A particle leaves the origin with an initial velocity=(3.76i)m/s and a constant acceleration =(-1.43i-2.69j) m/s^2. When the particle reaches its maximum x coordinate, what are (a) its velocity, (b) its position vector

The velocity with which the sandbag strikes the ground is  -28.44m/s (downward).

Given the initial velocity of balloon (u) = 5m/s

The height of balloon (h) = 40m

The acceleration is due to the gravity = g = 9.8m/s^2 acting downwards.

A sandbag is released from height h of the balloon.

The velocity of sandbag as it reaches the ground = v

We know that from Newtons laws of motion v = u + at

We know that the bag strikes the ground at y =0m,

then y = h + ut - 1/2gt^2

0 = 40 + 5t - 1/2 x 9.8 x t^2

t = 3.41s

As we know that v = u - gt

v = 5 - 9.8 x 3.41 = -28.44m/s

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complete question: A hot-air balloonist, rising vertically with a constant velocity of magnitude 5.00m/s releases a sandbag at an instant when the balloon is 40.0m above the ground. With what magnitude of velocity does it strike the ground?

To maintain the same resistance, we need to increase either the length or decrease the cross-sectional area to compensate for the increased resistivity of metal B. One option could be to increase the length of the resistor to 18 cm and keep the cross-sectional area the same. Another option could be to decrease the cross-sectional area to 1.5 cm^2 and keep the length the same.

The resistance of the resistor can be calculated using the following formula:

R = ρ * L / A

where

ρ = resistivity (2 ohm-cm for metal A)

L = length (9 cm)

A = cross-sectional area (3 cm^2)

R = 2 ohm-cm * 9 cm / 3 cm^2 = 6 Ω

To design a resistor with the same resistance using metal B (ρ = 6 ohm-cm), we need to keep the resistance formula constant:

R = ρ * L / A

6 Ω = 6 ohm-cm * L / A

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Two equations represent double replacement reactions are:

C. 2C2H6+7O2=4CO2 +6H2o

D. Ca+MgS=CaS+Mg

A metathesis reaction, sometimes referred to as a double exchange reaction, double replacement reaction, or multiple decomposition reaction, is a chemical reaction involving the exchange of bonds between two non-reacting chemical species resulting in the formation of products with the same type of bond. This reaction is illustrated by the following scheme:

A-B + C-D → A-D + C-B

A metathesis reaction involves the exchange of two groups or ions between the reactants.

The bond between reacting species can be either ionic or covalent. Usually, this reaction produces an insoluble product from the soluble reactant. This product is referred to as precipitate.

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The maximum height reached by the ball which a student throws upwards is calculated to be 25 m.

The ball is going upward with a kinetic energy of 40 J and a potential energy of 60 J at a height of 15 m.

Let us find out the maximum height reached by the ball.

As potential energy is given as 60 J,

m g h = 60

m g (15) = 60

m g = 4 ----(1)

The total energy of the system at 15 meters is given as PE + KE = 100 Joules. From the conservation of energy the total energy in the system still remains the same at the maximum height, this is because energy cannot be generated or destroyed; it can be transformed from one type to other.

At the maximum height the velocity (v) of the system is 0, which means all its kinetic energy (KE) is converted to potential energy. Therefore the system consist only of potential energy.

KE + PE = 100

1/2 m v² + m g h = 100

Velocity v = 0 at the maximum height.

So, m g h = 100 ----(2)

From equation (1), m g = 4

Let us substitute in (2),

m g h = 100

4 h = 100

h = 25 m

Thus, the maximum height achieved by the ball is 25 m.

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Star A is thus (3.24^4 = 51.2) times brighter than star B.

In physics, brightness is the subjective visual feeling associated with the intensity of light emerging from a surface or a point source (see luminous intensity). Luminance is a quantitative and measurable property. Whereas brightness cannot be measured scientifically, it can only be sensed. We can tell if a light source is bright or dim, therefore brightness is the visual sense that alerts us to changes in luminance.

Here,

The relationship between temperature and brightness in stars is described by the Stefan-Boltzmann law, which states that the total energy emitted by a star per unit time (its luminosity) is proportional to the fourth power of its temperature.

L ∝ T^4

where L is the luminosity and T is the temperature.

If star A is 3.2 times hotter than star B, then its temperature is 3.2 times higher:

T_A = 3.2 T_B

So, its luminosity is proportional to the fourth power of its temperature:

L_A ∝ T_A^4 = (3.2 T_B)^4 = 3.2^4 T_B^4 = 3.2^4 L_B

Therefore, star A is (3.2^4 = 51.2) times brighter than star B.

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a. Kinetic Energy = 49j

b.  Potential Energy= 147 j

c. Mechanical Energy = 196 j

Kinetic energy of an object is the energy that it possesses due to its motion which is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity.

a. Kinetic Energy = 1/2 * m * v^2,

KE = 1/2 * 3kg * (7m/s)^2 = 49 J.

b. Potential Energy  = m * g * h,

PE = 3kg * 9.8 m/s^2 * 5m = 147 J.

c. Mechanical Energy  = KE + PE,

ME = 49 J + 147 J = 196 J.

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Taking into account the definition of kinetic, potencial and mechanical energy, if a 3kg ball 5m in the air is moving at 7m/s, the kinetic energy is 73.5 J, the potential energy is 147.15 J and the mechanical energy is 220.65 J.

Kinetic energy is the energy possessed by a body or system due to its movement.

Kinetic energy is defined as the amount of work necessary to accelerate a body of a certain mass and in a position of rest, until it reaches a certain speed. Once the final speed is reached, the amount of kinetic energy accumulated will remain constant, that is, it will not vary, unless another force acts on the body again.

Kinetic energy is represented by the following expression:

Ec = 1/2×m×v²

Where:

Gravitational Potential Energy is the energy that an object possesses due to its position in a gravitational field and represents the potential that an object has to do work as a result of being located in a particular position within that gravitational field.

For an object with mass m, at height h, the expression applied to the gravitational energy of the object is:

Ep= m×g×h

Where:

Mechanical energy is that which a body or a system obtains as a result of the speed of its movement or its specific position, and which is capable of producing mechanical work. This is:

Potential energy + kinetic energy = total mechanical energy

The principle of conservation of mechanical energy indicates that the mechanical energy of a body remains constant when all the forces acting on it are conservative (a force is conservative when the work it does on a body depends only on the initial and final points and not the path taken to get from one to the other.)

In this case, you know:

Replacing the definition of kinetic energy:

Ec = 1/2×3 kg× (7 m/s)²

Solving:

Ec= 73.5 J

The kinetic energy is 73.5 J.

You know:

Replacing in the definition of potential energy:

Ep= 3 kg× 9.81 m/s²× 5 m

Solving:

Ep= 147.15 J

The potential energy is 147.15 J.

Being:

the mechanical energy can be calculated as:

Potential energy + kinetic energy = total mechanical energy

147.15 J + 73.5 J = total mechanical energy

Solving:

220.65 J = total mechanical energy

The mechanical energy is 220.65 J.

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The  tension in the string of a conical pendulum is 18.6 N.

The  tension in the string of a conical pendulum can be determined using the following formula:

T = mg(L / L + lcos(θ))

where:

The  tension in the string of a conical pendulum is calculated as

T = 2.5 x 9.8 x (0.68 / (0.68 + (2.5 x 9.8 x cos(35°)))

T = 18.6 N.

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The average shear stress developed in the shear plane where the collar A and shaft are connected is 50.265 kPa.

The average shear stress can be calculated using the formula:

τ_avg = F / A

where F is the applied axial force of 5 kN and A is the shear area.

The shear area can be calculated using the formula:

A = π * d * t

where d is the diameter of the shaft (60 mm) and t is the thickness of the collar (15 mm).

Substituting the values, we get:

A = π * 60 * 15 * 10^-6 m^2

Calculating the average shear stress:

τ_avg = 5 kN / (π * 60 * 15 * 10^-6 m^2) = 50.265 kPa

Therefore, the average shear stress developed in the shear plane where the collar A and shaft are connected is 50.265 kPa.

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A bond involves the sharing of electron pairs between atoms, also known as a molecular bond.

The given statement is True.

A covalent bond is a chemical relationship that requires the sharing of electrons between atoms to generate electron pairs. These electron couples are known as bonding pairs or sharing pairs. Covalent bonding is the steady equilibrium of attractive and repulsive forces between atoms when they share electrons.

The number of atoms that can be bound together to create molecules is fixed; for example, every water molecule has two hydrogen atoms and one oxygen atom. Chemical compounds are distinguished from solutions and other mechanical mixes by this property.

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The force of gravitational attraction between the man and woman is 1.0672 × 10⁻⁶ N, if the mass of the man & woman is 80 kg & 50 kg respectively.

Let the Mass of the man, m₁ = 80 kg

Mass of the woman, m₂ = 50 kg

Distance between them, d = 0.5 m

We know the universal gravitational constant, G = 6.67 × 10⁻¹¹ Nm²/kg²

According to Newton's law of gravitation, Gravitational force between two objects having mass m₁ & m₂ at a distance apart d meter, is mathematically formulated as, F = Gm₁m₂/d²

F = (6.67 × 10⁻¹¹ × 80 × 50)/0.5²

F = (2.668 × 10⁻⁷) /0.25

F = 1.0672 × 10⁻⁶ N

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It was Shiloh's initial archaeological dig. At the location, he found the most well-known relic.

From from 500 B.C. to roughly 1650 A.D., the Adena, Hopewell, and Fort Ancient Native American societies constructed mounds and enclosures in the Ohio River Valley for burial, religious, and occasionally defence purposes. In 1899, "Mound C" was penetrated by a trench that was built by Shiloh Park Commission chairman Cornelius Cadle. The first archaeological dig at Shiloh took place in 1350 CE, after which the site was abandoned. Around 1000 CE, indigenous people of the Late Woodland civilization first inhabited the area, followed by those of the Early Mississippian culture. The largest stone pipe carved into the form of a kneeling man was the most well-known relic he found at the location. Therefore, choice A is right.

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Proton is subject to a dipole-induced force of F = 32.40 10-15 N. [(proh-ton)] A positively charged elementary particle that can be found in the atom's nucleus.

A proton, a subatomic particle, is found in the nucleus of every atom. The particle has a positive electrical charge, similar to the electron but moving in the other direction. The H+ ion or the hydrogen atom's nucleus are examples of protons. Each hydrogen atom, regardless of isotope, has one proton, each helium atom, two, each lithium atom, three, and so on. The electron, which is negatively charged, is a very light particle. These electrons go around the nucleus in different orbits. Protons are positively charged particles that have a mass of about 1 amu. These positively charged particles are found in the center of the atom, the nucleus.

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The point between the two charges where the electric field equal to zero is calculated to be 0.32 m.

The charge q₁ is given as 2 μc = 2 × 10⁻⁶ c

It is located at x₁ = 0.

The charge q₂ is given as 5 μc = 5 × 10⁻⁶ c

It is located at x₂ = 1 m.

Let us suppose that, electric field is zero at the point x, it is in between 0 and 1 m.

We know the formula for electric field as,

E = k q /r²

Let us equate the electric field at both the charges.

k q₁/x² = k q₂/(x₂ - x)²

q₁ (x₂ - x)² = q₂ x²

2 × 10⁻⁶× (1 - x)² = 5 × 10⁻⁶× x²

2 × ( 1 + x² - 2x) = 5 × x²

2 + 2x² - 4x = 5x²

7 x² + 4x - 2 = 0

The two values of x are,

x = 0.32, -0.892

The distance cannot be negative. So, the electric field at x = 0.32 m is said to be zero.

Thus, the required value of x is 0.32 m.

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False. The terminator of a gene is located downstream of the coding region.The terminator of a gene is a DNA sequence that signals the end of transcription, or the process by which genetic information is converted from DNA to RNA.

It is located downstream of the coding region, which is the part of the gene that contains the instructions for making a particular protein. The terminator helps to regulate the amount of mRNA that is produced, as well as to prevent the production of unwanted transcripts. The precise location and sequence of the terminator vary among different genes, but its role in regulating transcription is an important aspect of gene expression.

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The electric field within the sphere is given by E = (4p/3) * (R^3 - r^3) / (R^2 - r^2). The electric field inside the slab is given by E = pd/2. The electric field at the center of the spherical cavity is given by E = pd/2 * (R/d)2.

Electric flux is the measure of the electric field through a particular surface in electromagnetism, despite the fact that an electric field cannot flow. At any location in space, the electric field E can impose a force on an electric charge. The gradient of the potential is represented by the electric field.

Here,

(a) According to Gauss's Law, the electric flux through any closed surface is proportional to the charge contained inside the surface. The electric field at a location inside a solid sphere may be computed by splitting the sphere into concentric shells and calculating the electric field owing to each shell. Inside the sphere, the electric field is given by:

E = (4πp/3) * (R^3 - r^3) / (R^2 - r^2)

(b) The electric field inside a charged slab may be calculated by splitting the slab into thin charge layers and adding the electric field owing to each layer. Inside the slab, the electric field is given by:

E = pd/2

(c) Subtracting the electric field owing to the slab from the electric field due to the entire space yields the electric field at the center of a spherical cavity in an indefinitely large charged slab. The electric field at the spherical cavity's center is given by:

E = pd/2 * (R/d)^2

The electric field inside the sphere is given by: E = (4πp/3) * (R^3 - r^3) / (R^2 - r^2). The electric field inside the slab is given by: E = pd/2. The electric field at the center of the spherical cavity is given by: E = pd/2 * (R/d)^2.

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The time cannot be calculated without those values but if we take R= 1 and C= 1, the switch opens at almost 4 milliseconds according to the question.

The time constant, τ, of the RC circuit would be τ = R × C = 1 × 1 = 1 (Where R denotes the resistance and C the capacitance).

The time it takes for the energy stored in the capacitor to fall to 79% of its final value after the switch opens is approximately equal to

4 × τ = 4 × 1 = 4 milliseconds.

After the switch opens, it takes around 4 times for the energy stored in the capacitor to decrease to 79% of its final amount.

Therefore, knowing the values of R and C is necessary in order to calculate the time in milliseconds. The time cannot be calculated without those values.

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A.

The handle of the hammer could possibly have sweat or skin on it.

The final speed of the wreckage after the collision is 17.5 km/h north.

The final speed of the wreckage after the collision is calculated by applying the principle of conservation of linear momentum.

m₁u₁ + m₂u₂ = v ( m₁ + m₂ )

where;

let north be positive and let south be negative direction

The final speed is calculated as follows;

(2 x 70) - (1.2 x 70) = v ( 2 + 1.2 )

56 = 3.2v

v = 56/3.2

v = 17.5 km/h north

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Answer:

1500 Ω

Explanation:

The resistance of the sensor circuit can be found using Ohm's law, R = V/I, where R is resistance, V is voltage, and I is current.

R = 3.0V / 2.0 x 10^-4 A = 1500 Ω.

So the resistance of the sensor circuit is 1500 Ω.

The lines in the emission spectrum of hydrogen are measured to become more widely spaced and longer in wavelength when the observer is moving away from the source of light.

This effect is known as redshift and is a result of the Doppler effect, which occurs when a light source is in motion relative to an observer.

As the observer moves away from the source of light, the wavelength of the emitted light is stretched, making the spectral lines appear longer and more widely spaced.

This is because the speed of light is reduced relative to the observer, causing the wavelength of the light to be longer than it would be in the rest frame of the observer.

Question should be like this

The lines in the emission spectrum of hydrogen are measured when observer moving away from the source of light ?

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The minimum index of refraction of the prism is 1.414.

What does light ray is incident mean?

Light ray incident is a term used to describe when a light ray strikes a surface. This can refer to light from any source, such as the sun, a light bulb, or a laser. When light rays are incident on a surface, they may be reflected, absorbed, or transmitted. The behavior of the light depends on the properties of the surface, such as its color, texture, and composition.

This double internal reflection requires that the angle of incidence (45º) at the 1st prism side is at least = critical angle. This reflected ray then meets the other prism side at the same angle of incidence (45º). so we only need to consider the first internal reflection.

Applying [ n sin i = constant ] to the prism-air boundary.

(np= ref.index for prism material, nₒ = ref.index for air =1.0 )

At a critical angle of incidence 45º, external angle = 90º

np sin 45 = nₒ sin90

np = nₒ sin90 / sin45=1 x 1 / 0.7071

np(min) = 1.414

Therefore, 1.414 is the minimum index of refraction of the prism.

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The minimum index of refraction of the prism for which the ray will totally internally reflect at each of the two sides making the right angle is 1.414.

What does light ray is incident mean?

Light ray incident is a term used to describe when a light ray strikes a surface. This can refer to light from any source, such as the sun, a light bulb, or a laser. When light rays are incident on a surface, they may be reflected, absorbed, or transmitted. The behavior of the light depends on the properties of the surface, such as its color, texture, and composition.

This double internal reflection requires that the angle of incidence (45º) at the 1st prism side is at least = critical angle. This reflected ray then meets the other prism side at the same angle of incidence (45º). so we only need to consider the first internal reflection.

Applying [ n sin i = constant ] to the prism-air boundary.

(np= ref.index for prism material, nₒ = ref.index for air =1.0 )

At a critical angle of incidence 45º, external angle = 90º

np sin 45 = nₒ sin90

np = nₒ sin90 / sin45=1 x 1 / 0.7071

np(min) = 1.414

Therefore, 1.414 is the minimum index of refraction of the prism.

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The ICF reflects a radical shift in the way practitioners view disability by moving away from a medical model of disability to a more holistic and person-centered approach. It recognizes that disability is a complex interaction between an individual's health condition, personal factors, and the environment and that the impact of a health condition on an individual's ability to participate in life activities cannot be understood in isolation.

The International Classification of Functioning, Disability and Health (ICF) is a framework for understanding the impact of health conditions on individuals and their ability to participate in life activities. The ICF represents a significant shift in the way practitioners view disability, as it moves away from a medical model of disability to a more holistic and person-centered approach.

Traditionally, disability was seen as a medical problem caused by a physical or mental impairment. This led to a focus on diagnosing and treating the underlying health condition, with the goal of reducing or eliminating the disability. This medical model of disability placed the individual with a health condition in the center and viewed their disability as a problem to be fixed.

The ICF, however, views disability as a complex interaction between an individual's health condition, personal factors, and the environment. It recognizes that disability is not just a result of a health condition but also a result of the individual's abilities and limitations in interacting with the environment. This means that disability is not just about the health condition but also about the social, cultural, and physical barriers that prevent the individual from participating in life activities.

The ICF takes a person-centered approach, where the focus is on the individual and their experiences, rather than just their health condition. It recognizes that the impact of a health condition on an individual's ability to participate in life activities is not just determined by the health condition itself, but also by the individual's personal factors, such as their age, education, and level of support, and the environment, such as the availability of accessible transportation and accommodations.

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The speed of a proton that is accelerated from rest through an electric potential difference of 144 V is 160 km/s.

Proton Electric field system as an isolated system for energy. Applying energy conservation: ΔK+ΔU=0

(1/2​ mp× vf² − 1/2mp​× vi² )−qp×​ ΔV=0. Where vi=0 since the proton is accelerated from rest, so, (1/2​ mp× vf²)−qp×​ ΔV=0. The electric potential difference,∆V= 144 volts. Now solving for vf=[(2×qp×∆V)/mp]^½ =[(2×1.602×10⁻¹⁹×144)/1.674×10⁻²⁷]^½  =16×10⁴ m/s = 160 km/s.

A proton has about 2000 times the mass of an electron, so it would have to travel at about ¹/₂₀₀₀ the speed of an electron to have the same momentum — 3.90×10⁶m/s2000 ≈ 2000 m/s and the same wavelength.

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Simple diffusion of a molecule down its concentration gradient requires an input of energy to the system is false.

Diffusion is a type of molecule movement down its concentration from a higher concentration to a lower concentration. Because of that, it doesn’t require the energy (ATP) from respiration. The molecule only uses kinetic energy. Based on these characteristics, diffusion is included in passive transport.

Diffusion can either be simple diffusion or be facilitated by another molecule. Simple diffusion is the movement of molecules along their concentration gradient without the direct involvement of any other molecules, while facilitated diffusion is the transport of molecules via a protein membrane.

Thus, simple diffusion doesn’t need energy for regulating the molecule passing through the membrane.

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No, it is not true that the speed of the object is equal to zero. Hence, it is impossible for an object to have zero speed and non-zero velocity.

Since distance is also a scalar, it will not be negative even if we move in the opposite direction. It never stops adding, regardless of the direction. Therefore, a moving body's total travel distance cannot be zero. Therefore, the total average speed cannot be zero, and if the body is moving, it will be nonzero.

In meters per second, speed is the rate at which an object changes position. For instance, if an object moves three meters in three seconds from its origin, its speed is one meter per second. The formula for speed is straightforward: time divided by distance.

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One way to write Coulomb's law is F = where F is the p2 magnitude of the electric force, k is a constant, Q and q are the two electrical charges and r is the distance between.

What is Coulomb's law?

Coulomb identified the following characteristics of the electric force for charges at rest: Contrary charges attract each other whereas like charges repel one another. Accordingly, two negative charges repel one another, but a positive charge pulls a negative charge toward it. In between the two charges, there is an area of attraction or repulsion.

What is electric charge?

Protons and electrons, which function as charge carriers, frequently carry both positive and negative electric charges. By moving charges, energy is produced. Charge—also referred to as electric charge, electrical charge, or electrostatic charge—is a property of a unit of matter in physics and is denoted by the letter q.

Therefore, One way to write Coulomb's law is F = where F is the p2 magnitude of the electric force, k is a constant, Q and q are the two electrical charges and r is the distance between.

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Given the power PP of an electric circuit is related to the circuit's resistance RR and current II by the equation P = RI^2

we want to find dP/dt, dR/dt and dI/dt if none of P, R and I are constant:

P = RI^2 = dP/dt = R. 2I dI/dt+I^2dR/dt = dP/dt = 2RIdI/dt= I^2dR/dt.

At the point when an electric current courses through a bulb or any conveyor, the channel offers a check to the current and this obstacle is known as electrical resistance and is indicated by R. Each material has an electrical resistance and this is the motivation behind why conveyors give out heat when current goes through it

As per Ohm's law, there is a connection between the current moving through a guide and the likely distinction across it. It is given by,

V ∝ I V = IR

Where,

V is the potential contrast estimated across the guide (in volts)

I is the current through the guide (in amperes)

R is the consistent of proportionality called resistance (in ohms)

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Answer:

51.2 m/

Explanation:

The headwind will slow down the airplane and make it move slower relative to the ground     98.7 - 47.5 = 51.2 m/ relative to ground

This is repeated three times in 60 spaces, with a 1.5 m/s average speed.

The player runs a total distance of 30 m * 3 = 90 m in 60 s,

so the player's average speed is 90 m / 60 s = 1.5 m/s.

The size or extent of the displacement between two points is referred to as distance. Keep in mind that the distance between two points and the distance travelled between them are not the same. The length of the entire journey taken to go from one point to another is the distance travelled.

Calculating the ratio of the body's total distance traveled to the time needed to complete that distance yields the average speed formula. The formula describing the average speed of an item traveling at a variable speed is called an equation.

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Note: The correct question would be as bellow,

In a drill during basketball practice, a player runs the length of the 30 meter court and back. The player does this three times in 60 seconds. The magnitude of the player's average velocity during the drill is...

Height of cliff where a diver jumps  is 36.9m and from base the diver will be out by 3.6m distance.

The distance of a point from the y-pivot is called its x-direction, or abscissa. The distance of a point from the x-hub is called its y-direction, or ordinate. The directions of a point on the x-hub are of the structure (x, 0), and of a point on the y-hub are of the structure (0, y).

For calculating distance in horizontal direction (in positive x-axis),we need to use second equation of motion which is given by the formula

S=ut + (1/2)at²

In x-direction acceleration in x-direction=0m/sec²

So, value of a=0m/sec²

Value of u=1.6m/sec, t=3.0sec

=>S=1.6 ×3=3.8m

Similarly, for calculating distance in vertical direction (in positive x-axis),we need to use second equation of motion which is given by the formula

S=ut+ (1/2)at²

In y-direction,acceleration is 9.8m/sec²

Also,in y-direction initial velocity(u) is 0m/sec.

=>S=0×t + (1/2)×9.8×(3.0)²

=>S=0+4.9×9

=>S=36.9m

Hence,height is 36.9m and distance in horizontal direction is 3.8m

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