a cyclist rides 6.8 km east for 19.4 minutes, then he turns and heads west for 4.1 km in 5.8 minutes. finally, he rides east for 15.3 km, which takes 38.6 minutes. take east to be the positive direction.(a) What is the final displacement of the cyclist? (b) What is his average velocity?

Answer:

Explanation:

Δt = Δv/a = (4.5 m/s) / (8.37 m/s²) = 0.538 s  = time to reach top speed

d = Vi + 1/2at²

d = 0 + 1/2(8.37 m/s²)(0.538 s)² = 1.21 m = distance snake traveled while accelerating

t = d/v = (2.60 m - 1.21 m) / (4.5 m/s) = 0.31 s = reaction time before snake tail passes mongoose nose

According to the question of speed, ftop is 0.9578 s, dsnake is 2.14 m, freact is 0.4773 s.

What is speed?
Speed is the rate at which an object moves from one place to another. It is expressed in units of distance per unit of time, such as miles per hour or kilometers per hour. Speed is a scalar quantity, meaning that it has magnitude but no direction. Acceleration, on the other hand, is a vector quantity that has both magnitude and direction. Speed is directly related to the amount of time it takes an object to move from one point to another, and is inversely proportional to the time it takes to cover a given distance. Speed can also be affected by external factors such as wind, terrain, and friction. Speed is an important concept in physics and is often used to calculate the kinetic energy of an object.

ftop = 0.5 × (8.37 m/s²) / (4.50 m/s) = 0.9578 s

dsnake = 0.5 × (4.50 m/s) × (0.9578 s) = 2.14 m

freact = 2.14 m / (4.50 m/s) = 0.4773 s

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The amount it take to run the compressor if the electricity cost 22 cents per kilowatt-hour is 233.21 cents.

A kilowatt-hour is a unit of energy: one kilowatt of power for one hour. In terms of SI derived units with special names, it equals 3.6 megajoules (MJ).

To calculate the the amount it takes to run the compressor daily, we use the formula below.

Formula:

Where:

Substitute these values into equation 1

Hence, the amount is 233.21 cents.

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The road force on the wheel weigh is 690.

Your automobile advances under the influence of static friction. The power to turn the tires is provided by the engine, which pushes the vehicle rearward against the road.

Example:

The axle of the wheel that is in touch with the road receives a 200 mN torque from a car's engine.

The vehicle moves rightward at a steady speed:

The automobile wheel measures 0.58 meters in diameter. What does the horizontal component of the road force on the wheel weigh?

Radius: 0.29 m

When formula is used, we obtain

Force = Torque / Radius = 200/0.29

=690.

It is the necessary response as a result.

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a) The change in the angular velocity is - 3.40 rad/s.

b) The angular acceleration is -1.36rad/s^2.

We have to note that the change in the angular velocity would be obtain as the difference between the initial and the final angular velocity of the bicycle tire.

Then we would have that;

Change in the angular velocity = 0 rad/s - 3.40 rad/s = - 3.40 rad/s

We know that the angular acceleration = Change in the angular velocity/Time

= - 3.40 rad/s/2.5 s

= -1.36rad/s^2

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(a) The limit of the exponential function is infinity. (b)the limit of the exponential function is infinity. (c)the limit of the exponential function is infinity.

A differential equation is an equation which has  one or more terms and the derivatives of one variable with respect to the other variable dy/dx = f(x), where “x” is an independent variable and “y” is dependent variable.

(a) P(t) = 50e^(0.02t^2)

The limit as t approaches infinity of P(t) is infinity. This can be seen by using L'Hopital's rule and finding that limit of exponential function is infinity. The graph of P(t) would be a parabola that starts at 50 and increases as t increases.

(b) P(t) = 300e^(0.02t^2)

The limit as t approaches infinity of P(t) is infinity. This can be seen by using L'Hopital's rule and finding that limit of the exponential function is infinity. The graph of P(t) would be parabola that starts at 300 and increases as t increases.

(c) P(t) = 500e^(0.02t^2)

The limit as t approaches infinity of P(t) is infinity. This can be seen by using L'Hopital's rule and finding that limit of exponential function is infinity. The graph of P(t) would be parabola that starts at 500 and increases as t increases.

All of the graphs are increasing and have no inflection point. They are increasing because the exponential function e^(0.02t^2) is positive, and it will always increase as the  t increases.

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One process and system that matches the following energy description: "the kinetic energy of an object becomes gravitational potential energy of the system" is a roller coaster.

The conversion of gravitational potential energy to kinetic energy and vice versa in a roller coaster contributes to the thrill and excitement of the ride because it creates a sense of acceleration, speed and height. As the roller coaster car goes up the hill, the rider feels a pull in their stomach as they gain potential energy, and as the car goes down the hill, they feel a rush of speed as they gain kinetic energy. This back and forth conversion of energy creates a sense of unpredictability and excitement for the rider. Additionally, the change in speed and direction also create an illusion of weightlessness as the riders feel themselves being pulled out of their seats. This all together creates an exciting and thrilling experience for the riders.

In a roller coaster, a train or cars are pulled to the top of a hill using a motor or chain lift. As the train goes up the hill, it gains gravitational potential energy. As the train goes over the hill and down the other side, it loses gravitational potential energy and gains kinetic energy. This process continues as the train goes through various hills and valleys on the roller coaster.

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Because a system's resonant frequency is related to its mass, the resonant frequency of a system falls as the level of fluid in the system drops.

Natural frequency, as it is commonly understood, is the usual supply source frequency, which is often 50 or 60 hertz. The resonant frequency is 1/2pi multiplied by 1/LC.

Depending on where you reside, the natural frequency is either 50Hz or 60Hz. Resonance can happen at any multiple of the fundamental frequency (natural).

A larger amplitude of sound waves signifies a higher sound pressure and hence a bigger volume in acoustics. In general, resonant frequencies are unfavourable for loudspeakers.

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A gas expands from I to f along the three paths shown in the diagram. compute the work done on the gas along paths (a) W = 810.4 J (b) W = 506.5 J (c) Wtot = 202.6 J

Along pathIAF,

the work done is the area under the curve,

W = (4 atm)(2 L)

W = 8 L-atm

Now, what's a liter-atmosphere? We solved that in the last chapter. But let's do it again here. 1.0 atm =1.013 x 10 + 5 Pa = 1.013 x 10 5N/m2

1 L-atm = 1 L-atm [ 10 - 3m3 / L] [(1.013 x 105 N/m2) /atm]

1 L-atm = 101.3 N-m = 101.3 J

W = 8 L-atm [101.3 J/L-atm]

W = 810.4 J

Along pathIBF,

the work done is still the area under the curve. Now we can describe that as the area of the rectangle BFDA plus the area of the triangle IBF.

W = ABFDA +AIBF

W = (1 atm)(2 L) +(1/2)(3 atm)(2 L)

W = 5 L-atm

W = 5 L-atm [101.3 J/L-atm]

W = 506.5 J

Along pathIAF,

There is no work done along the path IB; this is a constant volume process (this is also known as an isometric process). Along path BF, there is work done.

Wtot = WIB +WBF

Wtot  = 0 + 2L-atm

Wtot  = 2 L-atm

Wtot = 202.6J

Gas, along with liquid, solid, and plasma, is one of the four natural states of matter. A gas has neither a fixed shape nor a fixed volume. The gas's atoms or molecules fill the container. Even when gravity is present, the gas expands until it is uniformly distributed throughout the container.

Correct question is:

A gas expands from I to F along the three paths indicated in the figure below. Calculate the work done on the gas along each of the following paths.

(a) IAF (in J) =

(b) IF (in J) =

(c) IBF (in J) =

The images supporting question is attached below

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The answers are:

a.) The translational kinetic energy of its center of gravity:  638.144J  

b.)The rotational kinetic energy about its center of gravity 319.072 J

c.) Its total kinetic energy 957.216 J

Given:

M = 11.8 kg cylinder

V = speed of center of gravity = 10.2m/s

(a) Translational kinetic energy = 1/2mv²

1/2x 11.8kg x 10.2²

= 11.8x108.16/2

= 1276.288/2

= 638.144 J

This is the translational energy

(b) Rotational energy =1/2Iw²

I = mv²/2

w = v/r

When we substitute

1/2[mv²/2][v/r]²

= 1/4mv²

= 1/4 x 11.8 x 10.2²

= 1276.288/4

= 319.072

This is the rotational energy

(c) Total kinetic energy:

We add the values of A and B above to get this.

638.144 J + 319.072 J

= 957.216J

Complete question: A 11.8-kg cylinder rolls without slipping on a rough surface. At an instant when its center of gravity has a speed of 10.2 m/s, determine the following. (a) the translational kinetic energy of its center of gravity (b) the rotational kinetic energy about its center of gravity (c) its total kinetic energy.

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Answer:

11

Explanation:

MA = Fout / Fin = 55 N / 5 N = 11

Answer:

Approximately [tex]0.042\; {\rm kg \cdot m^{-3}}[/tex].

Explanation:

Note the unit conversion for mass:

[tex]1\; {\rm g} = 10^{3}\; {\rm mg}[/tex].

[tex]1\; {\rm kg} = 10^{3}\; {\rm g}[/tex].

Therefore:

[tex]\begin{aligned}& 10\; {\rm mg} \times \frac{1\; {\rm g}}{10^{3}\; {\rm mg}} \times \frac{1\; {\rm kg}}{10^{3}\; {\rm g}} \\ =\; & 10\; {\rm mg} \times \frac{1\; {\rm kg}}{10^{6}\; {\rm mg}} \\ =\; & 10^{-5}\; {\rm kg}\end{aligned}[/tex].

Similarly, for volume:

[tex]1\; {\rm mL} = 1\; {\rm cm^{3}}[/tex].

[tex]1\; {\rm m^{3}} = 10^{3}\; {\rm dm^{3}} = 10^{6}\; {\rm cm^{3}}[/tex].

Thus, [tex]1\; {\rm m^{3}} = 10^{6}\; {\rm mL}[/tex].

[tex]\begin{aligned}& 240\; {\rm L} \times \frac{1\; {\rm m^{3}}}{10^{6}\; {\rm mL}} = 2.40\times 10^{-4}\; {\rm m^{3}}\end{aligned}[/tex].

Divide mass by volume to find the mass-to-volume ratio:

[tex]\begin{aligned}\frac{10^{-5}\; {\rm kg}}{2.40 \times 10^{-4}\; {\rm m^{3}}} \approx 0.042\; {\rm kg \cdot m^{-3}}\end{aligned}[/tex].

c. the gravity acceleration is in the same direction as the force of gravity, and thus toward the center of the earth: accurately describes the force of gravity.

The force that pulls items toward the centre of a planetary or other body is known as gravity. The gravitational pull maintains each of the planet in orbit about the sun. The degree to which a coordinate in space-time is invisibly bent determines the intensity of the gravitational "field" at any given place in space or time. Massive items tumble down these bends in the direction of one another. The stronger the attraction between items, the more matter there is, and the closer together things are. And unlike electricity and magnetism, which may either repel or attract, gravity always draws objects together.

Thus, correct option is: c

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The linear density of the string is 2.86 x 10^-5 kg/m.

What is linear density?

Linear density, also known as linear mass density, is a measure of the mass of a material per unit length. It is typically used to describe the properties of thin, elongated objects such as strings, wires, and fibers. The unit of measurement for linear density is typically kilograms per meter (kg/m) or grams per centimeter (g/cm). It is calculated by dividing the mass of the material by its length.

To find the linear density of the string, we need to use the relationship between the tension, linear density, and wave properties, which is given by the equation:

Tension = (linear density) * (wave speed)^2

where wave speed is the product of the frequency and wavelength of the wave.

Given the tension, period and wavelength, we can find the linear density using the following steps:

frequency = 1 / period = 1 / 3.82 x 10^-3 s = 261.9 Hz

wave speed = wavelength * frequency = 1.26 m * 261.9 Hz = 331.9 m/s

Tension = (linear density) * (wave speed)^2

944 N = (linear density) * (331.9 m/s)^2

linear density = Tension / (wave speed)^2 = 944 N / (331.9 m/s)^2 = 2.86 x 10^-5 kg/m

Therefore, the linear density of the string is 2.86 x 10^-5 kg/m.

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When a wave travels through a medium, the particles in that medium vibrate in a direction perpendicular to the direction the wave travels it is a transverse mechanical waves only.

When a wave travels through a medium, the particles in that medium vibrate in a direction parallel to the direction the wave travels it is a longitudinal mechanical waves only .

Then a wave travels through a medium, the wave speed will depend on an inertial property of that medium it is for both transverse and  longitudinal mechanical waves .

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The power supply that technician should use 500 W.

A power supply is a component that transforms the output of an ac power line into one or more constant dc outputs. A smooth voltage is created by filtering the ac voltage after it has first been rectified to create a pulsing dc. In spite of fluctuations in the ac line voltage or circuit loads, the voltage is finally regulated to produce a consistent output level.

The power use of the server as whole is,

100 W+ 5×9 W + 200 W

Power use=445 W.

So, the power should be more than the 445 W in order that there should not be any short circuit.

and from all the given options the power supply that is feasible is 500 W.

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500 W of power should be used by the technician.

One or more consistent dc outputs are produced from an ac power line's output by a component known as a power supply. After rectifying the ac voltage to produce a pulse dc, a smooth voltage is produced by filtering the result. Despite changes in the ac line voltage or circuit loads, the voltage is eventually controlled to create a constant output level.

The entire server's energy consumption is,

100 W+ 5×9 W + 200 W

Using 445 W of power.

Therefore, the power must be more than 445 W to prevent short circuits.

Choose the power supply that is practical from the possibilities presented

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Cassius accuses Brutus of wrongdoing in this scenario. Brutus responds by accusing Cassius of bribery and reminding him that they killed Caesar in order to prevent him from becoming corrupt, not to become corrupt themselves.

Cassius' resentment is revealed through these contrasting elements as a result of his perceived equality with Caesar, but his reality that he is lower than him. As a result, Cassius' anger demonstrates how perceived disparity promotes resentment and envy, causing a poisonous relationship.

The argument becomes heated, and Cassius pulls his knife, daring Brutus to murder him

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A nickel coin contains 5.2 x 10^22 Ni atoms as coulombs of charge.

In the International System of Units, the unit of electric charge is the coulomb. It is equivalent to the electrical charge delivered by a 1 ampere constant current in 1 second in the current version of the SI. The amount of charge carried by a current of one amp for one second is measured in coulombs, which is the unit of measurement used in the SI for electric charge. It may also be a property of a substance that causes electrical and magnetic effects to occur. The symbol for it is C. According to math, 1 Coulomb equals 1 Ampere x 1/sec.

Here,

The mass of a nickel coin is 5 g.

1 mol of Ni weighs 58 g.

1 mol=6.022 x 10²³ atoms of Ni.

in 58 g,  

=6.022 x 10²³ atoms of Ni

then in 5 g the number of Ni atoms = - 6.022 x 10²³ /58 x 5

= 5.2 x 10²² Ni atoms,

Therefore number of Ni atoms as coulombs of charge are 5.2 x 10²² atoms in a nickel coin.

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A golf ball will travel 166 feet before landing if it is struck with an 80 ft/s velocity.

The directional speed of an object in motion, as measured by a specific unit of time and observed from a specific point of reference, is what is referred to as velocity. The direction of a body or object's movement is defined by its velocity. In its basic form, speed is a scalar quantity. In essence, velocity is a vector quantity. It is the speed at which distance changes. It is the displacement change rate. Speed is the absence of direction; velocity is the presence of direction. Since velocity is a vector quantity, we must specify both the magnitude (the speed) and the direction of travel when expressing it.

Here,

(Va)x= 80cos(10+45)°= 44.886

(Va)y= 80sin(10+45)°= 65.532

S=So + Vot + 1/2at^2

d sin 10°= 0 + 65.532t + 1/2 (-32.2)t^2

0.17d= 0 + 65.532t + (-16.1)t^2

Solving the equation gives,

d=166ft

t= 3.57seconds

The distance d to where it will land is 166 feet when a golf ball is struck with a velocity of 80 ft/s.

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The correct formula for determining total resistance in a circuit containing three resistors in parallel is [tex]\mathbf{R_t=R_1+R_2...+R_n}[/tex]. Thus, option C is correct.

Two or more resistors are said to be connected in series when the same amount of current flows through all the resistors. In such circuits, the voltage across each resistor is different. In a series connection, if any resistor is broken or a fault occurs, then the entire circuit is turned off. The construction of a series circuit is simpler compared to a parallel circuit.

the total resistance is given as:

Rₜₒₜₐₗ = R₁ + R₂ + ….. + Rₙ

The total resistance of the system is just the total sum of individual resistances.

For example, consider the following sample problem.

A resistor with an electrical resistance value of 100 ohms is connected to another with a resistance value of 200 ohms. The two resistances are connected in parallel. What is the total resistance across the system?

Here, R₁ = 100 Ω and R₂ = 200 Ω

Rₜₒₜₐₗ  = 100 + 200 = 300 Ω

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Complete question:

Which is the correct formula for determining total resistance in a circuit containing three resistors in parallel?

a. [tex](R_1^{-1}+R_2^{-1}...R_n^{-1})^{-1}[/tex]

b. [tex]L_t=L_1+L_2...+L_n[/tex]

c. [tex]R_t=R_1+R_2...+R_n[/tex]

d. [tex]X_L_ = 2 \pi f \times L[/tex]

Due to challenges with recombinant expression and protein purification, T1r molecular studies have been impeded. The mechanisms underlying taste perception are so poorly understood. The claim is accurate.

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In this situation, the pressure will change in direct proportion to the temperature. Double both the pressure and the temperature.

When the temperature is held constant, pressure decreases as volume increases and vice versa. As a result, when the volume is cut in half, the pressure is also cut in half, and vice versa.

According to Boyle's Law, pressure and volume have an inverse relationship. The volume reduces as the pressure rises, and the volume rises as the pressure falls.

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According to Newton's second law, there is no acceleration in the horizontal plane because there is no net force operating in that direction.4.63 m is the highest height attained.

The man's initial speed (u) is 31.0 m/s.

The trajectory's top speed is 29.5 m/s.

Gravitational acceleration (g) equals 9.8 m/s²

The vertical component of velocity becomes zero as the man reaches the top of the trajectory, leaving just the horizontal component to affect him.

Additionally, according to Newton's second law, there is no acceleration in the horizontal plane because there is no net force operating in that direction.As a result, the horizontal component of velocity never changes.

Thus, the horizontal component of beginning velocity is all that is referred to as speed at the top of the trajectory.where Ux and Uy are the man's initial vertical and horizontal velocities, respectively.

To find "H," enter the value from equation (1) and 9.8 for "g."

H = 90.75/2*9.8

H = 4.63 as a result.

As a result, 4.63 m is the highest height attained.

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The behavior of things is predicted by Newton's first law of motion when all external forces are equal.

The first law, sometimes known as the law of inertia, asserts that if an object's forces are balanced, its acceleration will be zero meters per second.

When all forces are balanced, an object is said to be in equilibrium and won't accelerate. Newton postulated that an item will only accelerate in the presence of a net or unbalanced force. An object will accelerate if there is an imbalanced force present, changing its direction, speed, or both.

Newton's second law of motion pertains to the behavior of objects for which all existing forces are not balanced. The second law states that the acceleration of an object is dependent upon two variables - the net force acting upon the object and the mass of the object.

Therefore, The behavior of things is predicted by Newton's first law of motion when all external forces are equal.

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Answer:

45.9 m

Explanation:

KE = 1/2mv² = 225 J

PE = mgh

If all the KE is converted to PE, then:

(0.50 kg)(9.8 m/s²)(h) = 225 J

h = (225 J) / (0.50 kg)(9.8 m/s²) = 45.9 m

-Borrows = 0 , -Returns > 0, Since these two statements have the same truth value, they are both indicating that a particular laptop is not currently borrowed.

What is Equivalence theory?

This question is using the Theory of Equivalence, which states that two statements are logically equivalent if they have the same truth value.

In this case, the two statements are:

1) Borrows = 0

2) Returns > 0

Both choices indicate that a particular laptop is not currently borrowed from the library.

Borrows = 0 indicates that the laptop has not been borrowed at all. Since the library keeps track of the number of times a laptop is borrowed, if the number is zero, then it has not been borrowed.

Returns > 0 indicates that the laptop has been borrowed before, but it is not currently borrowed.

Since the library keeps track of the number of times a laptop is returned, if the number is greater than zero, then it has been returned and is therefore not currently borrowed.

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Pluto masses 1.3e22 kg, and its average distance from the sun is about 6e15 km. The sun’s mass is 2e30 kg. G is 6.7e−11 m^3 / kg⋅s^2.

What is meant by mass?

So the force of gravity is

f = G M1 M2 / d^2

= 6.7e-11 x 1.3e22 x 2e30 / 5e15^2

= .7e11 N = 70 billion newtons.

One might say, not insignificant.

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The particles in a liquid have enough energy to transform into gases at a specific temperature. Boiling (or vapourization) is the conversion of a liquid into a gas; condensation is the conversion of a gas into a liquid.

Melting is the process through which a solid transforms into a liquid (an older term that you may see sometimes is fusion). It is known as solidification when a liquid turns into a solid. Any pure substance's melting point, or the temperature at which melting starts, is a property of that substance. For a solid to turn into a liquid, energy is needed. Each pure material requires a specific quantity of energy to transform from a solid to a liquid. The symbol for this quantity, Hfus, stands for the substance's enthalpy of fusion (also known as heat of fusion). In Table 10.2, "Enthalpies of Fusion for Various Substances," a number of Hfus values are provided;

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The spring constant of this spring is 50 N/m, therefore, 4th option is correct.

Spring constant is the amount of force (in newtons) required to extend a spring by one meter. In this case, the spring constant is 25 N/m. This can be calculated by taking the force (10 N) divided by the amount of extension (0.60 m - 0.40 m = 0.20 m).

[tex]$ \Rightarrow \mathrm{ \frac{10 N}{0.20 m} = 50N/m}[/tex]

The force necessary to expand or compress the spring by a specific quantity is measured, and the spring constant is then calculated. The force needed to extend or compress the spring by a specific amount may be calculated by measuring it, multiplying it by the extension or compression, and then dividing the result by the force.

The behavior of a system using springs, such as a shock absorber or any other device that employs springs, is significantly influenced by the spring constant. It may also be used to figure out how much force a spring can produce when it is squeezed or expanded.

Thus, The spring constant of this spring is 50 N/m, therefore, 4th option is correct.

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Answer:

576 joules

Hope this helped :)