.5 m/s.

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The spring in the hydraulic chamber is compressed by 24.5 cm from its unstrained position when a 40.0 kg rock is resting on the output plunger. This is calculated using Hooke's Law.

The key to solving this problem is understanding that the force exerted by a spring follows Hooke's Law, which states that F = -kx, where F is the force, k is the spring constant, and x is the displacement of the spring from its equilibrium position. Given that the spring constant k = 1600 N/m and the force exerted by the rock of mass 40.0 kg is F = mg = 40.0 kg * 9.81 m/s² = 392.4 N, we can find the displacement as follows:

x = F/k = 392.4 N / 1600 N/m = 0.245 m or 24.5 cm

Therefore, the spring is compressed by 24.5 cm from its unstrained position when the 40.0 kg rock is resting on the output plunger.

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The spring is compressed by 24.5 cm from its unstrained position.

The amount by which the spring is compressed from its unstrained position can be calculated using Hooke's Law. Hooke's Law states that the force exerted by a spring is directly proportional to its displacement from its equilibrium position. In this case, the force exerted by the spring is equal to the weight of the rock.

Using the equation F = kx, where F is the force exerted by the spring, k is the spring constant, and x is the displacement of the spring, we can rearrange the equation to solve for x:

x = F / k = (m * g) / k

Plugging in the values, we have x = (40.0 kg * 9.8 m/s²) / 1600 N/m.

Simplifying the equation, we get x = 0.245 m = 24.5 cm.

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Answer:

A capacitor

Explanation:

From experimental findings,the plates are connected to a 10Hz ac generator and a potential difference of 1.5V.The ITO is a transplant conducting material,charges accumulates on it when a voltage is applied to it.Exactly what is seen on a parallel plate capacitor