How does newton’s three laws of motion explain how any type of rockets work?
Answers
Newton's laws explain how rockets work by providing a framework for understanding how they generate thrust through the burning of fuel, which creates an equal and opposite reaction, propelling the rocket forward.
Newton's three laws of motion are crucial to understanding how any type of rocket works. Here's how each of the laws applies to rockets:
1. Newton's First Law: The Law of Inertia: An object at rest tends to stay at rest, and an object in motion tends to stay in motion with a constant velocity, unless acted upon by an external force.
This law is important because it explains how rockets can overcome the force of gravity and achieve lift-off. When a rocket is sitting on the launchpad, it is at rest. But when the rocket engines ignite, they produce a force that propels the rocket forward. As the rocket moves, it gains momentum and continues to move forward with a constant velocity, even as it encounters the force of gravity pulling it back down towards Earth.
2. Newton's Second Law:The Law of Acceleration: The acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass.
This law explains how rockets can generate the necessary thrust to achieve escape velocity and leave Earth's gravitational pull. The rocket engines produce a force, or thrust, that propels the rocket forward. As the force of the thrust increases, the acceleration of the rocket also increases, allowing it to overcome the force of gravity and achieve lift-off. The mass of the rocket also plays a crucial role, as a lighter rocket requires less force to achieve the same acceleration as a heavier rocket.
3. Newton's Third Law: The Law of Action and Reaction: For every action, there is an equal and opposite reaction.
This law explains how rockets can generate thrust by expelling mass in the opposite direction. The rocket engines work by expelling a stream of hot gases out of the back of the rocket at a high velocity. According to Newton's Third Law, for every action (the expulsion of the gases), there is an equal and opposite reaction (the forward thrust of the rocket). This reaction force propels the rocket forward and allows it to overcome the force of gravity and achieve lift-off.
In summary, Newton's laws of motion provide the foundation for understanding how rockets work. By generating thrust through the expulsion of mass, rockets are able to achieve lift-off and overcome the force of gravity to reach space.
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Related Questions
A dog runs 300m North and sees the dog catcher and runs 120 m south .Whats the dogs displacement.The same jogger runs 3 miles around the track, starting and finishing in the same time after completing exactly 12 laps. What is the average velocity now
Answers
Answer:
1. 180 m
2. 1.5 miles/hour
3. 0 m/s
Explanation:
The complete question is
A dog runs 300 m North and sees the dog catcher and runs 120 m south Whats the dogs displacement.
A jogger runs north for 3.0 miles. If this took 2.0 hours, what is the jogger’s average velocity in miles per hour?
The same jogger runs 3.0 miles on the track, starting and finishing his run after completing exactly 12 laps around the track. What is his average velocity?
1. Displacement is how far the dog moves from the original starting point.
If the dog runs 300 m north, and then 120 m south, then the displacement from the starting point will be
displacement = 300 - 120 = 180 m
2. Displacement of the jogger = 3 miles
Time taken by the jogger = 2 hours
velocity of the jogger = ?
Velocity is = displacement/time
velocity = 3/2 = 1.5 miles/hour
3. velocity = displacement/time
if the jogger completes exactly 12 laps around the track, then the jogger will return to the starting point. This means that the jogger's displacement from the starting point is 0 miles
Jogger's velocity will therefore be = 0 m/s
Twelve seconds after starting from rest a freely-falling cantaloupe has a speed of?
Answers
Answer:
117.6 m/s
Explanation:
The formula of free-falling velocity is:
\(\displaystyle{v = u + gt}\)
where u is initial velocity, g is gravitational force (defined to be 9.8 m/s^2) and t is time.
Since cantaloupe does not have initial velocity then u will equal to 0 which makes the equation to:
\(\displaystyle{v = gt}\)
Since cantaloupe is free-falling and has its direction or motion same as gravitational force. Therefore, g = 9.8 m/s^2 and t = 12:
\(\displaystyle{v = 9.8 \times 12}\\\\\displaystyle{v = 117.6 \ \, \sf{m/s}}\)
Since distance and displacement have same magnitude in this case with positive value then speed will equal to velocity in sign (positive/negative).
Hence, speed for free-falling cantaloupe after 12 seconds will be 117.6 m/s
Which statements are true of the reactions in the Sun?Check all that applyA. They occur between hydrogen atoms.B. They occur only between helium atoms.c. High speed collisions cause the reactionsD. They are fission reactions
Answers
The sun is a dense collection of gas having high temperatures and high pressure.
This high temperature and pressure force the atoms of hydrogen to move faster and collide with each other.
This results in the nuclear fusion of hydrogen atoms into helium.
Thus, options A and C are correct.
how does 1 horsepower compare to 1 watt power
Answers
Answer:
they both use power how much it has
Explanation:
i think
Answer:
1 horsepower is a unit of power equal to 746 watts 1 watt is a unit of power equal to 1 joule per second.
Explanation: Working on it for homework right now and using my textbook
Another group of students also wants try to identify an unknown
metallic substance by determining its specific heat capacity.
Identification of this substance is done by comparing the
experimentally determined specific heat capacity with an accepted
value from a table of specific heat capacities.
For each of the 12 trials, the measurements were used to calculate
individual specific heat values for the metal. The average specific
heat for these trials was 213.89- J
and the
kg.
standard deviation was 111.51 J
kg. C
Using Table 14.1 from the OpenStax College Physics textbook, identify
what material or materials this unknown substance could potentially
be. Remember that the 95% confidence interval is ±2Ax, where Ax
is the standard uncertainty. Select all that apply.
Answers
According to the question Aluminum Iron Copper Silver and Lead could potentially be.
What is Copper?Copper is a chemical element with the symbol Cu and atomic number 29. It is a soft, malleable, and ductile metal with very high electrical and thermal conductivity. It is a reddish-orange metal that occurs naturally in the environment and is found in many different minerals. Copper has been used by humans since ancient times, and was the first metal to be used by humans. It is considered a base metal, meaning that it is not especially rare or valuable. Copper is often used in many different areas, such as electrical wiring, plumbing, and cooking utensils. It is also used in construction and manufacturing, and is a key component in many alloys. Copper is highly corrosion resistant, making it an ideal material for many different uses. Copper is also believed to have some health benefits, as it is an essential trace mineral and can be found in many foods and supplements. Copper is an important part of a healthy diet and is essential for life.
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Which sound wave features are being described? number of wavelengths over time. distance travelled over time.
Answers
The sound waves are defined as the frequency of sound waves and the speed of the sound wave.
What do you understand by Sound Wave?The sound wave is defined as the back and forth motion of the particles in an elastic medium of mechanical waves.
The number of wavelengths passing through a point per unit of time is known as the frequency of the sound wave. Frequency is the number of waves produced by a source per second, it is measured in hertz (Hz).
The period of the sound waves is defined as when a sound wave completes one complete oscillation it is termed as the period and we measure it per second.
The speed of the sound waves is defined as the distance traveled by the sound wave in one second it is measured in meters per second. The speed of the sound wave describes the frequency as well the wavelength also.
Thus the sound waves are defined as the frequency of sound waves and the speed of the sound wave.
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Answer:
frequency and speed
Explanation:
2022
In which one of the following situations will there be an increase in kinetic energy? A kicked football approaches its maximum height as it passes through the goal posts. О В. A filing cabinet is pushed across a rough floor at constant speed. OC. A fan is switched from low speed" to "high speed' OD A train is pulled up a mountain at a constant speed by a motor, O E. The planet Venus moves in its nearly circular orbit around the Sun
Answers
The situation in which there will be an increase in kinetic energy is C. A fan is switched from "low speed" to "high speed."
Kinetic energy is the energy of motion. When an object's speed increases, its kinetic energy also increases. In the case of the fan, switching from "low speed" to "high speed" will increase the speed of the fan blades, and therefore increase the kinetic energy of the fan.
In the other options, there is no increase in kinetic energy. A kicked football approaching its maximum height is actually losing kinetic energy as it slows down due to gravity. A filing cabinet pushed across a rough floor at constant speed has a constant amount of kinetic energy, as does a train pulled up a mountain at a constant speed. And the planet Venus moving in its nearly circular orbit around the Sun also has a constant amount of kinetic energy, as its speed does not change.
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for each of the following cases, indicate whether the work done is positive or negative. explain your answers. a) work done by an applied force in lifting a bucket of water upward. fa mg b) work done by the weight of the bucket c) work done by the applied force and mg if the bucket were lowered.
Answers
The work done in case a) is positive, in case b) is negative and in case c) is positive.
Work is said to be done when the displacement is occur in the direction of the applied force.
W = F×d×cosθ
Where F is the force, d is the displacement and θ is the angle between the displacement and the direction of the force.
In case a) as the work is done against the direction of the gravity so the work is positive. In case b) the weight of the buckets acts in downwards direction, that is the direction of the acceleration due to gravity. So the work is negative. In case c) the bucket were lowered, it means the displacement is in the direction of the applied force. Hence the work done is positive.
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if a dvd is spinning at 100 mph and has a radius of 14 inches, what is the linear speed of a point 3 inches from the center.
Answers
The linear speed of a point 3 inches from the center of a DVD spinning at 100 mph and with a radius of 14 inches is approximately 219.91 mph.
Linear speed is the rate at which an object moves along a circular path. It is measured in distance per unit time, such as miles per hour (mph) or meters per second (m/s).
The formula for linear speed is:
v = rω where:
v = linear speed
r = radius of the circle
rω = angular speed (measured in radians per second)
To calculate the linear speed of a point on a DVD spinning at 100 mph and with a radius of 14 inches, we need to convert the units of the given speed from mph to inches per second:
100 mph = (100 x 5280 feet) / 3600 seconds = 146.67 feet/second
146.67 feet/second = 1760 inches/second
Next, we need to find the angular speed ω of the DVD.
Angular speed is the rate at which an object rotates about an axis, and it is measured in radians per second. The formula for angular speed is:
ω = 2πf where:
ω = angular speed
f = frequency (measured in hertz)
π = 3.14159...
The frequency f of the DVD is equal to its rotational speed divided by the number of revolutions per second. One revolution is a complete turn around the circle, or 2π radians. Therefore, the frequency is:
f = (100 mph) / (2π x 14 inches x 3600 seconds/5280 feet) = 0.862 hertz
Finally, we can substitute the given values into the formula for linear speed:
v = rωv = (14 + 3) inches x 2π x 0.862 hertz = 219.91 inches/second
Therefore, the linear speed of a point 3 inches from the center of a DVD spinning at 100 mph and with a radius of 14 inches is approximately 219.91 mph.
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A linear machine has a magnetic flux density of 0.5 T directed into the page, a resistance of 0.25?, a bar length l = 1.0 m, and a battery voltage of 100 V.
(a) What is the initial force on the bar at starting? What is the initial current flow?
(b) What is the no-load steady-state speed of the bar?
(c) If the bar is loaded with a force of 25 N opposite to the direction of motion, what is the new steady-state speed? What is the efficiency of the machine under these circumstances?
Answers
(a) The initial force on the bar at starting is 200 N and the initial current flow is 400 A.
The initial force on the bar at starting can be calculated using the equation for force in a linear machine, which is given by the product of the magnetic flux density (B), the bar length (l), and the current (I) flowing through the bar. The force is given by:
Force = B * l * I
Given that B = 0.5 T, l = 1.0 m, and the battery voltage is 100 V, we can calculate the initial current flow (I) by dividing the battery voltage by the resistance of the bar (R). The equation for current is given by:
I = V / R
Substituting the given values, we get:
I = 100 V / 0.25 Ω = 400 A
So, the initial force on the bar at starting is 200 N (calculated as 0.5 T * 1.0 m * 400 A) and the initial current flow is 400 A.
(b) The no-load steady-state speed of the bar can be calculated using the equation for speed in a linear machine, which is given by the ratio of the force (F) on the bar to the product of the resistance (R) and the magnetic flux density (B). The equation for speed is given by:
Speed = F / (R * B)
Given that F = 200 N (as calculated in part (a)), R = 0.25 Ω, and B = 0.5 T, we can calculate the no-load steady-state speed of the bar by substituting these values into the equation:
Speed = 200 N / (0.25 Ω * 0.5 T) = 1600 m/s
(c) If the bar is loaded with a force of 25 N opposite to the direction of motion, the new steady-state speed of the bar can be calculated using the same equation for speed as in part (b), but with the force (F) being reduced by the load force of 25 N. So, the new force (F') on the bar is given by:
F' = F - Load force = 200 N - 25 N = 175 N
Substituting this value, along with the given values of R = 0.25 Ω and B = 0.5 T, into the equation for speed, we get:
Speed = 175 N / (0.25 Ω * 0.5 T) = 1400 m/s
To calculate the efficiency of the machine under these circumstances, we can use the equation for efficiency in a linear machine, which is given by the ratio of the output power to the input power.
The output power is given by the product of the force (F') on the bar and the speed (v), and the input power is given by the product of the battery voltage (V) and the current (I). So, the efficiency (η) is given by:
Efficiency = (F' * v) / (V * I)
Given that F' = 175 N (as calculated above), v = 1400 m/s (as calculated above), V = 100 V, and I = 400 A (as calculated in part (a)), we can substitute these values into the equation to calculate the efficiency:
Efficiency = (175 N * 1400 m/s) / (100 V * 400 A) = 0.1225 or 12.25%
So, the efficiency of the machine under these circumstances is 12.25%.
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To make a glass marble, cm3 of molten glass is poured into a mold. Jennet finds the circumference of the marble using the steps below.
V = 4/3Ïr3
1/6Ï =4/3Ïr3 1/8 = r3 r = 1/2cm
C = Ïr2
C = 1/4Ï cm2
Answers
The circumference of the glass marble is approximately 1.954 cm.
There seems to be an error in the calculation you provided. Let me walk you through the correct calculations to find the circumference of the glass marble.
First, we can use the formula for the volume of a sphere to find the radius of the marble:
V = (4/3)π\(r^3\)
We know that a certain volume of molten glass is poured into the mold, which we can represent as V. Therefore, we can rearrange the above equation to solve for r:
r = (3V/4)π\(r^3\)
Substituting the given value of the volume of the molten glass, we get:
r = (3 x cm / (4 ))π\(r^3\) = 0.62035 cm
Next, we can use the formula for the circumference of a circle to find the circumference of the marble:
C = 2π
r we just found, we get:
C = 2π x 0.62035 cm = 1.954 cm (rounded to 3 decimal places)
Therefore, the circumference of the glass marble is approximately 1.954 cm.
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the greenish blue of water is evidence for the group of answer choices absorption of red light. interaction between green and blue frequencies of light. absorption of greenish-blue light. reflection of red light. reflection of greenish-blue light.
Answers
The greenish-blue color of water is evidence for the absorption of red light.
The water absorbs the red frequency of light and reflects or transmits the remaining frequencies, which in this case are mainly green and blue. This absorption process is also known as selective absorption. It is the reason why water appears blue or greenish-blue in color. The interaction between green and blue frequencies of light also plays a role in the color of water, but it is not the main reason for the color we observe. Reflection of red light and reflection of greenish-blue light are not significant factors in the color of water.
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what matches ????????????????
Answers
Answer:
1st: Radiation
2nd: Conduction
3rd: Convection
Explanation:
I actually learned this before in school. Yay
An airplane is flying with a velocity of 185km / hr at an angle of 36 degrees north of east. What is the horizontal (eastward) component of the plane's velocity?
Answers
Explanation:
To find the horizontal (eastward) component of the plane's velocity, we need to determine the component of the velocity in the eastward direction.
Given:
Velocity magnitude: 185 km/hr
Angle north of east: 36 degrees
To calculate the eastward component, we can use trigonometric functions. The eastward component can be found by multiplying the velocity magnitude by the cosine of the angle.
Eastward component = Velocity magnitude * cos(angle)
Eastward component = 185 km/hr * cos(36 degrees)
Using a calculator or trigonometric table, we find that cos(36 degrees) is approximately 0.809.
Eastward component ≈ 185 km/hr * 0.809
Eastward component ≈ 149.965 km/hr
Therefore, the horizontal (eastward) component of the plane's velocity is approximately 149.965 km/hr.
In the diagram below, a 10-kilogram ball is fired with a
velocity of 500 meters per second from a 1,000 kilogram
cannon. What is the recoil velocity of the cannon?
A. 5 m/s
B. B) 2 m/s
C. C) 10 m/s
D. D) 500 m/s
Answers
Answer:
A) 5m/s
Explanation:
Momentum of ball in one direction=momentum of cannon in other direction
mv = mv
(10)(500)=(1000)v
5000=1000v
∴v=5m/s
When a ball is fired with a velocity its momentum remains conserved. The recoil velocity of the cannon is 5m/s.
What is recoil velocity?
The velocity with which the cannon is pushed backwards after firing is called the recoil velocity.
The momentum remains conserved . So, according to the momentum conservation principle, initial momentum is equal to the final momentum.
Mu +mu=Mv +mv
where, M is the mass of cannon and m is the mass of ball.
u is the initial velocity and v is the final velocity.
10 kg ball is fired with a velocity of 500 meters per second from a 1,000 kg cannon.
mu = Mv
(10)(500)=(1000)v
5000=1000v
v=5m/s
Thus, the recoil velocity of the cannon is 5 m/s.
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what is latent inhibition? the time it takes to move from a broad idea to a specific idea that can be implemented
Answers
An individual's capacity to notice and learn about a stimulus is diminished if they have previously been exposed to it in a neutral or irrelevant environment. This phenomenon is known as latent inhibition.
With the use of traditional training procedures, latent inhibition is frequently examined. In a typical experiment, an individual or an animal is repeatedly exposed to an unimportant stimulus with no noticeable results. In following trials, the neutral stimulus is coupled with a physiologically important stimulus (such as food or an electric shock).
The goal is to determine how the subject's capacity to build an association between the neutral stimulus and the important stimulus is affected by the subject's prior exposure to the neutral stimulus. According to the phenomena of latent inhibition, prior exposure to a stimulus without any discernible effects results in a reduction in attention or learning when the stimulus is subsequently encountered in a pertinent context.
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Use the data provided to calculate the gravitational potential energy of each cylinder mass. Round your answers to the nearest tenth.
3 kg: kJ
6 kg: kJ
9 kg: kJ
Answers
Answer: 3kg: 14.7 6kg: 29.4 9kg: 44.1
Explanation: just did it on Edge
Answer:
Explanation:
3 kg 14.7
6kg 29.4
9kg 44.1
what is the mass of density=2 g/mL volume= 20mL?
Answers
m = 40 g
Explanation:d = m/V => m = d×V
m = 2g/ml×20ml
= 40 g
what is the density of a substance that has a mass of 2.0 g , and when placed in a graduated cylinder the volume changed from 70 ml to 75 ml ?
Answers
A material with a mass of 2.0 g when placed in a graduated cylinder the volume changed from 70 ml to 75 ml has a density of 0.4 g/mL.
How do I calculate the substance's density?
We'll start by getting the substance's volume. This is attainable as follows:
Water volume: 70 mL
75 mL = volume of material + water.
Substance volume =?
Substance volume equals (substance volume plus water) - (Volume of water)
Substance volume = 75 - 70
5 mL is the substance's volume.
Finally, we will calculate the substance's density. Below is an example to help:
2.0 g is the substance's mass.
5 mL is the substance's volume.
Substance density =?
Mass / volume equals density.
Substance density = 2/5
0.4 g/mL is the substance's density.
The density is therefore 0.4 g/mL.
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Suppose you are riding on a merry – go – round and you move out to the edge. What happens to the rotational rate of the system?
a.) It decreases because there is a net force on the entire system, slowing it down.
b.) It increases because there is a net force on the entire system, speeding it up.
c.) It decreases because angular momentum is conserved and the moment of inertia increases.
d.) It increases because angular momentum is conserved and the moment of inertia increases.
e.) It decreases because angular momentum is conserved and the moment of inertia decreases
Answers
The correct answer is d.
It increases because angular momentum is conserved and the moment of inertia increases. When you move out to the edge of a merry-go-round, the moment of inertia of the system increases and the rotational rate of the system increases as well.
In physics, momentum is a vector quantity that can be expressed as the product of an object's mass and its velocity. Therefore, mass and speed are the main factors that affect the magnitude of a force of motion on an object.
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Momentum is usually not exactly conserved in a real world demonstration of momentum conservation. What is a possible reason for this fact?
Answers
Answer:
For any collision occurring in an isolated system, momentum is conserved. The total amount of momentum of the collection of objects in the system is the same before the collision as after the collision.
Explanation:
Hope this helps
What is the density of a block of wood with a mass of 12g and a volume of 6 cm3?
Answers
Answer:
The density is 2g/cm3.
The formula is basically Mass/Volume = density, so in this case... it is 12÷6 :))
URGENT: Two horizontal forces act on an object on a surface. There is a 20 Newton applied force to the left and a sliding frictional force of 5 Newtons to the right.
What is the net force on the object?
Answers
Answer:
xbzcfhkuvy
Explanation:
dvdvxvdzdx
Which wave has the greatest distance between consecutive troughs?
OA. A
OB. B
О с. с
OD. D
Answers
The wave with the greatest distance between consecutive troughs is the wave with the longest wavelength. This is because wavelength is defined as the distance between consecutive points with the same phase in a wave, which can be from crest to crest or from trough to trough.
What is a wave?A wave is a disturbance that travels through a medium or space, transferring energy from one point to another without causing any net displacement of matter. Waves can take many forms and can be described by several different characteristics, including amplitude, frequency, wavelength, and velocity.
In a mechanical wave, such as a sound wave or a water wave, the disturbance travels through a material medium, such as air or water. The wave causes the particles of the medium to vibrate back and forth, but does not actually transport any matter from one place to another.
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a block of mass 5 kg is being pulled along a board horizontally with a constant velocity; the coefficient of friction between the two surface is 0.25, then what is the frictional forces that opposes the motion
Answers
The block is in equilibrium, so the net forces parallel and perpendicular to the surface are
∑ F[para] = F[normal] - mg = 0
∑ F[perp] = F[pull] - F[friction] = 0
where mg is the weight of the block. It follows that
F[normal] = mg = (5 kg) (9.8 m/s²) = 49 N
and so the frictional force has magnitude
F[friction] = 0.25 F[normal] = 12.25 N ≈ 12 N
Help ASAP I’ll mark you as brainlister
Answers
Answer:
The MoonMarsThe ISS ( The international space station)What type of energy is at the top of a roller coaster PLZ HELP DUE TONIGHT
Oh and tell me a joke plz
Answers
Answer:
Gravitational potential energy
Explanation:
I can't think of any jokes right now.
determine the force of gravitational attraction between a 78 kg boy sitting 2 meters away from a 65 kg girl. circle your answer and include units
Answers
Answer:
The force of gravitational attraction is 8.454 x 10⁻⁸ N.
Explanation:
Given;
mass of the boy, m₁ = 78 kg
mass of the girl, m₂ = 65 kg
distance between the boy and the girl, r = 2 meters
The force of gravitational attraction is given as;
\(F = \frac{Gm_1m_2}{r^2}\)
where;
G is gravitational constant = 6.67 x 10⁻¹¹ Nm²/kg²
r is the distance between two masses, m₁ and m₂
\(F = \frac{Gm_1m_2}{r^2} \\\\F = \frac{(6.67 \times 10^{-11})(78 \times 65)}{2^2}\\\\F = 8.454 \times 10^{-8} \ N\)
Therefore, the force of gravitational attraction is 8.454 x 10⁻⁸ N.
(10 points) A uniform magnetic field B has constant strength b teslas in the z-direction 11.0. B = (0,0,01 (a) Verity that A = Bxr is a vector potential for B, where r = {x,y,0) (b) Calculate the flux
Answers
(a) A = B × r is a vector potential for B, where r = {x, y, 0}.
(b) The flux through a surface S can be calculated as Φ = ∫B·dA, where B is the magnetic field and dA is an infinitesimal area vector perpendicular to the surface.
Determine the vector potential?(a) To verify that A = B × r is a vector potential for B, we need to show that ∇ × A = B.
Using the cross product property, we have ∇ × A = ∇ × (B × r). Applying the vector identity (A × B) × C = B(A · C) - C(A · B), we get ∇ × (B × r) = B(∇ · r) - r(∇ · B).
Since ∇ · r = 0 (as r = {x, y, 0}), and ∇ · B = 0 (as B has a constant magnitude in the z-direction), we find that ∇ × A = B, verifying A = B × r as the vector potential for B.
(b) The flux through a surface S can be calculated as Φ = ∫B·dA, where B is the magnetic field and dA is an infinitesimal area vector perpendicular to the surface.
Given that B has a constant strength b teslas in the z-direction, the flux through surface S will be Φ = ∫B·dA = ∫(0, 0, b) · (dxdy) = b∫dxdy = bA, where A is the area of the surface S.
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A fish inside the water 12cm below the surface looking up through the water sees the outside world contained in a circular horizon. If the refractive index of water is 4/3 the radius of circle is
Answers
Answer:
13.6 cm
Explanation:
From Snell's law:
n₁ sin θ₁ = n₂ sin θ₂
In the air, n₁ = 1, and light from the horizon forms a 90° angle with the vertical, so sin θ₁ = sin 90° = 1.
Given n₂ = 4/3:
1 = 4/3 sin θ
sin θ = 3/4
If x is the radius of the circle, then sin θ is:
sin θ = x / √(x² + 12²)
sin θ = x / √(x² + 144)
Substituting:
3/4 = x / √(x² + 144)
9/16 = x² / (x² + 144)
9/16 x² + 81 = x²
81 = 7/16 x²
x ≈ 13.6
