Horizontal lines are referred to as being parallel to a x-axis in coordinate geometry. A line is referred to as horizontal if two points on the line share the same y-coordinate points.
What does a graph's x-axis / horizontal line represent?The intersection of the vertical and horizontal (X axis) real number lines is shown on the axis graph (Y axis). The Y axis is known as the dependent variable of the data set, whereas the X axis is typically used to refer to the independent variable of the data set.
In the line graph, how does X show up?The horizontal x-axis and vertical y-axis are the two axes of a line graph (vertical). A different type of data is indicated at each of the points where the axes connect, and (0,0). The x-axis is referred to as an independent axis since the numbers it represents are not reliant on any of the variables being assessed.
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Larry finds a lens and shows it to his friends, Mirez and Sherly.
All three look through it. Larry looks at the window across the room with the lens and says the window looks upside down. Mirez said that he must be using it incorrectly, because when he looks at his thumb through the lens, it is definitely not upside down. Sherly says that she thinks it is broken, because when she looks through it, everything just looks blurry.
Using your understanding about image formation, explain each of their observations.
Larry observes that the window looks upside down because the lens forms an inverted image. When light passes through a convex lens, it is refracted (bent) towards the center of the lens. The degree of bending depends on the angle of incidence and the refractive index of the lens. This bending of light rays causes the image to be inverted.
Mirez observes that his thumb looks right side up because the orientation of the object being viewed through the lens matters. When an object is placed at a distance greater than the focal length of the convex lens, the lens forms a real and inverted image. However, when the object is placed at a distance less than the focal length of the lens, the lens forms a virtual and erect image. In this case, Mirez's thumb is closer to the lens than the focal length, and hence, the lens forms a virtual and erect image of the thumb.
Sherly observes that everything looks blurry because the lens is not able to form a sharp image. The blurriness is due to spherical aberration, which is a common problem in lenses. When light passes through the curved surface of the lens, the rays passing through the edges of the lens bend more than those passing through the center. This causes the light to converge at different points on the image plane, resulting in a blurry image. To overcome spherical aberration, lenses are designed with multiple curved surfaces, or with non-uniform thickness.
The lens that produces an upside-down image is called a convex lens. Hence, Larry finds the lens called a convex lens.
What is the convex lens?The lens that converges the ray of light is called a convex lens. The lens that curved inwards, has a thicker middle portion and thinner at the lower and the middle part.
Convex lenses produce virtual and real images depending on the object's position. It also produces an upside-down image. It also produces a magnified image.
From the observation,
The convex lens produces an upside-down image. The lens produces an upside-down image, when light passes through the lens, it bends toward the center. This bending of light rays causes an inverted image.
Mirez's observation is based on the focal length of the convex lens. When an object is placed at a larger distance than the focal length of the convex lens, it produces a real and inverted image whereas the object's distance is lesser than the focal length, it produces a virtual and erect image.
Hence, he placed his thumb closer to the convex lens, the focal length is decreased and it produces a virtual and erect image. Sherly saw the blurred image because the lens does not produce sharp images. The lens doesn't produce sharp images as it has certain spherical aberrations.
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Physics problem in the photo that I have no clue how to answer, please, and thank you!
The resistive force of friction (Fr) divided by the normal or perpendicular force (N) pushing the objects together yields the coefficient of friction (fr), which is a numerical value. It is expressed by the equation: fr = Fr/N.
What is the coefficient of friction μ?coefficient of friction, ratio of the frictional force opposing the motion of two surfaces in contact to the normal force pushing the two surfaces together.
Typically, it is represented by the Greek letter mu (). In terms of math, is equal to F/N, where F stands for frictional force and N for normal force. The things creating friction will determine the coefficient of friction. The value is often between 0 and 1, although it can also be higher. A number of 0 indicates that there is absolutely no friction between the items; superfluidity makes this feasible.
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Full Question ;
A concrete highway curve of radius 80.0 m is banked at a 18.0 degrees angle.
What is the maximum speed with which a 1100 kg rubber-tired car can take this curve without sliding? (Take the static coefficient of friction of rubber on concrete to be 1.0.)
A negative lightning strike occurs when a negatively charged cloud discharges its excess electrons to the positively charged ground. If you observe a cloud-to-cloud lightning strike, what can you say about the charge on the area of the cloud struck by lightning?
1. The area of the cloud that was struck by lightning is neutral.
2. The area of the cloud that was struck by lightning had a positive charge.
3. The area of the cloud that was struck by lightning had a negative charge.
The area οf the clοud that was struck by lightning had a negative charge, sο, οptiοn (d) is cοrrect.
What is electrοns ?The negatively charged atοm's electrοns are respοnsible fοr this. An atοm's tοtal negative charge, which is prοduced by all οf its electrοns, cοunteracts the pοsitive charge οf the prοtοns in the atοmic nucleus.
What is electric charge?Prοtοns and electrοns, which functiοn as charge carriers, frequently carry bοth pοsitive and negative electric charges. By mοving charges, energy is prοduced. Charge—alsο referred tο as electric charge, electrical charge, οr electrοstatic charge—is a prοperty οf a unit οf matter in physics and is denοted by the letter q.
Therefοre, The area οf the clοud that was struck by lightning had a negative charge, sο, οptiοn (d) is cοrrect.
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2.1 State the principle of conservation of linear momentum.
2.2 Calculate the magnitude of the velocity after the learner jumped on the
skateboard.
Answer:
2.1 The principle of conservation of linear momentum states that in the absence of any external forces, the total momentum of a system remains constant. This means that the total momentum before an event is equal to the total momentum after the event.
2.2 To solve the problem, we can use the principle of conservation of linear momentum, which states that the momentum of the system before the learner jumps on the skateboard is equal to the momentum of the system after the learner jumps on the skateboard.
Explanation:
PLEASEEEEEEE HELPPPPPPPPP
Follow these directions:
1. Let your partner hold a ruler or meter stick in his/her hand vertically between the thumb and index finger, making sure he/she holds the meter stick so that the zero mark is between his/her fingers with the 1 cm mark above it. Your friend should hold the meter stick toward the top end, while your fingers are open at the bottom end of the ruler, ready to catch it between your index finger and your thumb . You should not be touching the meter stick or ruler.
2.Have your partner release the meter stick or ruler. As soon as you see the ruler released, snap your fingers shut and catch it.
3. Record in a data table the centimeter mark that was closest to your fingers.
4.Repeat this procedure several times, and average your results.
5.Change centimeters to meters.
6. Then calculate your reaction time by using the formula above and 9.8 m/s2 for g.
7. Compare your reaction time with that of your partner. Write out your comparison and possible reasons for differences.
A particular insulating container has a total surface area of 1.10 m2 and walls that are 4.00 cm thick. Suppose that a 10.0 W electric heater keeps the inside of the container 13.0°C warmer than the temperature outside. What is the thermal conductivity k of the material that the container is made of? (Enter your answer in W/(m · °C).)
The thermal cοnductivity οf the material is 0.024 W/(m·K).
What is the heat transfer fοrmula?We can use the fοrmula fοr heat transfer thrοugh a material with a temperature difference and knοwn surface area:
Q/t = kA(T1-T2)/d
where Q/t is the rate οf heat transfer (pοwer) prοvided by the electric heater,
k is the thermal cοnductivity οf the material,
A is the surface area οf the cοntainer,
d is the thickness οf the walls,
T1 is the temperature inside the cοntainer, and
T2 is the temperature οutside the cοntainer.
Plugging in the given values:
Q/t = 10.0 WA = 1.10 m²d = 0.04 mT1 - T2 = 13.0 °C
We can rearrange the fοrmula tο sοlve fοr k:
k = Qtd / (A*(T1-T2))
Plugging in the values and cοnverting units tο SI units:
k = (10.0 W)(1 s)(0.04 m) / (1.10 m² * 13.0 K) = 0.024 W/(m·K)
Therefοre, the thermal cοnductivity οf the material is 0.024 W/(m·K).
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PLEASEEEEEEE HELPPPPPPPPP
Follow these directions:
Let your partner hold a ruler or meter stick in his/her hand vertically between the thumb and index finger, making sure he/she holds the meter stick so that the zero mark is between his/her fingers with the 1 cm mark above it. Your friend should hold the meter stick toward the top end, while your fingers are open at the bottom end of the ruler, ready to catch it between your index finger and your thumb . You should not be touching the meter stick or ruler.
Have your partner release the meter stick or ruler. As soon as you see the ruler released, snap your fingers shut and catch it.
Record in a data table the centimeter mark that was closest to your fingers.
Repeat this procedure several times, and average your results.
Change centimeters to meters.
Then calculate your reaction time by using the formula above and 9.8 m/s2 for g.
Compare your reaction time with that of your partner. Write out your comparison and possible reasons for differences.
We can see here that carrying out the experiment and comparing your reaction time with that of your partner, we see that if one person has a faster reaction time, possible reasons could be faster reflexes or better anticipation of when the ruler will be released.
What is reaction time?Reaction time is the interval of time that elapses between the presentation of a stimulus and the initiation of a response. It is the time it takes for an individual to process and react to a stimulus, such as a sound, sight, or touch.
Carrying the experiment, we assume that the data table is gotten thus:
Trial Centimeter Mark
1 20
2 17
3 21
4 19
5 18
To change centimeters to meters, divide the average centimeter mark by 100. So, the average centimeter mark is
(20+17+21+19+18)/5 = 19 cm,
which is equal to 0.19 meters.
To calculate reaction time, we can use the formula:
t = √(2d/g)
where t is the reaction time, d is the distance traveled by the ruler, and g is the acceleration due to gravity (9.8 m/s^2).
Assuming the distance traveled by the ruler is equal to the distance between the top of the ruler and the point where it was caught by the fingers, we can calculate the reaction time as follows:
t = √(2 x 0.19 / 9.8) = 0.197 seconds ≈ 0.2 seconds.
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If electricity costs $0.18 per kwh, how much does it cost to run the air conditioner in the problem above?
A)$5.76
B)$7.87
C)$9.45
D)$12.12
Answer:
the answer is A) $5.76.
We found in the previous problem that the air conditioner uses 32 kWh per day. To find the cost, we multiply the number of kWh by the cost per kWh:
32 kWh/day x $0.18/kWh = $5.76/day
So, it costs $5.76 per day to run the air conditioner.
Therefore, the answer is A) $5.76.
Why cant an object become positively charged by gaining protons?
Answer:
An object can become positively charged by losing electrons, but it cannot become positively charged by gaining protons. This is because the charge on an object depends on the balance of protons and electrons it has. Protons have a positive charge, while electrons have a negative charge. So, when an object gains electrons, it becomes negatively charged because it now has more negative charges than positive charges. On the other hand, when an object loses electrons, it becomes positively charged because it now has more positive charges than negative charges.
However, protons cannot be gained or lost easily because they are tightly bound within the atomic nucleus of an atom, and they are not free to move around like electrons. Therefore, the only way for an object to become positively charged is to lose electrons, not by gaining protons.
Explanation:
State the first law of thermodynamics and apply this to the system/surrounding model.
Answer:
The first law of thermodynamics, also known as the law of conservation of energy, states that energy cannot be created or destroyed, only transferred or transformed from one form to another. In other words, the total energy of a closed system and its surroundings remains constant.
When applying this law to a system/surrounding model, the energy exchanged between the system and its surroundings can take different forms, such as heat, work, or a combination of both. For example, if a gas is compressed in a piston, work is done on the gas by the surroundings, increasing the internal energy of the gas. Alternatively, if a gas is heated, energy is transferred to the gas from the surroundings, increasing the internal energy of the gas.
Overall, the first law of thermodynamics serves as a fundamental principle in the study of thermodynamics, allowing us to analyze and predict energy transfers and transformations in various physical and chemical systems.
Explanation:
Two point charges are arranged in a straight line.
The point charge q1 has a charge of +7 μC . The point charge q2 is located 0.02 m to the left of q1 and has a charge of +2 μC.
What is the net electrostatic force on q2?
Answer:
100 force
Explanation:
did math if not correct worth a search
a rocket is fired with an inital velocity of 100m/s at an angle of 55 degree above the horizontal.it explodes on the mountain side 12 second after its firing .A.what is the x and t cordinates of the rocket relative to its firing piont ? x and h B. time to reach the maximu height ( tmax ) ? C. total time of flight ? D. range? (R) E.h max ?
The rocket's x and t coordinates are 688.32 meters and 277.44 meters, respectively, from where it will launch.
What does velocity vs. speed mean?Velocity, as opposed to speed, refers to the pace & direction of such an object's movement as it moves down a path. In other respects, whereas velocity is a scalar, speed is really a scale parameter.
Is speed always the same as velocity?Speed does not necessarily have to match average velocity in magnitude. Many people mistakenly believe that cruising velocity and flow rate are merely two different labels for the same quantity. Nevertheless, average speed relies on both distance and displacement.
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Consider a situation where over the course of a 24-mile long run, a runner becomes increasingly tired. In the first hour he runs 12 miles, in the second hour 6 miles, in the third hour 3 miles, and so on, so that each hour he runs half the distance to go. How long will it take to finish the race?
The runner will take a full day to complete the race, assuming he maintains the same pattern of slowing down by half the previous hour's distance each hour.
How did we get this assertion?We can approach this problem by using a formula for the sum of an infinite geometric series, since the distances covered by the runner in each hour form a geometric sequence with a common ratio of 1/2. The formula is:
S = a / (1 - r),
where S is the sum of the series, a is the first term, and r is the common ratio.
In this case, the first term a is 12 miles, and the common ratio r is 1/2. We want to find the total distance S covered by the runner over the entire 24-mile race, so we can set:
S = 12 / (1 - 1/2) = 24
This means that the runner will cover the remaining 12 miles in the final hour, and so the total time taken to finish the race will be:
1 + 1 + 1 + ... (24 times) = 24 hours
So, the runner will take a full day to complete the race, assuming he maintains the same pattern of slowing down by half the previous hour's distance each hour.
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Examine two items that use more than one battery, such as a flashlight, a 2-way radio, or a battery operated toy. Look at the arrangement of the batteries in the item. Are they connected in series? For each item, state the number and type of batteries, the voltage of each battery and the total voltage
produced.
Flashlight: The flashlight typically uses multiple batteries, arranged in series to provide a higher voltage output.
What is the battery about?In continuation, The number and type of batteries used in a flashlight can vary depending on the model, but a common arrangement is to use two or three 1.5V AA batteries. The batteries are connected in series, with the positive end of one battery connected to the negative end of the next battery, and so on.
For example, if the flashlight uses three 1.5V AA batteries, the total voltage produced would be 4.5V (1.5V x 3).Secondly, 2-way radio:
A 2-way radio also typically uses multiple batteries, arranged in series to provide a higher voltage output. Again, the number and type of batteries used can vary depending on the model, but a common arrangement is to use four or six 1.5V AA batteries. The batteries are connected in series, with the positive end of one battery connected to the negative end of the next battery, and so on.
For example, if the 2-way radio uses six 1.5V AA batteries, the total voltage produced would be 9V (1.5V x 6).Therefore, Note that the arrangement of batteries in series increases the total voltage produced by the batteries.
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What is the wavelength of water waves which have a frequency of 0.60 Hz and a speed of 4.0 m/s?
Answer:
1.9 m/s
Explanation:
1 point Which two sentences best state the central ideas of Wiesel's speech? Remember those who were killed at Auschwitz. Allow memories of Auschwitz to help prevent similar tragedies. Understand that what happened at Auschwitz could never be repeated. Choose to move on from Auschwitz and embrace a hopeful future. Pay honor to those who survived Auschwitz.
The two sentences that best state the central ideas of Wiesel's speech are:
Remember those who were killed at Auschwitz.Allow memories of Auschwitz to help prevent similar tragedies.Elie Wiesel's speech
Elie Wiesel's speech focuses primarily on the Holocaust and the atrocities that were committed during that time, particularly at Auschwitz. The central ideas of his speech are:
Remember those who were killed at Auschwitz: Wiesel emphasizes the importance of remembering and honoring the memory of those who died at Auschwitz. He believes that we must never forget the victims of the Holocaust, and we must ensure that their memory lives on.Allow memories of Auschwitz to help prevent similar tragedies: Wiesel believes that by remembering the horrors of Auschwitz, we can work to prevent similar tragedies from occurring in the future. He believes that it is our duty to learn from the past and use our knowledge to create a better world.More on Wiesel's speech can be found here: https://brainly.com/question/30338903
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Two point charged objects produce an electric force on each other of 11 N. What will the force between them be if both charges increase by a factor of 2?
Answer:
the factor of 2is 78
Explanation:
7th 8th is 9th is 3th which is 90000
3. The Leatherback is the largest sea turtle. If one has a
kinetic energy of 12 J while swimming at 0.2 m/s, what is
his mass in kg?
The answer to the given question is 150Kg. The leatherback sea turtle weighs about 150 kg.
To calculate the mass of the Leatherback sea turtle, we can use the formula for kinetic energy:
KE = 1/2 × m × v²
where KE is the kinetic energy, m is the mass of the object, and v is the velocity.
Given that the Leatherback sea turtle has a kinetic energy of 12 J while swimming at 0.2 m/s, we can plug in these values into the formula and solve for the mass:
12 J = 1/2 × m × (0.2 m/s)²
12 J = 1/2 × m × 0.04 m²/s²
m = (12 J) / (1/2 × 0.04 m²/s²)
m = 150 kg
Therefore, the mass of the Leatherback sea turtle is approximately 150 kg.
The Leatherback sea turtle is known for being the largest of all living sea turtles, with an average weight of around 500 to 1500 pounds (225 to 680 kg). Its size and weight enable it to swim vast distances across the ocean, traveling from nesting beaches to feeding grounds.
By using the formula for kinetic energy and the given values of velocity and kinetic energy, we can calculate the mass of the Leatherback sea turtle. The mass of the Leatherback sea turtle is significant, weighing approximately 150 kg, which is required for it to be able to swim through the vast oceans.
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Do you guys have any ideas for physics projects??
Answer:
What all topics do you have?
Question : What is the relationship between Orbital Radius- a ) AU ) and Period- ( years )?
The relationship is , the square of the period of an orbit is proportional to the cube of its Orbital Radius.
What is the relationship between orbital radius?The relationship between orbital radius and period is described by Kepler's Third Law of Planetary Motion, which states that the square of the period of an orbit is proportional to the cube of its semi-major axis.
In other words, if we denote the orbital radius (semi-major axis) by "a" in units of astronomical units (AU) and the period by "T" in years, then:
a³ = (T²)k
where;
k is a constant of proportionality that depends on the mass of the central body around which the object is orbiting.For objects orbiting the sun, k is approximately equal to 1.
So, if you know the orbital radius of an object around the sun, you can use Kepler's Third Law to calculate its period, or vice versa.
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fish swimming in a horizontal plane has velocity v with arrowi = (4.00 î + 1.00 ĵ) m/s at a point in the ocean where the position relative to a certain rock is r with arrowi = (14.0 î − 2.80 ĵ) m. After the fish swims with constant acceleration for 19.0 s, its velocity is v with arrow = (23.0 î − 1.00 ĵ) m/s. (a) What are the components of the acceleration of the fish? ax = m/s2 ay = m/s2 (b) What is the direction of its acceleration with respect to unit vector î? ° counterclockwise from the +x-axis (c) If the fish maintains constant acceleration, where is it at t = 26.0 s? x = m y = m In what direction is it moving? ° counterclockwise from the +x-axis
Answer:
sorryyyyijyyyyyyyyyyyyyyyyyyyy&
Explanation:
soryyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy
Set the charged object in motion by dragging it and releasing it. What do you observe about the behavior of the field lines in the vicinity of the object
When a charged object is at rest, the electric field lines emanating from it are radially symmetric and point outward in all directions, forming a pattern that depends on the magnitude and sign of the charge. If the charged object is set in motion, it creates a changing electric field that propagates outward from the object at the speed of light.
How is the direction of the magnetic field line depicted?The direction of magnetic field lines is depicted using arrows or lines that indicate the direction of the magnetic field at each point in space. The convention for drawing magnetic field lines is that they always form closed loops, and the direction of the field is tangential to the bar at each point.
Does the electric field affect the magnetic field?Yes, electric fields can affect magnetic fields and vice versa. Electric and magnetic fields are intimately related and form two sides of the same coin, as described by Maxwell's equation of electromagnetism.
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A balloon has a charge of -1.0 x 10-6 C and is held 0.97 m away from a steel tube. If the force between them is -5.5 N, what is the charge of the tube?
We can use Coulomb's Law to solve this problem:
F = k * (q1 * q2) / r^2
where:
F = -5.5 N
k = Coulomb's constant (9.0 x 10^9 N·m^2/C^2)
q1 = charge of the balloon (-1.0 x 10^-6 C)
q2 = charge of the steel tube= ?
r = distance between the balloon and the steel tube (0.97 m)
Plugging in the given values and solving for q2:
-5.5 N = (9.0 x 10^9 N·m^2/C^2) * (-1.0 x 10^-6 C) * q2 / (0.97 m)^2
Solving for q2, we get:
q2 = (-5.5 N) * (0.97 m)^2 / [(9.0 x 10^9 N·m^2/C^2) * (-1.0 x 10^-6 C)]
q2 ≈ -6.4 x 10^-6 C
Therefore, the charge of the steel tube is approximately -6.4 x 10^-6 C.
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Use the work energy theorem to rank the final kinetic energy of a ball based on the initial kinetic energy Ki, the magnitude of a constant force F on the ball, the displacement of the ball, d and the angle, theta between the displacement of the ball and the net force on the ball. Rank from greatest kinetic energy (1) to least kinetic energy (4).
1. ki= 150 J, F= 10 N, d=15 m, theta= 90 degrees
2. Ki= 300 J, F= 200 N, d= 1.5 m, theta= 180 degrees
3. ki= 200 J, F= 25 N, d= 4 m, theta= 0 degreee
4. ki= 450 J, F= 15 N, d= 30 m, theta= 150 degrees
4.
Answer:
150 J
-300 J
300 J
256.8 J
Explanation:
Use the following equation: W = ΔK = Kf - Ki
Calculations below:
Ki = 150 J, F = 10 N, d = 15 m, θ = 90°
The work done on the ball is:
W = Fd cos θ = 10 × 15 × cos 90° = 0 J
Therefore, the final kinetic energy is:
Kf = Ki + W = 150 + 0 = 150 J
Ki = 300 J, F = 200 N, d = 1.5 m, θ = 180°
The work done on the ball is:
W = Fd cos θ = 200 × 1.5 × cos 180° = -600 J
Therefore, the final kinetic energy is:
Kf = Ki + W = 300 - 600 = -300 J
Ki = 200 J, F = 25 N, d = 4 m, θ = 0°
The work done on the ball is:
W = Fd cos θ = 25 × 4 × cos 0° = 100 J
Therefore, the final kinetic energy is:
Kf = Ki + W = 200 + 100 = 300 J
Ki = 450 J, F = 15 N, d = 30 m, θ = 150°
The work done on the ball is:
W = Fd cos θ = 15 × 30 × cos 150° = -193.2 J
Therefore, the final kinetic energy is:
Kf = Ki + W = 450 - 193.2 = 256.8 J
Explain how slavery transformed from modern times through the transatlantic slave trade
Answer:
While the transatlantic slave trade mainly involved enslaving people from West Africa and forcing them to work on plantations in the Americas, modern slavery is more widespread in countries across the world, including the UK. The Atlantic slave trade contributed to the activity of many provision and redistribution markets, and enabled the creation of large fortunes that were invested in highly diverse activities and forms of consumption.
Explanation:
hope that helps
Two piloted satellites approach one another at a relative speed of 0.25 m/s, intending to dock. The
first has a mass of 4.00 × 103 kg, and the second a mass of 7.50 × 103 kg. If the two satellites collide
elastically rather than dock, what is their final relative velocity?
The electricity received at an electric substation has a potential difference of 2.80 x 105 V. If the required output is 440 V, what should be the ratio of the turns of the step-down transformer?
A
Explanation: sorry sir but its required step up transformer for high voltage not step
convert 1 Celsius to Fahrenheit
What geologic feature would you be most likely to find at a divergent plate boundary where two oceanic plates move away from each other? a mid-ocean ridge a rift valley an island arc an ocean trench
Answer: When two plates are moving away from each other, we call this a divergent plate boundary. Along these boundaries, magma rises from deep within the Earth and erupts to form new crust on the lithosphere. Most divergent plate boundaries are underwater and form submarine mountain ranges called oceanic spreading ridges.
Explanation:
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A 2.0-kilogram particle has an initial velocity of (5.0i-4.0j) m/s. Sometime later, its velocity is (7.0i+3.0j) m/s. What work was done by the resultant force during this time interval?
the work done by the resultant force during this time interval is 106.0 J.
What is the principle that relates the work done by the net force on an object to its change in kinetic energy?
To find the work done by the resultant force on the particle, we need to use the work-energy principle, which states that the work done by the net force on an object is equal to its change in kinetic energy.
First, we need to find the net force acting on the particle. We can use Newton's second law, which states that the net force is equal to the mass times the acceleration:
F_net = m*a
To find the acceleration, we can use the formula:
a = (v_f - v_i) / t
where v_f is the final velocity, v_i is the initial velocity, and t is the time interval.
a = [(7.0i+3.0j) m/s - (5.0i-4.0j) m/s] / t
a = (2.0i+7.0j) m/s / t
Now we can calculate the net force:
F_net = m*a
F_net = 2.0 kg * (2.0i+7.0j) m/s / t
F_net = (4.0i+14.0j) N / t
Next, we need to calculate the work done by this net force during the time interval. Since the force is not constant, we need to use the work-energy principle in integral form:
W = integral(F_net dot ds)
where dot denotes the dot product, and ds is the infinitesimal displacement vector.
To perform this integration, we need to know the path of the particle. Let's assume that the particle moves in a straight line from its initial position to its final position.
Then, the displacement vector is given by:
ds = (v_f - v_i) * t
ds = [(7.0i+3.0j) m/s - (5.0i-4.0j) m/s] * t
ds = (2.0i+7.0j) m * t
Now we can calculate the dot product between the net force and the displacement vector:
F_net dot ds = (4.0i+14.0j) N / t dot (2.0i+7.0j) m * t
F_net dot ds = 8.0 N + 98.0 N
F_net dot ds = 106.0 J
Therefore, the work done by the resultant force during this time interval is 106.0 J.
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