3) Vector A is 2.8 cm at 60° above the positive x-axis. Vector B is 1.90 cm at 60 below the
positive x-axis. Use components to find the following
a) A+ B
b) A-B
c) B-A

The final velocity of the puck, v, is determined as 3 m/s.

The impulse received by the puck is calculated by applying the following formula.

impulse received = change in momentum of the puck = area under the curve

Area under the curve = area of triangle

Area of triangle = ¹/₂ x b x h

where;

Area = ¹/₂ x 0.003 s x 160 N

Area = 0.24 Ns

Therefore, impulse (J) = change in momentum (ΔP) = 0.24 Ns

The final velocity of the puck is calculated as follows;

m(vf - vi) = ΔP

where;

Let vf be in positive direction,

then vi will in negative direction

0.03 kg(vf - (-5 m/s)) = 0.24 Ns

vf + 5 = 0.24/0.03

vf + 5 = 8

vf = 8 - 5

vf = 3 m/s

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Answer:

In short no , there is always minimum 2 forces.

Explanation:

First force: Weight force ( The force of gravity on the object attracting the block of masse m to earth)

Second force: Normal reaction ( This force is perpendicular to the surface )

Answer:

no

Explanation:

if only single force acts on the block it will stay at rest and it will accelarate in direction of force

A beaver runs at a speed of 2.0 m/s with 45 J of kinetic energy, then the mass is approximately 1.74 kg, and this can be calculated by using the  kinetic energy (KE) of an object that is KE = (1/2) ×m × [tex]v^2[/tex].

KE = (1/2) ×m × [tex]v^2[/tex].

where m= mass of the object, v=its velocity.

The beaver runs at a speed of 2.0 m/s with 45 J of kinetic energy. Substituting these values into the above equation

45 J = (1/2) ×m × [tex](2.0 m/s)^2[/tex]

Simplifying this equation:

45 J = (1/2) × m × 4.0[tex]m^2/s^2[/tex]

45 J = 2 m × 2 [tex]m^2/s^2[/tex]

45 J = 4 [tex]m^3/s^2[/tex]

[tex]m^3[/tex] = 45 J / 4 [tex]s^2[/tex]

[tex]m^3[/tex] = 11.25 kg×[tex]m^2/s^2[/tex]

Taking the cube root of both sides to solve for mass,

m = (11.25 kg×[tex]m^2/s^2)^(^1^/^3^)[/tex]

m = 1.74 kg (rounded to two decimal places)

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Answer:

24.85 m/s.

Explanation:

PE = mgh = 250 kg x 9.81 m/s^2 x 550 m = 1,358,725 J

PE' = mgh' = 250 kg x 9.81 m/s^2 x 125 m = 308,062.5 J

PE = KE

1,358,725 J = 0.5mv^2

Solving for v, we get:

v = sqrt(2PE/m) = sqrt(2 x 1,358,725 J / 250 kg) = 59.15 m/s (rounded to two decimal places)

PE' + KE' = PE + KE

Since the cart starts from rest at the top of the incline, KE = 0. Therefore:

PE' = KE'

mgh' = 0.5mv'^2

Solving for v', we get:

v' = sqrt(2gh') = sqrt(2 x 9.81 m/s^2 x 125 m) = 24.85 m/s (rounded to two decimal places)

Therefore, the speed of the cart at a height of 125 m above the bottom of the incline is 24.85 m/s.

The average of the three trials for

Mystery A = 30 and for Mystery B = 2.8.

1. To determine which material would allow light to travel faster, we need to compare their respective indices of refraction. The index of refraction is defined as the ratio of the speed of light in a vacuum to the speed of light in the medium. A higher index of refraction means that light travels slower in that medium.

Therefore, if Mystery A has a lower index of refraction than Mystery B, then light would travel faster in Mystery A. Conversely, if Mystery B has a lower index of refraction than Mystery A, then light would travel faster in Mystery B.

2. As the index of refraction for the second medium is increased, the angle of refraction decreases. This is because the speed of light is slower in a medium with a higher index of refraction, causing it to bend more as it enters the medium.

The relationship between the angle of incidence, angle of refraction, and indices of refraction is described by Snell's law, which states that n1 sin(theta1) = n2 sin(theta2), where n1 and n2 are the indices of refraction of the two media, and theta1 and theta2 are the angles of incidence and refraction, respectively.

3. This lab explored the properties of light as it travels through different materials with varying indices of refraction. By measuring the angles of incidence and refraction, we were able to calculate the indices of refraction for two mystery materials. Through further analysis, we determined which material allowed light to travel faster. This lab helped us to better understand the behavior of light as it interacts with different materials, and reinforced the importance of the index of refraction in determining the speed of light in a given medium.

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The magnitude of current in the 6Ω resistor is 0.72A.

EMF stands for electromotive force, which is the energy supplied by a source (such as a battery or generator) per unit of charge that passes through it, measured in volts. It represents the potential difference between the two terminals of the source when it is not connected to any circuit.

From the circuit diagram, we can see that the current flowing through the 6Ω resistor can be found by using Ohm's Law:

V = IR

where V is the voltage across the 6Ω resistor, I is the current flowing through it, and R is the resistance of the resistor.

To find V, we need to use Kirchhoff's Voltage Law (KVL) to determine the total voltage drop across the circuit. Starting from the top left corner and moving clockwise, we have:

V1 (emf) = IR1 + V2 (emf)

V2 (emf) - IR2 - IR1 = 0

Substituting V2 = -IR2 - 0.2I (since emf 2 has an internal resistance of 0.2Ω) into the first equation, we get:

V1 = I(R1 + R2 + 1) + 0.2I

Simplifying, we get:

V1 = I(7Ω) + 0.2I

Now we can solve for I:

I = V1 / (7Ω + 0.2Ω)

I = V1 / 7.2Ω

To find V1, we can use KVL again, starting from the bottom left corner and moving clockwise:

V1 - IR1 - V2 = 0

V1 - IR1 - (IR2 + 0.2I) = 0

Substituting V2 = -IR2 - 0.2I, we get:

V1 = I(R1 + R2 + 0.2) = I(7.2Ω)

Now we can substitute this expression for V1 into the equation for I:

I = (I(7.2Ω)) / (7Ω + 0.2Ω)

Simplifying, we get:

I = 0.72A

Therefore, the magnitude of current in the 6Ω resistor is 0.72A.

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The minimum amount of work required to make the enemy satellite inoperative and push it out of its circular orbit is 6.972 × 10^9 joules.

To calculate the minimum amount of work required to knock the satellite out of its circular orbit, we need to determine the change in kinetic energy required to change the satellite's velocity. This change in kinetic energy can be calculated using the conservation of energy, which states that the total energy in a closed system remains constant.

The kinetic energy of an object in motion can be expressed as:

K = (1/2)mv^2

Where:

K = Kinetic energy

m = Mass of the object

v = Velocity of the object

To determine the velocity of the satellite, we can use the following formula:

v = sqrt(GM/r)

Where:

G = Universal gravitational constant = 6.6743 × 10^-11 N m^2/kg^2

M = Mass of the Earth = 5.98×10^24 kg

r = Altitude of the satellite above the Earth's surface + radius of the Earth = 6,997 km

v = sqrt(6.6743 × 10^-11 × 5.98×10^24 / 6,997×10^3) = 7,650 m/s

To change the satellite's velocity, we need to calculate the new velocity required to push the satellite out of its circular orbit. We can use the following formula to calculate the escape velocity required to leave the Earth's gravitational field:

Ve = sqrt(2GM/r)

Ve = sqrt(2 × 6.6743 × 10^-11 × 5.98×10^24 / 6,997×10^3) = 11,186 m/s

To calculate the change in kinetic energy required to change the satellite's velocity from its initial velocity to the escape velocity, we can use the following formula:

ΔK = (1/2)m(Δv)^2

Where:

ΔK = Change in kinetic energy

m = Mass of the satellite

Δv = Change in velocity required to reach escape velocity = Ve - v

Δv = 11,186 m/s - 7,650 m/s = 3,536 m/s

ΔK = (1/2) × 993 kg × (3,536 m/s)^2 = 6.972 × 10^9 J

Therefore, The adversary spacecraft must be rendered inoperable and forced out of its elliptical orbit with a minimum of 6.972 × 10^9 joules of work.

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When two magnets are close to each other, the magnets experience a repulsive or attractive force. The magnetic field strength is affected by the orientation of the magnet.

The direction in which the bar magnet obtains its maximum magnetic property is called the orientation of the magnet. The magnetic field strength depends on the orientation of the magnet.

The magnetic field lines emerge from the north pole and end in the south pole. When the two bar magnets of opposite poles face each other, an attractive force will be produced and magnetic field strength increases.

When the bar magnet of the same poles faces each other, repulsive force will produce and magnetic field strength decreases. Hence from the orientation of the bar magnet,  the magnetic field strength gets affected.

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The final velocities of the car and truck just after the collision will be as per the conservation of momentum.

Momentum is defined as product of mass and velocity of the body. It is denoted by letter p and it is expressed in kg.m/s. Mathematically p = mv. it discuss the moment of the body. body having zero mass or velocity has zero momentum. The dimensions of the momentum is [M¹ L¹ T⁻¹].

According to conservation of momentum, Initial momentum will be equal to the final momentum. In the elastic collision there is no loss of energy, both energy and momentum is conserved.

if the the car is coming with velocity equal to the mass of the truck and truck is coming with mass of the car, then they have same momentum in opposite direction when they collide each other the final velocity of both car and truck becomes zero.

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Answer:

We can solve this problem using the kinematic equation:

y = 1/2 * g * t^2

where y is the height of the tree, g is the acceleration due to gravity (9.8 m/s^2), and t is the time taken to fall to the ground.

We can solve for t using:

t = sqrt(2y/g)

Plugging in the values, we get:

t = sqrt(2(19)/9.8)

t = 2.19 seconds

So, it takes 2.19 seconds for the acorn to fall from the tree to the ground.

To find the velocity of the acorn just before it hits the ground, we can use:

v = g * t

Plugging in the values, we get:

v = 9.8 * 2.19

v = 21.46 m/s

So, the acorn is going approximately 21.46 m/s just before it hits the ground.

Explanation:

The lab experiment found that light travels faster in Mystery A compared to Mystery B, with average speeds of 3.0 and 2.8, respectively. The increase in the index of refraction for the second medium led to a higher angle of refraction, resulting in light bending more. These findings have practical implications for optics and communications.

1. Light would travel faster in Mystery A since the average speed of light in Mystery A (3.0) is higher than Mystery B (2.8).

2. Increasing the index of refraction for the second medium leads to an increase in the angle of refraction. When light comes in at a lower angle, it bends more.

3. In conclusion, this lab experiment showed that the speed of light in a material is influenced by the material's index of refraction. Mystery A had a higher average speed of light compared to Mystery B, indicating that light travels faster in Mystery A. Additionally, the angle of refraction increased as the index of refraction for the second medium was increased. These findings have practical applications in the field of optics and communications.

Hence,The laboratory experiment discovered that, with average speeds of 3.0 and 2.8, respectively, light moves more quickly in Mystery A than Mystery B. Light bent more as a result of the second medium's increased index of refraction due to a higher angle of refraction. For optics and communications, these findings have real-world applications.

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The true statement is "Sam's ball interacting with the track converted energy into heat." The correct option is B.

The law of conservation of energy states that energy cannot be created or destroyed, only transferred or converted from one form to another. This means that the total amount of energy in a closed system remains constant.

The friction between Sam's ball and the track caused some of the energy to be lost as heat, while Keyana's ball experienced no such loss due to the absence of friction in her experiment. Therefore, Keyana's ball retained more of its initial potential energy as kinetic energy, resulting in a greater velocity and hence more kinetic energy at the bottom.

Option A (Sam's ball lost mass as it traveled along the track) is not true because it is not possible for the ball to lose mass during the experiment. The mass of the ball is a constant value and is not affected by the experiment.

Option C (Keyana's ball was able to gain momentum) is not the best explanation because momentum is not conserved in this scenario since external forces like friction are acting on the ball. The ball is only gaining kinetic energy.

Option D (Keyana's ball had more potential energy) is not true because both Keyana and Sam released the ball from the same vertical height. Therefore, both balls had the same initial potential energy. The difference in their kinetic energies at the bottom can be explained by the difference in their conservation of energy due to friction.

Therefore, The correct statement that best explains why Keyana's ball had more kinetic energy than Sam's when it reached the bottom, even though energy is conserved, is: Sam's ball interacting with the track converted energy into heat.

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If There are two resistors connected in parallel: R1-43 Ohms and R2-43 Ohms,  then the equivalent resistance is 21.5Ω.

A resistor is a passive two-terminal electrical component used in circuits to implement electrical resistance. Resistors have a variety of purposes in electronic circuits, including lowering current flow, adjusting signal levels, dividing voltages, biassing active components, and terminating transmission lines. High-power resistors that can generate many watts of heat instead of electrical energy can be utilised as test loads for generators, power distribution systems, and motor controls. With temperature, time, or operating voltage changes, fixed resistors' resistances only slightly fluctuate. Variable resistors can be utilised as force sensors, heat sensors, light sensors, volume controls, lamp dimmers, humidity sensors, and chemical activity sensors.

The equivalent resistance in parallel combination is

R(p) = R₁R₂÷R₁+R₂

putting all values,

R(p) = 43×43÷(43+43)

R(p) = 21.5Ω

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Answer:

To find the frequency of heartbeats in hertz, we need to convert the beats per minute (BPM) to beats per second (BPS), since frequency is measured in hertz (Hz) which is equivalent to cycles per second.

Frequency = BPM / 60

Frequency = 65 / 60

Frequency ≈ 1.083 Hz

To find the period for each heartbeat in seconds, we need to find the reciprocal of the frequency, which gives the time duration for one complete cycle.

Period = 1 / Frequency

Period = 1 / 1.083

Period ≈ 0.922 seconds per beat

The distance of the blue car from the edge of the intersection, when it stops, is 35.9 m, the time interval of the blue car within the boundaries of the intersection is 4.04 s, the minimum distance is 45.8 m, and the speed of the car is 22.6 m/s.

From the given,

A) the distance of the blue car from the south edge of the intersection when it stops =?

The width of the intersection = 28m

Acceleration = -2.10 m/s²

time interval = 3.10 s

By using the equation

x = x₀ + v₀t + 1/2 (at²)

28 = 0 + v₀(3.10) + 1/2 (-2.10 ×(3.10)²)

v₀ = 12.3 m/s

v² = v₀² + 2a (x-x₀)

(x-x₀) = Δx = v²-v₀² / 2a

  Δx  = 35. 9m

B) the time interval=?

distance covered by the blue car = 4.52 + 28 = 32.52 m

By using the relation,

x = x₀ + v₀t + 1/2 (at²)

32.52 = 0 + (12.3)t + 1/2 (-2.10)t²

-1.05t²+12.3t-32.52 = 0

This is the quadratic equation. By solving it, time t= 4.04s,7.66s. The desired time is t = 4.04 s, and the tail of the blue car leaves the intersection.

C) the minimum distance is=?

x = x₀ + v₀t + 1/2 (at²)

  = 0 + 0 + 1/2 (5.60 (4.04)²)

 = 45.8 m

The minimum distance of the blue car is 45.8m

D) speed of the car=?

the velocity equation

v = v₀ + at

= 0 + (5.60 ×4.04)

= 22.6 m/s

The velocity of the car is 22.6 m/s.

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(a) The vector diagram of the acceleration is attached.

(b) -13.5 m/s²

(c) speed is 2.95 m/s and velocity is (1.79 i + 2.95 j) m/s.

(b) At the highest point, the velocity of the ball is horizontal and the acceleration is vertical. So, radial acceleration:

radial acceleration = ar = a sin(θ) = (-22.5 m/s²) sin(36.9°) ≈ -13.5 m/s²

(c) The speed of the ball using the conservation of energy equation:

mgh + (1/2)mv² = constant

where m = mass of the ball,

g = acceleration due to gravity,

h = height of the ball above the lowest point, and

v = speed of the ball.

At the lowest point, the speed of the ball is equal to the square root of 2gh, where h is the height of the ball above the lowest point. At the point where the ball is 36.9° past the lowest point, the height of the ball above the lowest point is:

h = L(1 - cos(θ)) = 1.5(1 - cos(36.9°)) ≈ 0.665 m

Therefore, the speed of the ball is:

v = √(2gh) = √(2g(L-h)) = √(2(9.81 m/s²)(1.5 - 0.665) m) ≈ 2.95 m/s

The velocity of the ball is tangential to the circle and is perpendicular to the radial acceleration. At the point 36.9°, tangential component of the total acceleration is:

at = a cos(θ) = (20.2 m/s²) cos(36.9°) ≈ 16.1 m/s²

The angular acceleration:

α = ar / L = (-13.5 m/s²) / 1.5 m ≈ -9 m/s²

Therefore, the speed and velocity of the ball are:

speed = v ≈ 2.95 m/s

velocity = (at / α) i + v j ≈ (1.79 i + 2.95 j) m/s

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Answer:

the answer is 20mi/hr

Explanation:

The heat absorbed by the melting ice is Q = 4,875,600 J.

a, Given mass (m) = 14.6 kg, then the heat absorbed by the melting ice is Q = 4,875,600 J.

This can be determined using Q = 14.6 kg × 334,000 J/kg.

b. By utilizing the equation P = (0.01 W/m × K × 1.21 m^2 × 36 K) / 0.035 m, we can determine that P equals 12.396 watts.

To discover how long it will take for the ice to melt, we can use another formula: t = Q / P.

With the given value of Q as 4,875,600 joules and P is equal to 12.396 watts, we find that t evaluates to roughly 393,292 seconds.

In order to transform this result into hours, simply divide by 3600 which leads us to t ≈ 109.25 hours.

Therefore, it is predicted that the ice will melt in approximately 109.25 hours.

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The potential energy produced in a complete circuit with a capacitor is caused by the voltage difference across the capacitor.

A capacitor is an electrical component that stores electric charge. When a capacitor is connected to a complete circuit and a voltage is applied, it becomes charged. The voltage difference across the capacitor creates an electric field between its plates, which stores potential energy in the electric field.

As the capacitor charges, electrons accumulate on one plate, creating a negative charge, while the other plate becomes positively charged due to the loss of electrons. This separation of charge creates an electric potential difference (voltage) between the two plates of the capacitor.

The potential energy stored in the capacitor is directly proportional to the square of the voltage across it and the capacitance (C) of the capacitor, and is given by the formula:

Potential energy (PE) = (1/2) * C * V²

where V is the voltage across the capacitor.

As the voltage across the capacitor increases, more potential energy is stored in the electric field between its plates. When the circuit is turned off or the capacitor is discharged, this stored potential energy is released back into the circuit in the form of electrical energy. Capacitors play a crucial role in many electronic devices and circuits by providing energy storage and smoothing out voltage fluctuations.

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Most meteorites that enter the Earth's atmosphere burn up before they reach the Earth itself. When this happens, lots of energy is transferred from the meteorites' kinetic energy stores very quickly.

The kinetic energy storage of meteorites are communicated to the surrounding environment as heat, sound, and light energy.

A meteorite penetrates the atmosphere of the Earth. Friction acts on the meteorite when it reaches the Earth's atmosphere. When a meteorite enters the Earth's atmosphere, it gains kinetic energy. The meteorite catches fire due to friction. At this time, the meteorite's kinetic energy will be transformed into heat energy, sound energy, and light energy.

Hence kinetic word word completes the sentence.

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The Children's Health Insurance Program (CHIP) is designed to provide low-cost health coverage to children in families that receive Medicare.

Hence option D is correct.

The Children's Health Insurance Programme (CHIP) offers medical care to children under the age of 18 whose parents earn too much to qualify for Medicaid but not enough to pay for private coverage. CHIP was enacted by Congress during the Clinton administration in 1997.

The Children's Health Insurance Programme (CHIP) is a federal healthcare programme in the United States that is handled and designated differently by each state. For example, New York's programme is known as Child Health Plus, whereas Arkansas' programme is known as ARKids.

The federal government distributes matching funding to each state, similar to how Medicaid operates.

Hence option D is correct.

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Answer:

Scientists believe that elements were originally formed through fusion in stars.

Explanation:

Because lighter elements combine to form heavier ones under high temperatures and pressures, this process is known as nuclear fusion and occurs within stars' cores. When a star exhausts its fuel, it undergoes a supernova explosion that releases heavier elements into space, which can then be incorporated into new stars, planets, and other celestial bodies.

Answer: v = 4.17 x 10^5 m/s

Explanation:

The potential difference (ΔV) is given as 91 V. The charge of the proton is given by q = 1.6 x 10^-19 C.The mass of the proton is given by m = 1.67 x 10^-27 kg. The acceleration due to gravity is given by g = 9.81 m/s^2. The final speed of the proton can be calculated as follows:

The potential energy gained by the proton (ΔU) can be calculated using the formula:

ΔU = qΔV

where

q = charge of the proton

ΔV = potential difference

Substituting the given values, we get:

ΔU = (1.6 x 10^-19 C) x (91 V) = 1.456 x 10^-17 J

The kinetic energy gained by the proton (K) can be calculated using the formula:

K = (1/2)mv^2

where

m = mass of the proton

v = final speed of the proton

The kinetic energy gained by the proton is equal to the potential energy gained by the proton. Therefore, we have:

K = ΔU = 1.456 x 10^-17 J

Substituting the given values, we get:

1.456 x 10^-17 J = (1/2) x (1.67 x 10^-27 kg) x v^2

Simplifying the equation, we get:

v^2 = (2 x 1.456 x 10^-17 J) / (1.67 x 10^-27 kg)

v^2 = 1.743 x 10^10 m^2/s^2

Taking the square root of both sides, we get:

v = 4.17 x 10^5 m/s

Therefore, the final speed of the proton is 4.17 x 10^5 m/s.

When a proton is accelerated from rest through a potential difference of 91 V then final speed of this proton is

A proton is a stable subatomic particle with a +1 e (elementary charge) positive electric charge. It has a little lower mass than a neutron and a mass that is 1,836 times that of an electron (the proton-to-electron mass ratio). Protons and neutrons, each with a mass of around one atomic mass unit, are referred to collectively as "nucleons" (particles found in atomic nuclei).

Potential energy of the proton gets converted into kinetic energy.

i.e. 1/2 mv² = qV

Where m is mass of the proton, v is velocity of the proton and q is charge on proton, V is potential difference.

Given,

mass of the proton m = 1.6 × 10⁻²⁷ kg

charge on proton q =1.6 × 10⁻¹⁹ C

P.D. V = 91 V

putting values in equation,

1/2× 1.6 × 10⁻²⁷ kg × v² = 1.6 × 10⁻¹⁹ C × 91 V

0.8 × 10⁻²⁷ v² = 145 × 10⁻¹⁹ C

v = 1.34 × 10⁵ m/s

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The total distance travelled by the object is 175 m.

option B.

The total distance travelled by the object is calculated by applying the following kinematic equation as shown below;

Total distance = area rectangle + area of triangle

Total distance = (15 s - 0 s) x (10 m/s - 0 m/s) + ¹/₂(5s)((10 m/s)

Total distance = (15s)(10 m/s) + (5s )(5 m/s)

Total distance = 150 m + 25 m

Total distance = 175 m

Thus, the total distance travelled by the object is sum of all the distance covered from 0 second to 15 seconds.

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Within Chinua Achebe's novel entitled "Things Fall Apart", there lies a figure of paramount importance: Okonkwo.

This individual is marked by two fundamental traits - determination and an unyielding dread of revealing his vulnerability, for he places immense value in tradition and rampant masculinity.

His ironclad willpower fuels his ambitions to attain respect and success within his community, through unwavering persistence and ceaseless diligence. Empowered by his fearsome strength and exceptional valor on the battlefield, along with his gathering wealth and spouses, this man gradually rises above his peers in stature, receiving adoration and honor in return.

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Answer: Solar

Explanation: This is simple enough the only one of these options that do not require a pump or power plant is solar which is usually attained with a non-moving solar panel

hope this helps :)