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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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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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
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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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
convert 1 Celsius to Fahrenheit
I need this tomorrow 50 points
Answer: NUMBER - 275.5 N
Explanation:
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
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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5. What is the area of this figure? Please show your work.
20 in.
7 in
6. What is the area of this figure? Please show your
10 ft
8 ft
6 ft
work.
Answer:
The area of the figure 7 in the area of 6 ft
helpme please help me ples
It is female (XO).A karyotype can be used to diagnose a chromosomal disorder by examining the number and arrangement of a person's chromosomes.
What is chromosomes ?Chromosomes are thread-like structures located in the nucleus of cells that carry genetic information in the form of genes. They are composed of DNA and proteins and are responsible for directing the development and functioning of cells. In humans, chromosomes come in pairs of 23, with one copy of each pair inherited from each parent.
For example, Down Syndrome is caused by an extra chromosome 21, Klinefelter Syndrome is caused by an extra X chromosome in males (XXY), and Turner Syndrome is caused by a single X chromosome in females (XO).
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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
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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Help me please I’m begging
The total resistance is 3 ohm
The current is 1.5 A
What is the total resistance of the circuit?To calculate the total resistance of a circuit, you need to determine the equivalent resistance of all the resistors in the circuit. The equivalent resistance is the single resistance value that could replace all the individual resistors and produce the same overall resistance.
1) This is a parallel circuit thus;
1/RT = 1/6 + 1/6
RT = 3 ohm
2) This is a series circuit thus;
RT = 4 + 6 = 10 ohm
Current = 15V/10 ohm
= 1.5 A
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Which type of wave interaction allows us to hear sounds around corners and under doors?
A. Diffraction
B.Absorption
C.refraction
D.reflection
Answer: Diffraction
Explanation: It is diffraction, because due to diffraction, sound waves bend on the corner as their size is of the order of wavelength of sound waves.
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.)
1. Find the displacement of a
farmer who walked 80.0 m
[0°] and then 60.0 m [335°].
it of
The farmer had a displacement of 133.4 m at an angle of -15.5° after moving 80.0 m [0°] and then 60.0 m [335°].
To find the displacement of the farmer who walked 80.0 m [0°] and then 60.0 m [335°], we need to use vector addition. First, we need to convert the distances and angles into their respective x and y components. The x component of the first displacement is 80.0 m (cos 0°) = 80.0 m, and the y component is 80.0 m (sin 0°) = 0 m. Similarly, the x component of the second displacement is 60.0 m (cos 335°) = 49.5 m, and the y component is 60.0 m (sin 335°) = -35.1 m (negative because it is in the fourth quadrant).
Next, we add the x and y components separately to find the resultant x and y components.
Resultant x component
= 80.0 m + 49.5 m
= 129.5 m
Resultant y component
= 0 m - 35.1 m
= -35.1 m
Now, we can use the Pythagorean theorem to find the magnitude of the resultant displacement:
|displacement| = √(129.5 m)² + (-35.1 m)²
= 133.4 m
Lastly, we can use inverse tangent to find the direction of the displacement:
θ = a tan (-35.1 m / 129.5 m) = -15.5°
Therefore, the displacement of the farmer who walked 80.0 m [0°] and then 60.0 m [335°] is 133.4 m at an angle of -15.5°.
Finding displacement through vector addition is a common problem in physics and is an important concept in understanding motion. By breaking down distances and angles into their respective x and y components, we can add them together to find the resultant displacement.
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Do you guys have any ideas for physics projects??
Answer:
What all topics do you have?
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
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:
The Hertzsprung-Russell diagram shown is divided into four sections.
C Section 3
n
Luminosity (Lsun)
Cortion A
10%
10⁰
10²
10-2
104
Hertzsprung-Russell Diagram
400 200 100
55
Temperature (x10² K)
Which section of the diagram includes the coolest, brightest stars?
A Section 1
B
Section 2
75
45
●
30
The section of the diagram that includes the coolest, brightest stars is A, Section 1.
How is the Hertzsprung-Russell diagram described?On the Hertzsprung-Russell diagram, the vertical axis represents luminosity, which is the total amount of energy emitted by a star per unit time. The luminosity is measured in units of solar luminosity, which is the amount of energy emitted by the Sun per unit time.
The section that includes the coolest, brightest stars is Section 1. This is because in this section, the stars have a low temperature (around 3,000-4,000 K) and a high luminosity (around 1,000-10,000 times that of the Sun). These stars are called red giants, and they are nearing the end of their lives. As they run out of fuel, their outer layers expand and cool, making them appear red and bright.
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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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Explain why a football accelerates
faster than a soccer ball when the
same amount of force is applied?
Answer: Answer is below <3 (The underlined part is the answer)
Explanation: The reason why an object with a smaller mass has a larger acceleration than an object with a larger mass if the same force acts on each is because the acceleration of an object depends on its mass as well as the force exerted on it, and if the mass is smaller than the other object than it is faster.
The reason why a football accelerates faster than a soccer ball when the same amount of force is applied is because of the difference in their masses. The acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass. This means that the smaller the mass of an object, the greater the acceleration it experiences when the same amount of force is applied to it.
A football is typically smaller and lighter than a soccer ball, so when the same amount of force is applied to both balls, the football experiences a greater acceleration due to its lower mass. This is consistent with Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass.
Additionally, the surface area and shape of the balls can also affect their acceleration. A football is typically more aerodynamic with a pointed shape that reduces air resistance, allowing it to move through the air more easily and accelerate faster. In contrast, a soccer ball has a more spherical shape that can create more air resistance, slowing down its acceleration.
Therefore, the mass, shape, and surface area of the ball are all factors that can affect its acceleration when a force is applied.
Find I1, V1, and V2 for the circuit shown in Fig. 4
From the given circuit, the value of I1 = -4 Amp, V1 = -4 V, and the V2 = 4V. Ohm's law has three different variations that are related to voltage, current, and resistance. The relationship between the voltage across the terminals and the resistor's resistance determines the current for a constant flow of current.
What is the tenet of Ohm's law?According to Ohm's law, the voltage across a conductor determines how much current flows through it. For many materials, including metals, this is true so long as the temperature (as well as other physical parameters) stay constant.
What does "nodal analysis" mean?Any electrical network may be solved using nodal analysis, which is what it is called. the formula used to determine how much voltage is shared across circuit nodes. Since the node voltages are with respect to the ground, this method is also referred to as the node-voltage method.
Applying KCL,
I1 = -1 -3
I1 = -4 A
Applying concept of super-node,
V2 = 4V
[tex]\frac{4-V1}{2} -1-3=0[/tex]
[tex]2-\frac{V1}{2} =4[/tex]
[tex]\frac{-V1}{2} =4-2[/tex]
[tex]V1=-4V[/tex]
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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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A rocket at rest on the ground with initial mass 20,000 kg, 80% of which is fuel, burns 200kg/s as it flies
directly upwards. The exhaust gas exits the rocket at a relative speed of 1.80 km/s. Find (a) the thrust of
the rocket, (b) how long it takes to exhaust its fuel, and (c) the rocket’s speed at the end of its engine burn.
Assume g is constant and neglect air resistance.
For Part A I got: 360,000 Newtons, Part B: 20 Seconds, Part C 205.658 m/s
Are my answers correct?
To check your answers, we can use the following equations:
(a) Thrust = (mass flow rate of exhaust gas) * (exhaust velocity of gas) + (initial mass of rocket) * (acceleration due to gravity)
(b) Time to exhaust fuel = (0.8 * initial mass of rocket) / (mass flow rate of exhaust gas)
(c) Final velocity of rocket = (exhaust velocity of gas) * ln(initial mass of rocket / final mass of rocket)
Using the given values:
Mass flow rate of exhaust gas = 200 kg/s
Exhaust velocity of gas = 1.80 km/s = 1800 m/s
Initial mass of rocket = 20,000 kg
Acceleration due to gravity = 9.81 m/s^2
Final mass of rocket = 0.2 * initial mass of rocket = 4,000 kg
(a) Thrust = (200 kg/s) * (1800 m/s) + (20,000 kg) * (9.81 m/s^2) = 360,000 N
Your answer for part (a) is correct.
(b) Time to exhaust fuel = (0.8 * 20,000 kg) / (200 kg/s) = 800 s = 20 minutes
Your answer for part (b) is incorrect. The correct answer is 800 seconds or 20 minutes, not 20 seconds.
(c) Final velocity of rocket = (1800 m/s) * ln(20,000 kg / 4,000 kg) = 205.66 m/s
Your answer for part (c) is correct.
If the train set uses stronger magnets, will the distance between these train cars increase or decrease? Explain your answer.
The distance between the train cars will decrease, as stronger magnets will create a greater attractive force between them. This will cause the cars to be pulled closer together.
What is stronger magnet?The strength of a magnet depends on the type of magnet and the material it is made from. Generally, the strongest magnets are neodymium magnets, also known as rare earth magnets. These are made from a combination of neodymium, iron, and boron and can produce magnetic fields up to 1.4 teslas, or 14,000 gauss. Samarium cobalt magnets are also powerful, producing fields up to 1.4 teslas. Other types of magnets, such as ceramic and Alnico magnets, generally produce magnetic fields of around 0.5 teslas or 5,000 gauss.
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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.
On a hot summer day, a young girl swings on a rope above the local swimming hole. When she lets go of the rope her initial velocity is 2.25m/s at an angle of 35º above the horizontal. If she is in flight for 1.20s, how high above the water was she when she let go of the rope?
When she let go of the rope, her height above the water would be 3.20 meters.
Kinematic motionWe can use the equations of motion to solve this problem. Let's assume that the girl's initial height above the water is h, and that the acceleration due to gravity is -9.81 m/s^2 (negative because it is directed downward). Then we have:
Initial horizontal velocity (vx) = 2.25 cos(35º) = 1.84 m/s
Initial vertical velocity (vy) = 2.25 sin(35º) = 1.30 m/s
During the 1.20 s of flight, the girl's vertical motion can be described by the following equation:
h + vy*t + (1/2)gt^2 = 0
where t is the time of flight and g is the acceleration due to gravity. Substituting the known values, we get:
h + (1.30 m/s)(1.20 s) + (1/2)(-9.81 m/s^2)*(1.20 s)^2 = 0
Simplifying and solving for h, we get:
h = -1/2*(-9.81 m/s^2)(1.20 s)^2 - (1.30 m/s)(1.20 s) = 3.20 m
Therefore, the girl was 3.20 meters above the water when she let go of the rope.
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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
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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