A team of astronauts is on a mission to land on and explore a large asteroid. In addition to collecting samples and performing experiments, one of their tasks is to demonstrate the concept of the escape speed by throwing rocks straight up at various initial speeds. With what minimum initial speed esc will the rocks need to be thrown in order for them never to "fall" back to the asteroid? Assume that the asteroid is approximately spherical, with an average density =2.02×106 g/m3 and volume =1.71×1012 m3.Recall that the universal gravitational constant is =6.67×10−11 N·m2/kg2.

A Team Of Astronauts Is On A Mission To Land On And Explore A Large Asteroid. In Addition To Collecting

Answers

Answer 1
Answer: 117.626m/s
The escape velocity is given by the following equation:
(1)
Where:
is the Gravitational Constant and its value is
is the mass of the asteroid
is the radius of the asteroid
On the other hand, we know the density of the asteroid is and its volume is .
The density of a body is given by:
(2)
Finding :
(3)
(4) This is the mass of the spherical asteroid
In addition, we know the volume of a sphere is given by the following formula:
(5)
Finding :
(6)
(7)
(8) This is the radius of the asteroid
Now we have all the necessary elements to calculate the escape velocity from (1):
(9)
Finally:
This is the minimum initial speed the rocks need to be thrown in order for them never return back to the asteroid

Related Questions

6.
Sonography uses infrasonic waves to create images of objects found inside other objects.
True
MacBook Air
False

Answers

Answer:

False.

Explanation:

Sonography uses high-frequency sound waves, not infrasonic waves, to create images of objects found inside other objects. These sound waves bounce off the internal structures of the body and are detected by a transducer, which converts them into images that can be visualized on a screen.

Infrasonic waves are sound waves with frequencies lower than the range of human hearing, typically below 20 Hz.

A mass of 10kg suspended on a steel rod of length 2m and radius 1mm what is the elongation of the rod beyond it's original length (Take E = 200*10^9 Newton per metre square

Answers

The elongation of the rod beyond its original length would be 2.5 mm.

Elongation calculation

To elongation of the rod can be deduced using the formula:

ΔL = FL / AE

where:

ΔL is the elongationF is the force appliedL is the original length of the rodA is the cross-sectional area of the rodE is Young's modulus of elasticity of the material.

The cross-sectional area of the steel rod is given by:

A = π[tex]r^2[/tex]A = π[tex](0.001 m)^2[/tex] = 7.85 x [tex]10^{-7} m^2[/tex]

The force applied to the rod:

F = mgF = 10 x 9.81 = 98.1 N

Thus:

ΔL = (98.1 x 2) / ((7.85 x [tex]10^{-7[/tex]) x (200 x [tex]10^9[/tex] ))

ΔL = 0.0025 m = 2.5 mm

In other words, the elongation of the steel rod beyond its original length is 2.5 mm.

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What is the acceleration of a 650 kg racing camel that has a Ford net force of 897N

Answers

The acceleration of the racing camel is 1.38 m/s².

What is the acceleration of the racing camel?

From Newton's second law, force is expressed as;

F = m × a

Where is mass of object and a is the acceleration

Given that:

Mass of the camel m = 650 kg Net force f = 897NAcceleration of the camel a = ?

To determine the acceleration of the camel, pug the given values into the abovr formula and solve for a.

F = m × a

897N = 650 kg × a

Note that: Newton N is the same as kg·m/s²

Hence;

897kg·m/s² = 650 kg × a

Divide both sides by 650 kg

a = (897kg·m/s²) / (650 kg)

a = 1.38 m/s²

Therefore, the acceleration is 1.38 meters per second sqaure.

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2. Review the chart above. What information about ultraviolet radiation supports or
contradicts the safety of solar radiation exposure to astronauts on the international
space station?
The table shows the amount of time astronauts spent on the surface of Moon during

Answers

The information about ultraviolet radiation supports or contradicts the safety of solar radiation exposure to astronauts on the international space station. They have wore suits that protects the astronaut from the UV light.

A space station is a sort of space habitat because it can sustain a human crew in orbit for a lengthy period of time. Major landing or propulsion systems are absent. An artificial satellite, also known as an orbital station or orbital space station, is a kind of orbital spaceflight. To allow other spacecraft to dock and transfer personnel and cargo, stations need to have docking ports. Depending on the programmed, a given orbiting outpost has a different role. Military launches have also taken place, although scientific launches of space stations have predominated. astronaut have wore suits that protects the astronaut from the UV light.  

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A blue train of mass 50 kg moves at 4 m/s toward a green train of 30 kg initially at rest. What is the initial momentum of the blue train?
A. 20 kgm/s
B. 200 kgm/s
C. 50 kgm/s
D. 0 kgm/s

Answers

Answer:

B. 200 kgm/s

Explanation:

The initial momentum of the blue train can be calculated using the formula:

p = mv

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

The mass of the blue train is 50 kg and its velocity is 4 m/s. Therefore, the initial momentum of the blue train is:

p = 50 kg x 4 m/s = 200 kgm/s

Therefore, the initial momentum of the blue train is 200 kgm/s, which is option B.

B or 200 Kgm/s…. Let me know if I’m wrong

1 Consider a ring, sphere and Solidey clinder all with the same mass. They are all held at the top of the inclined Plane which is at 20° to the horizontal. the top of the inclined Plane is 1m high. The shapes are released simultaneously and allowed to roll down the inclined plane. Assume the abjects roll with out slipping and that they are all made from the same material. Assume the coefficient of static friction bin the objects and the plane is 0-3-
A) workout what order

they would get to the bottom of the Slope!
B) How long will it take each shape to reach the bottom of the Slope ?

C) which shapes have the greater moment

of inertia ?

D ) determine the linear acceleration(a)
e) calculate the tangential (linear) Veloci ty of each shapes-​

Answers

The ring will have the greater moment of inertia.

Acceleration of a body rolling down an inclined plane without slipping is given by,

α = gsinθ/(1 + K²/R²)

Acceleration of the ring,

α = gsinθ/(1 + R²/R²)

α = 1/2 gsinθ

Acceleration of the sphere,

α = gsinθ(1 + 5/2)

α = 2/7 gsinθ

Acceleration of the solid cylinder,

α = g sinθ(1 + 1/2)

α = 2/3 gsinθ

The ring has the highest acceleration. Therefore, the ring will reach the bottom of the slope first.

The ring will have the greater moment of inertia among the three.

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Brainliest for answer!! How does the light spectrum measured for a nearby star compare to the light spectrum of a distant galaxy that is moving rapidly away from the observer? Explain what causes the differences between the two spectra. Answer in 3-5 sentences please.

Answers

Answer:

The light spectrum measured for a nearby star can be used as a benchmark for more distant stars because two stars with identical spectra have the same intrinsic luminosity. Spectroscopy can be applied to light from a distant galaxy, but the dark lines in the solar spectrum give a unique pattern that can be used to identify the elements present in the star. The light spectrum of a distant galaxy that is moving rapidly away from the observer will be shifted towards the red end of the spectrum due to the Doppler effect, which causes the wavelengths of light to stretch out as the object moves away from the observer.

What is the S-P difference (sec)?
What is the amplitude (mm)?
What is the distance (km)?
What is the magnitude (M)?

Answers

(a) The S-P difference (sec) is 40 sec.

(b) The amplitude (mm) is 10 mm

(c) The distance (km) is 380 km

(d) The magnitude (M) is 4.5

What is the S-P wave difference (sec)?

The S-P wave difference (sec) is a measure used in seismology to determine the distance between a seismic station and an earthquake source.

From the graph, the S-P difference, that is between S and P = 40 s - 0 s

= 40 s

The distance (km) corresponding to 40 sec is 380 km.

The amplitude of the wave is the maximum displacement of the wave and it is equal to 10 mm.

The corresponding magnitude of the wave is 4.5.

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As clothing tumble in a dryer, they can become charged. If a small piece of lint with a charge of +1.62 E−19 C is attracted to the clothing by a force of 2.0 E−9 N, what is the magnitude of the electric field at this location?

0.38 E10 N/C
1.2 E10 N/C
3.2 E10 N/C
3.6 E10 N/C

Answers

Answer:

1.2 E10 N/C

Explanation:

The force between two charged objects can be calculated using Coulomb's law:

F = k * q1 * q2 / r^2

where F is the force, k is Coulomb's constant (k = 8.99 x 10^9 N m^2 / C^2), q1 and q2 are the charges of the two objects, and r is the distance between them.

Rearranging this equation to solve for the electric field at a point, we get:

E = F / q

where E is the electric field strength and q is the charge at that point.

Substituting the given values, we get:

E = (2.0 x 10^-9 N) / (1.62 x 10^-19 C)

E = 12345.68 N/C

Therefore, the magnitude of the electric field at this location is 1.235 x 10^4 N/C.

2.
How did Robert Boyle demonstrate that sound needs a medium through which to travel?
He found that an alarm watch in a vacuum did not make a
sound.
He found that the speed of sound varied under different
conditions.
MacBook Air
He found that an alarm watch under water did not make a
sound.
He recorded the time that distant pistol fire was heard.

Answers

In the 1600s, a scientist by the name of Robert Boyle made the first known demonstration of the fact that a sound cannot pass through void space. Boyle placed the clock in a glass jar with a tight lid.

How can an experiment demonstrate that sound travels through a medium?

Pump out the air from the sealed bell jar while putting an electrical bell inside. Set the electric bell to ringing. We cannot hear the sound that the bell makes with our ears. This indicates that sound waves require a material environment for propagation because they cannot move through a vacuum.

What justifies the notion that sound travels via a medium?

Since sound waves are carried from one location to another by the molecules of solids, liquids, and gases, sound requires a physical medium for propagation, such as a solid, liquid, or gas. Since there are no molecules in the vacuum that can vibrate and convey sound waves, sound cannot travel through it.

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A woman weighs 100 kg and wants to know the force that the heels of her different shoes put on the new carpet by standing on one foot. The different shoes, A, B, C, D have heels of area 1cm, 4cm, 8cm and 64cm.
Which heel applies greater force to the carpet?


Answer: ALL EQUAL
^^^^^^^^^^^^^^^^^^^^^^^
^^^^^^^^^^^^^^^^^^^^^^^
Answer: ALL EQUAL

Answers

Shoe D.

The heel of shoe D applies the greatest force to the carpet because it has the largest surface area in contact with it, and thus the largest force is distributed over that larger area.

Case (IV)
With the suspension point 30cm from the left edge of the meter stick, hang
a 200g mass 10cm from the left edge of the stick. Calculate the mass you must hang at a point 40cm to the right of the pivot point such that the stick hangs level and write it on the sketch.

Answers

The mass to be hung at a point 40cm to the right of the pivot point such that the stick hangs level is 15 g.

How to calculate mass?

To solve this problem, use the principle of moments which states that the sum of the clockwise moments about a pivot point is equal to the sum of the counterclockwise moments about the same pivot point. In this case, take the pivot point to be the suspension point of the meter stick.

Let x be the mass that needs to hang at a point 40cm to the right of the pivot point. Then, set up the following equation:

(clockwise moment) = (counterclockwise moment)

(0.2 kg) × (0.3 m) × (9.81 m/s²) = (x kg) × (0.4 m) × (9.81 m/s²) + (0.1 kg) × (0.1 m) × (9.81 m/s²)

Simplifying this equation:

0.05886 = 3.924x

x = 0.015 kg or 15 g

Therefore, we need to hang a 15 g mass at a point 40 cm to the right of the pivot point such that the stick hangs level.

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please help PLEASE NOW

Journal prompt to be answered in 2 fully developed paragraphs

Prompt: What are some products (or programs) that you could purchase to help your performance in your current physical activity? How would the product (or program help)? Do you really think it is effective? Use specific examples from your experience.

Answers

You could purchase a fitness tracker to help your performance in your current physical activity.

Fitness tracker would help you in the area of goal setting.

Fitness trackers are effective because they have helped my friends to improve workout routine.

What are some products and programs that do help to physical activity?

Wearable fitness trackers can monitor data like heart rate, number of steps taken, distance traveled, and number of calories burned.

Supplements including protein powders, creatine, and beta-alanine can enhance recovery, muscular growth, and endurance.

Working with a coach or personal trainer can help you attain your fitness objectives by offering personalized training regimens, comments on form and technique, and accountability.

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Consider a ring, sphere and Solidey clinder all with the same mass. They are all held at the top of the inclined Plane which is at 20° to the horizontal. the top of the inclined Plane is Im high. The shapes are released simultaneously and allowed to roll down the inclined plane. Assume the abjects roll with out slipping and that they are all made from the same material. Assume the coefficient of static friction bin the objects and the plane is 0-3-
a) worklout what order

they would get to the bottom of the slope.

b) How long will it take each shape to reach the bottom of the Slope ?

c) which shapes have the greater moment of inertia ?

d) determine the linear acceleration(a)
e) calculate the tangential (linear) Veloci ty of each shapes-​

Answers

Answer:

a) The order in which the shapes reach the bottom of the slope will be the sphere, solid cylinder, and ring.

b) The time it takes for each shape to reach the bottom of the slope can be calculated using the following equation:

t = (2d / g)^(1/2)

Where t is the time, d is the height of the inclined plane (1m in this case), and g is the acceleration due to gravity (9.8 m/s^2).

For the sphere:

t = (2 x 1 / 9.8)^(1/2) = 0.45 seconds

For the solid cylinder:

t = (2 x 1 / 9.8)^(1/2) x (5/7) = 0.36 seconds

For the ring:

t = (2 x 1 / 9.8)^(1/2) x (2/5) = 0.28 seconds

c) The moment of inertia depends on the shape of the object and how the mass is distributed around its axis of rotation. For a solid sphere, the moment of inertia is given by I = (2/5)MR^2, for a solid cylinder it is I = (1/2)MR^2, and for a ring it is I = MR^2. Therefore, the order of increasing moment of inertia is the ring, the solid cylinder, and the sphere.

d) The linear acceleration of each shape can be calculated using the following equation:

a = gsinθ / (1 + I / MR^2)

Where a is the linear acceleration, g is the acceleration due to gravity (9.8 m/s^2), θ is the angle of the inclined plane (20° in this case), I is the moment of inertia, M is the mass, and R is the radius.

For the sphere:

a = (9.8 x sin20) / (1 + (2/5)) = 2.34 m/s^2

For the solid cylinder:

a = (9.8 x sin20) / (1 + (1/2)) = 3.29 m/s^2

For the ring:

a = (9.8 x sin20) / (1 + 1) = 4.16 m/s^2

e) The tangential (linear) velocity of each shape at the bottom of the slope can be calculated using the following equation:

v = ωR

Where v is the tangential velocity, ω is the angular velocity, and R is the radius.

The angular velocity can be calculated using the following equation:

ω = (2a / R)^(1/2)

For the sphere:

ω = (2 x 2.34 / 0.05)^(1/2) = 21.8 rad/s

v = 21.8 x 0.05 = 1.09 m/s

For the solid cylinder:

ω = (2 x 3.29 / 0.05)^(1/2) = 30.7 rad/s

v = 30.7 x 0.05 = 1.53 m/s

For the ring:

ω = (2 x 4.16 / 0.05)^(1/2) = 36.4 rad/s

v = 36.4 x 0.05 = 1.82 m/s

mark me brilliant

Answer:

c

Explanation:

A satellite is in orbit around a planet. The orbital radius is 34 km and the gravitational acceleration at that height is 3.3 ms-2 . What is the satellite's orbital speed in m/s?

Answers

The orbital speed of the satellite orbiting around a planet of radius 34 Km is found to be 2.59 km/s.

To find the orbital speed (v) of the satellite, we can use the formula,

v = √(GM/r), gravitational constant (6.674 x 10⁻¹¹ N(m/kg)²) is G, mass of the planet is M, and orbital radius of the satellite is r. To calculate M, we can use the formula,

g = GM/r², rearranging this formula, we get,

M = gr²/G

Substituting the values, we get,

M = 3.3(34,000)²/(6.674 x 10⁻¹¹)

M = 6.06 x 10²⁰ kg

Now, substituting the values of G, M, and r into the formula for orbital speed, we get,

v = √((6.674 x 10⁻¹¹)(6.06 x 10²⁰)/(34,000))

v = 2.59 x 10³ m/s

Therefore, the satellite's orbital speed is approximately 2.59 km/s.

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What pressure does a 500N - pound girl produce while standing on the floor if the area of ​​the sole of one of her shoes is 60 cm²?​. pleaaasee guysss help meee

Answers

The pressure exerted by the girl is approximately 833,333.33 Pa (Pascals).

Please help me Quick !!!!

Answers

Answer:

Explanation:

Yes, an object can travel with a non-zero velocity even when the net external force on it is zero. The object in this case is moving to the right with constant velocity and will continue in its state of motion as long as there are no external unbalanced forces acting on it.  This is Newton's First Law of Motion (aka the Law of Inertia).

yes an object can travel with a non zero velocity.

A 0.530-kg cart moving at 0.572 m/s to the right collides elastically with a 0.25-kg cart initially at rest. The 0.25-kg cart then moves off rapidly and compresses a spring before the 0.530-kg cart can catch it again.

Answers

To solve this problem, we can use the conservation of momentum and the conservation of kinetic energy.First, let's find the velocity of the 0.530-kg cart after the collision. We can use the conservation of momentum:m1v1 + m2v2 = m1v1' + m2v2'where m1 and v1 are the mass and velocity of the 0.530-kg cart before the collision, m2 and v2 are the mass and velocity of the 0.25-kg cart before the collision, and v1' and v2' are the velocities of the carts after the collision.Plugging in the numbers, we get:(0.530 kg)(0.572 m/s) + (0.25 kg)(0 m/s) = (0.530 kg)v1' + (0.25 kg)v2'Solving for v1', we get:v1' = [(0.530 kg)(0.572 m/s) + (0.25 kg)(0 m/s)] / (0.530 kg + 0.25 kg) = 0.378 m/s to the rightSo the 0.530-kg cart moves off to the right at 0.378 m/s after the collision.Next, let's find the maximum compression of the spring. We can use the conservation of kinetic energy:(1/2)m2v2^2 = (1/2)kx^2where k is the spring constant and x is the maximum compression of the spring.We know the mass and velocity of the 0.25-kg cart before the collision (v2 = 0 m/s), so we can solve for k:k = 2(1/2)m2v2^2 / x^2 = m2v2^2 / x^2Plugging in the numbers, we get:k = (0.25 kg)(0 m/s)^2 / x^2 = 0This means that the spring constant is 0, which is not physically possible. Therefore, there must be an error in the problem statement or some missing information that would allow us to calculate the maximum compression of the spring.

b) A motorcycle moving at 75 mph starts to slow down at a constant rate of 0.25 m/s^2 for 15 seconds. Find its final velocity (in both m/s and mph) and the total distance (in meters) that it traveled during this 15 s timeframe.

Answers

The final velocity of the motorcycle is

29.78 m/s (66.7083 mph),

the total distance traveled during the 15-second timeframe is

516.98 meters.

How to find the final velocity

Convert the initial velocity from mph to m/s:

75 mph = 75 x 0.44704 m/s = 33.528 m/s

Using vf = vi + at

where

vf is the final velocity,

vi is the initial velocity

a is the acceleration, and

t is the time interval.

Plugging in the given values, we get:

vf = 33.528 m/s - (0.25 m/s^2)(15 s) = 32.59 m/s

convert the final velocity back to mph

32.59 m/s = 32.59 x 2.237 mph/m = 72.9 mph

distance traveled, d

d = vi*t + (1/2)at^2

d = 32.59 m/s * 15 s + (1/2)(-0.25 m/s^2)(15 s)^2

d = 516.98 m

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A block is attached to a spring and executes
simple harmonic motion according to x = 2.0
cos(50t), where x is in meters and t is in
seconds. The spring constant is k = 100 N/m.
What is the mass of the block?

Answers

Answer:

.04 kg

Explanation:

The equation for simple harmonic motion is x = A*cos(ωt), where A is the amplitude, ω is the angular frequency, and t is the time.

Comparing the given equation x = 2.0cos(50t) with the equation for simple harmonic motion, we see that A = 2.0 meters and ω = 50 radians/second.

The angular frequency is related to the spring constant and mass by the equation ω = sqrt(k/m), where sqrt denotes the square root.

Substituting the values given, we get:

50 = sqrt(100/m)

Squaring both sides and solving for m, we get:

m = 100/2500 = 0.04 kg

The second law of thermodynamics states that
a change in a system's energy is equal to the energy
transferred to the system.
energy cannot be created or destroyed.
energy can flow from a colder object to a warmer object
only if something does work.
the only way to reduce an object's temperature is to
increase the entropy of the environment.

Answers

Answer: energy can flow from a colder object to a warmer object

only if something does work.

Explanation: Consider the flow of water from a higher level to a lower level. There is no need to use energy to make this process occur. This type of process which does not need the application of energy to take place is said to be spontaneous. But to make water go up to the water tank, a pump must be used to make the process take place. This type of process which needs the use of energy to make it happen is said to be nonspontaneous.
 

but why not the only way to reduce an object's temperature is to

increase the entropy of the environment.?

coz the motion of particles decreases and their velocity decreases so they have less entropy at a lower temperature.

hope it helped:)

What force is responsible for the orbit of satellites?
- energy
- friction
- magnetism
- gravity

Answers

Gravity is the force responsible for the orbit of satellites. Gravity is an attractive force that acts between two objects with mass.

What is satellites?

Satellites are man-made objects that are sent into space to orbit around a planet or other celestial body. They are used for a variety of purposes, including communication, navigation, scientific research, weather forecasting, and more. Satellites are equipped with advanced technology that allow them to transmit signals and data back to Earth, helping to make our lives easier in many ways. They are powered by solar panels and come in a variety of shapes and sizes. They can be stationary, meaning they stay in the same position as they orbit, or they can be geostationary, meaning they stay in the same point relative to the Earth's surface. They are also capable of providing real-time data and images to Earth-based observers. By using satellite technology, we can gain a better understanding of our planet, its climate, and its inhabitants.

This force is what causes satellites to orbit around a planet or star, as the gravitational pull of the planet or star causes them to move in a curved path.

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Kinetic energy depends only on a system's_
Select all that apply
>
acceleration
height
mass
2
speed
volume

Answers

The answer for the I believe to be mass and speed

Answer: mass and speed

Explanation: Remember kinetic energy equals 1/2mv^2 so it is dependent on mass and velocity which is speed.

What is amplitude and phase in electrical and electronics circuit?

Answers

In electrical and electronics circuits, amplitude is the maximum value of a signal. This is known as the strength or intensity of the signal. Phase, can be seen as the timing relationship between two signals or waveforms. It tell the time it takes betwen the peaks or zero crossings of two waveforms

What more should you know about phase in electrical and electronics circuits?

In electrical and electronics circuits, phase tell us about the the relationship between currents in different parts of the circuit, For example in AC circuits with multiple components.

We the amplitude and phase of signals in electrical and electronics circuits is understood, it becomes easier to design and analyz circuits, and can even be used for troubleshooting and maintaining them.

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1.
Which of the following is not true concerning sound waves?
Sound requires a medium.
Sound waves are longitudinal waves.
MacBook Air
Sound requires a vibrating object.
Sound waves cause particles to vibrate perpendicular to
the direction of the wave.

Answers

Answer:

Sound waves cause particles to vibrate perpendicular to the direction of the wave.

Which of the following is not considered a bloodborne pathogen

Answers

Influenza virus is not considered  as a bloodborne pathogen. The correct answer is option D.

Bloodborne pathogens are infectious microorganisms that can cause disease when transmitted through contact with infected human blood or other body fluids.

They can include viruses, bacteria, and other microorganisms that can cause serious illness or even death.

Influenza virus is not considered a bloodborne pathogen because it is primarily a respiratory virus that spreads through droplets when an infected person talks, coughs, or sneezes.

It can also spread through contact with contaminated surfaces or objects, but it is not primarily transmitted through contact with blood or other body fluids.

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The probable question may be:

Which of the following is not considered a bloodborne pathogen

A. Hepatitis B virus

B. Human immunodeficiency virus (HIV)

C. Hepatitis C virus

D. Influenza virus

A megaphone amplifies sound by
all the above
increasing the range of frequencies that can be produced.
focusing sound energy into one specific direction.
spreading out the sound waves over a large area.

Answers

The answer to this question is All of the above

Why did Izzy fall when playing tug of war? Responses he tripped he tripped balanced forces balanced forces he was pushed he was pushed unbalanced forces

Answers

Answer:

he tripped ballanced forces ballanced forces

how old is alizea Martínez​

Answers

Answer: She passed at 19 years old.

Explanation:

You are a visitor aboard the New International Space Station, which is in a circular orbit around the Earth with an orbital speed of o=2.45 km/s
. The station is equipped with a high velocity projectile launcher, which can be used to launch small projectiles in various directions at high speeds. Most of the time, the projectiles either enter new orbits around the Earth or eventually fall down and hit the Earth. However, as you know from your physics courses at the Academy, projectiles launched with a sufficiently great initial speed can travel away from the Earth indefinitely, always slowing down but never falling back to Earth.

With what minimum total speed, relative to the Earth, would projectiles need to be launched from the station in order to "escape" in this way? For reference, recall that the radius of the Earth is E=6370000 m
, the mass of the Earth is E=5.98×1024 kg
, the acceleration due to gravity on the surface of the Earth is =9.81 m/s2
and the universal gravitational constant is =6.67×10−11 N·m2/kg2
.

Answers

Answer:

To calculate the minimum total speed required for the projectile to escape the Earth's gravitational pull, we can use the equation for escape velocity:

v_escape = sqrt(2GM/R)

where G is the gravitational constant, M is the mass of the Earth, and R is the radius of the Earth.

Plugging in the given values, we get:

v_escape = sqrt(26.67e-115.98e24/6370000)

v_escape = 11186.4 m/s

This is the minimum total speed required for the projectile to escape the Earth's gravitational pull. In order to achieve this speed, the projectile would need to be launched with a velocity of 11186.4 m/s relative to the Earth.

Explanation:

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