Use 9.81 m/s² for acceleration due to gravity.
An electric winch lifts a 20 kg crate 2.5 meters. If the winch must not exceed 100 watts during use, what is the fastest time that could be used to lift the crate?
A) 5 seconds
B) 3 seconds
C) 6 seconds
D) 4 seconds

If Galileo dropped two balls of the same size but different weights from the top of the Leaning Tower of Pisa, and air resistance was not negligible, the heavier ball would strike the ground first.

The reason is that the air resistance has a greater effect on the lighter ball, slowing it down more than the heavier ball. Therefore, the heavier ball experiences less deceleration due to air resistance and reaches the ground faster. According to Galileo's experiments, both balls would have hit the ground at the same time, regardless of their weight.

This is because Galileo discovered that objects fall at the same rate regardless of their mass. This is due to the force of gravity being the same for both objects, and any differences in weight would be offset by the difference in air resistance. Therefore, even if one ball was much heavier than the other, both would still hit the ground at the same time.

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The equation that relates Moment of Inertia (MoI) to Centroidal Radius of Gyration is: MoI = mk² Where MoI is the moment of inertia, m is the mass of the object, and k is the radius of gyration.

The radius of gyration, k, is the distance from the centroid of the object to a point where the entire mass of the object can be concentrated and its moment of inertia remains the same.

The root-mean-square distance of all electrons from their centres of gravity is the particle's radius of gyration, or R. With the exception of the fact that in this case, electrons stand in for mass elements, R is defined in exact similarity to the radius of inertia in mechanics.

Due to this, the radius of gyration of a frame rotating about a given axis of rotation is the radial distance from the axis, and the instantaneous moment of inertia of the frame about that axis is determined by raising the square of the radius of gyration (ok) by means of the body's entire mass.

The distance between a body's axis and the point in the frame whose moment of inertia is equal to that of the entire body is known as the radius of gyration. The square root of the ratio between the instantaneous moment of inertia of the entire body and the mass of the entire machine yields the radius of gyration.

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A thin prism of 18 has refractive indices 1. 56 for red and 1. 67 for violet then the angular dispersion produced by the prism is 10.98°.

A prism is a polyhedron composed of an n-sided polygon basis, a second base that is a translated copy (rigidly moved without rotation) of the first, and n additional faces, all of which must be parallelograms, connecting the two bases. All parallel cross-sections to the bases are translations of the bases. Prisms are termed for their bases; for example, a prism with a pentagonal base is referred to as a pentagonal prism. Prisms are a kind of prismoids.

We know that the angle of deviation is given by:

δ = (μ - 1)A

where A is the angle of the prism and μ is the refractive index of the prism for the given color.

For red light, μ = 1.56, so the deviation produced by the prism for red light is:

δ_r = (1.56 - 1) × 18 = 10.08°

For violet light, μ = 1.67, so the deviation produced by the prism for violet light is:

δ_v = (1.67 - 1) × 18 = 21.06°

The angular dispersion produced by the prism is the difference between the deviations produced by the prism for the two colors:

Angular dispersion = δ_v - δ_r = 21.06° - 10.08° = 10.98°

Therefore, the angular dispersion produced by the prism is 10.98°.

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Based on the graphs, it is clear that there is a strong correlation between the amount of CO₂ in the atmosphere and the atmospheric temperature over time.

When CO₂ levels increase, so does the temperature. When CO₂ levels decrease, so does the temperature. This correlation has been observed over millions of years, and it is likely that this correlation will continue into the future.

Human activity is currently increasing the amount of CO₂ in the atmosphere at an alarming rate. This is due to the burning of fossil fuels, such as coal, oil, and natural gas. When these fuels are burned, they release CO₂ into the atmosphere. This CO₂ then traps heat from the sun, which causes the Earth's temperature to rise.

If human activity continues to increase the amount of CO₂ in the atmosphere, the Earth's temperature is likely to continue to rise. This could have a number of negative consequences, such as more extreme weather events, rising sea levels, and the extinction of species.

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Based on the graphs below, the conclusion that can be made regarding the amount of CO₂ in the atmosphere and the atmospheric temperature over time is: Both the temperature and CO₂ concentration are positively related.

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The operator of a vessel is required to stay at least 100 feet clear of a diver's down flag on a river, inlet, or channel.

When a diver is in the water, a down flag is typically displayed to indicate their presence. This flag serves as a signal to boaters to maintain a safe distance and avoid the area where the diver is located. To ensure the safety of both divers and boaters, regulations often require vessel operators to maintain a specific distance from the diver's down flag.

In this case, the required distance is 100 feet, which allows for an adequate buffer zone to prevent any potential collisions or disturbances that could endanger the diver or disrupt their activities.

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The angle θ between the field vector [tex]\vec{E}[/tex] and an area vector [tex]\vec{dA}[/tex] on the external end cap is found by determining the directions of both vectors and measuring the angle between them.

A vector field in the plane can be visualized as a collection of arrows with a given magnitude and direction, each attached to a point in the plane.

To find the angle θ between the field vector [tex]\vec{E}[/tex] and an area vector [tex]\vec{dA}[/tex] on the external end cap, proceed as follows:

1. Determine the direction of the field vector [tex]\vec{E}[/tex]. This is usually given or can be deduced based on the problem's context.

2. Determine the direction of the area vector [tex]\vec{dA}[/tex]. For an external end cap, the area vector points outward, perpendicular to the surface.

3. Identify the angle θ between the field vector [tex]\vec{E}[/tex] and the area vector [tex]\vec{dA}[/tex]. This angle can be found by visualizing or drawing the vectors and measuring the angle between their directions.

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The impulse (J) is defined as the product of the force (F) and the time (Δt) for which it is applied:

J = FΔt

Substituting the given values, we get:

J = 10 N × 2.5 s = 25 N·s

Therefore, the impulse when an average force of 10 N is exerted on a cart for 2.5 s is 25 N·s.

Parallax is the apparent shift in the position of an object when viewed from two different angles. It allows us to measure directly the distance between the observer and the object being observed.

By measuring the angle of parallax, we can calculate the distance between the observer and the object. This technique is commonly used in astronomy to measure the distance between stars and other celestial objects.

Parallax is an observational phenomenon in which an object's apparent position changes when viewed from different locations or perspectives. This effect occurs due to the difference in the observer's line of sight. In astronomy, parallax is used to measure the distance to nearby stars.

Parallax allows us to measure the distance to a celestial object directly. By observing an object from two different points, astronomers can calculate the angle between the two lines of sight. Then, by knowing the baseline distance between the observation points and using basic trigonometry, the distance to the object can be determined. This method is most effective for nearby stars, as their parallax angles are larger and easier to measure.

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True, the Kinetic Energy (KE) per unit mass for turbulent flow is approximately um^2/2.

True, the KE per unit mass flowing in turbulent flow is approximately given by the expression um^2/2, where "u" represents the flow velocity and "m" represents the mass.

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The electric field is a quantity used to determine the effect of electric charges on other charges in space.

The electric field is a quantity used to determine the effect of electric charges on other charges in space.

It is a vector field that describes the direction and magnitude of the force experienced by a charged particle in the presence of other charges.

The electric field at a given point is defined as the force per unit charge experienced by a test charge placed at that point. It is calculated by dividing the force exerted on the test charge by the magnitude of the charge.

The electric field is an important concept in electromagnetism and is used in many applications, including the design of electrical devices and the understanding of the behavior of charged particles in space.

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When the charge is developed at the capacitor because of the potential difference, the transfer of charges in the parallel plate capacitor is stopped.

The capacitor is a device used to store electrical energy. When a parallel plate capacitor is connected to the battery, The charges are acquired on one plate of the conductor by the positive terminal of the battery.

Thus, one plate acquires a positive charge on the plate. Because of this positive charge, the other plate acquires the negative charge. As the amount of charges increases, the voltage developed on the plate is opposite to the applied voltage.

The current flow in the circuit gradually decreases and thus, the charge is accumulated on the conductor. When the capacitor acquires charges, the transfer of charges between plates is stopped.

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The energy absorbed by the surface in 10 seconds is 1.3275 x 10⁻⁷ J.

The energy absorbed by the surface can be calculated using the formula:

Energy = Power x Time

The power absorbed by the surface can be calculated using the formula:

Power = Intensity x Area

where Intensity is the intensity of the electromagnetic wave, given by:

Intensity = (1/2) * ε0 * c * E²

where ε0 is the permittivity of free space, c is the speed of light, and E is the electric field amplitude of the wave.

Substituting the given values, we get:

Intensity = (1/2) * ([tex]8.85 x 10^-12 C^2/N*m^2[/tex]) * ([tex]3 x 10^8 m/s[/tex]) * ([tex]100 V/m)^2[/tex]

Intensity = 1.3275 x [tex]10^-^4[/tex] W/[tex]m^2[/tex]

Power = Intensity x Area = ([tex]1.3275 x 10^-^4 W/m^2[/tex]) x (1 [tex]cm^2[/tex]/10000 [tex]m^2[/tex]) = 1.3275 x [tex]10^-^8[/tex] W

Now, we can calculate the energy absorbed by the surface in 10 seconds:

Energy = Power x Time = (1.3275 x [tex]10^-^8[/tex] W) x (10 s) = 1.3275 x [tex]10^-^7[/tex] J

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The mass attached to a vertical spring will be located at the point of maximum displacement when its total energy is at a minimum. Therefore, the energy of the system is at a minimum at this point, and the mass will be located there.


When a mass is attached to a vertical spring and bobs up and down between points A and B, the total energy consists of the potential energy stored in the spring (spring potential energy) and the kinetic energy of the mass. The total energy is at its minimum when the kinetic energy is at its maximum and the spring potential energy is at its minimum.
This is because at this point of displacement, the potential energy of the spring is at its lowest (since the spring is neither compressed nor stretched to its maximum), and the kinetic energy of the mass is also at its lowest (since the mass is momentarily stationary before changing direction).
This occurs when the mass is at equilibrium, which is the point where the spring is neither stretched nor compressed. At this position, the spring potential energy is at its minimum value and the kinetic energy is at its maximum value. Therefore, the mass is in equilibrium when its total energy is at a minimum.

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The Stefan-Boltzmann law is a fundamental principle of thermodynamics that relates the energy radiated by a body to its temperature. By measuring the total energy emitted by a star, astronomers can calculate its effective temperature using the Stefan-Boltzmann law.

The Stefan-Boltzmann Law is a crucial tool in understanding and interpreting stellar properties. This law relates the luminosity (energy emitted per unit time) of a star to its temperature and size. Mathematically, it is expressed as:

L = σ × A × T^4

Where:
L is the luminosity of the star.
σ is the Stefan-Boltzmann constant (5.67 10-8 W m-2 K-4).
A is the surface area of the star (A = 4R2, where R is the radius).
T is the temperature of the star in Kelvin.

By using this law, astronomers can determine various properties of a star, such as its radius, temperature, and luminosity, by measuring either the temperature or luminosity and using the known values of the Stefan-Boltzmann constant and the star's surface area.

For example, if the temperature and luminosity of a star are known, the radius can be calculated by rearranging the equation:

R = sqrt(L / (4T4))
This allows them to determine the star's luminosity and radius, as well as other important parameters such as its mass and age. The law is particularly useful for understanding the behavior of different types of stars, from cool red dwarfs to hot blue supergiants. Overall, the Stefan-Boltzmann law is a key tool for astronomers in interpreting the complex properties of stellar objects.

Additionally, the Stefan-Boltzmann Law allows astronomers to classify stars based on their temperature and luminosity, enabling a better understanding of stellar evolution and the life cycle of stars.

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The statement is true. In fluid mechanics, the basic conservation laws are those of volume, energy, and momentum.

In fluid mechanics, the basic conservation laws are those of volume, energy, and momentum. These laws are fundamental principles that govern the behavior of fluids, and they are derived from basic physical principles such as the law of conservation of mass, the first law of thermodynamics, and Newton's laws of motion.

The law of conservation of volume states that the total volume of a fluid is constant, which means that the amount of fluid entering a region must be equal to the amount leaving it.

The law of conservation of energy states that the total energy of a fluid system is constant, which means that the sum of the kinetic, potential, and internal energies of the fluid must be conserved.

The law of conservation of momentum states that the total momentum of a fluid system is constant, which means that the sum of the forces acting on the fluid must be equal to the rate of change of momentum of the fluid.

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To convert a vector into a single-linked list, you can follow these steps:

1. Create an empty single-linked list.
2. Iterate through each element in the vector.
3. For each element, create a new node in the single-linked list.
4. Set the value of the new node to the corresponding element in the vector.
5. Link the new node to the previous node (if there is one) in the single-linked list.
6. Set the head of the single-linked list to the first node.

Here's an example code snippet in Python:

```
class Node:
   def __init__(self, val):
       self.val = val
       self.next = None

def vector_to_linked_list(vector):
   head = None
   prev = None
   for val in vector:
       node = Node(val)
       if prev:
           prev.next = node
       else:
           head = node
       prev = node
   return head
```

In this code, `Node` represents a node in the single-linked list. The `vector_to_linked_list` function takes a vector as input and returns the head of the corresponding single-linked list. The function iterates through each element in the vector, creates a new node with that element as the value, links the node to the previous node (if there is one), and updates the head and previous node pointers. Finally, the function returns the head of the single-linked list.

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Velocity and mass flux are related but distinct physical quantities, therefore, the answer is F (false).

Velocity and mass flux are two related but different physical quantities that are commonly used in the study of fluid mechanics. Velocity refers to the speed and direction of fluid flow or the rate at which a fluid moves through a given space. Velocity can be measured using a variety of methods, including using a flow meter or tracking particles in the fluid to determine their movement.

On the other hand, mass flux (or mass flow rate) is a measure of the amount of mass that is flowing through a given area over time. This quantity is particularly useful in situations where the amount of fluid flowing through a system is important, such as in chemical or industrial processes, or in the design of fluid transport systems. Mass flux can be calculated by multiplying the density of the fluid by its velocity and cross-sectional area.

The equation Q = ρAV, where Q is the mass flux, ρ is the density, A is the cross-sectional area, and V is the velocity, is commonly used to calculate mass flux. The density of the fluid can be obtained from experimental measurements or calculated from the fluid's properties. Cross-sectional area can be calculated if the geometry of the system is known.

In summary, while velocity and mass flux are related quantities, they measure different aspects of fluid flow. Velocity refers to the speed and direction of fluid motion, while mass flux measures the amount of mass flowing through a given area over time. Understanding these concepts is important for many applications in fluid mechanics and related fields.

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The speed of Sheena with respect to her starting point on the bank would be 3.20 mi/h.

Let's first calculate the speed of the river current component along the direction of Sheena's desired motion (straight across the river):

Current velocity component = 1.90 mi/h x sin(25.0°)

Current velocity component = 0.805 mi/h

Now, let's calculate the speed of Sheena's boat relative to the water while she is rowing straight across the river:

Speed of boat relative to water = 3.10 mi/h

Therefore, the speed of Sheena's boat with respect to the starting point on the bank is:

Speed = √[(3.10 mi/h)² + (0.805 mi/h)²]

Speed = 3.20 mi/h

So, Sheena's speed with respect to the starting point on the bank is approximately 3.20 mi/h.

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Water is an essential and fundamental resource for life on Earth.

It is used for various purposes in our daily lives, including

Hence, water is an essential resource for life, and we need it for various purposes to survive and thrive.

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Decreasing  the mass of the system would increase the resonant frequency, all else being equal.

Increasing the mass (M) of a mass-and-spring system while keeping the spring constant (K) constant will cause a decrease in the resonant frequency of the system.

The resonant frequency of a mass-and-spring system is given by the equation:

f = 1/(2π) √(K/M)

where f is the resonant frequency, K is the spring constant, and M is the mass of the system.

From this equation, we can see that the resonant frequency is inversely proportional to the square root of the mass. This means that as the mass of the system increases, the resonant frequency decreases.

Intuitively, this makes sense because increasing the mass of the system makes it harder for the system to oscillate back and forth at high frequencies. The spring has to work harder to move the heavier mass, which results in a lower resonant frequency. Conversely, decreasing the mass of the system would increase the resonant frequency, all else being equal.

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When a positive charge +q is suspended at the center of a hollow spherical conductor that is electrically neutral, induced charges appear and the electric field becomes zero at specific location

Induced charges appear on the inner surface of the spherical conductor, and they will be negative charges due to the presence of the positive charge at the center. The electric field is zero inside the conductor's material and in the space between the positive charge and the inner surface of the conductor. This is because the spherical conductor distributes the induced charges evenly on its inner surface, which cancels out the electric field within that region.

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The resistance of a copper wire increases by 20%, So, we need to raise the temperature of the wire by approximately 58.4 ˚C.

To determine the temperature at which the resistance of a copper wire would increase by 20%, we need to understand the relationship between temperature and resistance. The resistance of a wire increases with temperature due to the increased vibrations of the wire's atoms, which leads to an increase in the number of collisions between the electrons and the atoms.

The resistance of a copper wire can be calculated using the formula R = ρL/A, where R is resistance, ρ is the resistivity of copper, L is the length of the wire, and A is the cross-sectional area of the wire. At a given temperature, the resistivity of copper is constant, so we can assume that it is not a factor in the change in resistance.

If we increase the temperature of the copper wire by ΔT, then we can calculate the new resistance using the formula R' = R(1 + αΔT), where α is the temperature coefficient of resistance for copper, which is approximately 0.00428 ˚C⁻¹.

To increase the resistance of the copper wire by 20%, we can set R' = 1.2R and solve for ΔT:

1.2R = R(1 + αΔT)
1.2 = 1 + αΔT
ΔT = (1.2-1)/α
ΔT = 58.4 ˚C

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The wavelengths of absorption lines of hydrogen are the same as the wavelengths of emission lines of hydrogen.

This is because the absorption lines occur when atoms of hydrogen absorb certain wavelengths of light, while the emission lines occur when atoms of hydrogen release that same absorbed energy as light of the same wavelength. Therefore, the wavelengths of absorption and emission lines of hydrogen are identical.

Here's a step-by-step explanation:
1. When a hydrogen atom absorbs energy, its electrons move from a lower energy level to a higher energy level. This process creates absorption lines at specific wavelengths.
2. When the electrons in the hydrogen atom return to their original lower energy level, they release the absorbed energy in the form of light. This process creates emission lines.
3. The wavelengths of the emitted light (emission lines) exactly match the wavelengths of the absorbed light (absorption lines) because the energy difference between the energy levels remains constant.

In conclusion, the wavelengths of absorption lines and emission lines of hydrogen are the same, as they correspond to the energy transitions of electrons within the hydrogen atom.

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When two people each exert a force of 300N, pulling a car by a separate ropes in the east direction. the first person pulls at an angle of 20° N of E and the second person pulls at an angle of 20° S of E. then the work done on the car by each worker is 1578 J if the the car moves 0.5 m/s for 5.6s.

Given,

x component of Force F₁  = Fcos20° = 300cos20° = 281.9 N

y component of Force F₂  = Fcos20° = 300cos20° = 281.9 N

The actual force acting on the car is,

F₁(x) + F₂(x) = 281.9 N + 281.9 N = 563.8 N.

The distance travelled by the car,

d = v×t = = 0.5 × 5.6 = 2.8 m

The work W is force times distance

W = F.s = 563.8 N.× 2.8 m = 1578 J

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Electromagnetics waves do not need to travel through a medium

Mechanical waves need to travel through a medium

All electromagnetic waves travels at a speed of  3 x 10^8 m/s..

Mechanical waves are the type of waves that require material medium for its propagation.

Examples of include;

Electromagnetic waves are the type of waves that do not require material medium for their propagation.

Examples include;

All electromagnetic waves travels at speed of light = 3 x 10^8 m/s.

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A speedometer does not directly indicate whether or not acceleration is occurring in a straight-line motion.

A speedometer is a device that measures and displays the instantaneous speed of a vehicle or object. It provides information about the rate at which the object is changing its position over time. However, acceleration refers to a change in velocity, which includes changes in speed and changes in direction. Since a speedometer only measures the magnitude of the speed, it cannot directly indicate whether or not acceleration is occurring.

To determine whether or not acceleration is occurring in a straight-line motion, one would need to analyze the changes in speed over time or examine other factors such as the object's position and time elapsed. The speedometer alone cannot provide this information.

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Based on the information provided, the astronomer is likely studying an elliptical galaxy. Elliptical galaxies are composed mainly of old, low-mass stars and typically have little interstellar dust or gas.

This would also be in line with the observation of population II stars, which are typically found in older stellar populations. An alternative explanation could be that the galaxy is a dwarf spheroidal galaxy, but more information would be needed to make a definitive determination.

An astronomer studying a galaxy that has a spectrum showing only old, low-mass, population II stars, and photographs revealing little or no interstellar dust or gas is most likely studying an elliptical galaxy. The explanation for this observation is that elliptical galaxies primarily consist of old, low-mass stars and have less interstellar matter compared to other types of galaxies, such as spiral galaxies.

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As the power supply voltage was increased, the current flowing in the circuit also increased. This is because as the voltage increases, the resistance in the circuit remains constant,

which means that the current must also increase in order to maintain Ohm's law. This agrees with my prediction that increasing the voltage would lead to an increase in current flow.

However, it is important to note that there is a limit to how much current can flow through the circuit before it becomes overloaded, which could potentially damage the components.

Therefore, it is important to always use caution and follow the specifications of the components being used when working with electrical circuits.

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The speed of the 2000 kg compact car that has the same kinetic energy as a 20000 kg truck going 25 km/hr is approximately 34.6 m/s.

To find the speed of the 2000 kg compact car that has the same kinetic energy as a 20000 kg truck going 25 km/hr, we can use the formula for kinetic energy, which is KE = 1/2 [tex]mv^2[/tex].
First, we need to find the kinetic energy of the 20000 kg truck going 25 km/hr. We convert 25 km/hr to m/s by multiplying by 1000/3600, which gives us 6.94 m/s. Then, we plug in the values into the formula:

KE = 1/2 (20000 kg) [tex](6.94 m/s)^2[/tex] = 959,200 J.
Next, we set this equal to the kinetic energy of the compact car: KE = 1/2 (2000 kg) [tex]v^2[/tex]. We can simplify this equation by dividing both sides by 1/2 (2000 kg), which gives us v^2 = 959,200 J / (1/2) (2000 kg).
Solving for v, we take the square root of both sides: v = √(959,200 J / (1/2) (2000 kg)) = 34.6 m/s.
Therefore, the speed of the 2000 kg compact car that has the same kinetic energy as a 20000 kg truck going 25 km/hr is approximately 34.6 m/s.

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Given that A⃗ +B⃗ = C⃗ and that |A|^2 + |B|^2 = |C|^2 then vectors A and B oriented with respect to each other perpendicular to one another. Hence option C is correct.

Vector is a colloquial phrase in mathematics and physics that refers to some quantities that cannot be described by a single integer (a scalar) or to elements of specific vector spaces.

Vectors were first used in geometry and physics (usually in mechanics) to represent variables with both a magnitude and a direction, such as displacements, forces, and velocity. In the same way as distances, masses, and time are represented by real numbers, same quantities are represented by geometric vectors.

In certain circumstances, the term vector also refers to tuples, which are finite sequences of integers of a defined length.  |A|^2 + |B|^2 = |C|^2 then vectors A and B oriented with respect to each other perpendicular to one another

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