using the z table, determine the critical values for a two-tailed test when α = 0.03.

The initial speed of the car with a length of the skid mark of about 64 m long and kinetic friction of 0.70 is 29.63 m/s.

A force that acts between moving surfaces is referred to as kinetic or sliding friction. It is the frictional force that prevents relative motion between surfaces in contact. The formula to calculate this kind of friction is, [tex]f _k =\mu_kN[/tex] where uk is the coefficient of friction and N is the normal force.

Given the length of the skid mark (Δd) is 64 m and the coefficient of kinetic friction is 0.70. The final velocity vf is 0 because the car stops.

Let us assume the initial velocity vi, mass m,  and deceleration a. Then, the normal force acting on the car is N = mg. The kinetic friction will be,

[tex]f _k =\mu_kN\\f_k=\mu_kmg[/tex]

Let's assume the only force acting on the system is kinetic friction, then friction force=ma. Solve this equation with the above equation,

[tex]\begin{aligned}ma&=\mu_kmg\\a&=\mu_kg\end{aligned}[/tex]

Then, the initial speed is calculated as follows

[tex]\begin{aligned}v_f^2&=v_i^2-2a\Delta d\\0&=v_i^2-2\mu_kg\Delta d\\v_i^2&=\mathrm{2\times0.70\times9.80\;m/s^2\times64\;m}\\v_i^2&=\mathrm{878.08\;m^2/s^2}\\v_i&=\mathrm{29.63\;m/s}\end{aligned}[/tex]

The answer is 29.63 m/s.

The complete question is -

Police investigators, examining the scene of an accident involving two cars, measured 64 m long skid marks on one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.70. Estimate the initial speed of that car, assuming a level road.

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the intensity level of the combined sounds is 67.76 dB

Calculation :

Sound Intensity level L= 63 dB

We know L = 10 log(I/Io)

63 = 10 log(I/Io)

6.3 = log (I/Io)

I /Io = [tex]10^{6.3}[/tex]

I = [tex]10^{6.3}[/tex] Io

= [tex]10 ^{6.3 }[/tex]x [tex]10 ^{-12}[/tex]

= [tex]10^{ -5.7}[/tex] W/m 2

  = 1.995 x[tex]10 ^{-6}[/tex] W/m 2

Sound Intensity level L '= 66 dB

We know L ' = 10 log(I '/Io)

66 = 10 log(I '/Io)

6.6 = log (I'/Io)

I ' /Io = [tex]10 ^{6.6}[/tex]

I ' =  [tex]10 ^{6.6}[/tex] Io

=  [tex]10 ^{6.6}[/tex] x [tex]10 ^{-12}[/tex]

= [tex]10 ^{-5.4}[/tex]W/m ^2

  = 3.981 x[tex]10 ^{-6}[/tex] W/m^ 2

Combined intensity I " = I + I ' = 5.976 x10 -6 W/m 2

the intensity level of the combined sounds L " = 10 log(I" / Io)

 L " = 10 log [( 5.976 x[tex]10 ^{-6}[/tex] )/([tex]10 ^{-12}[/tex] ) ]

      = 10 log [5.976 x10 6]

      = 10(6.776)

      = 67.76 dB

Intensity is the amount of energy a wave transports in one unit of area per unit time and is also equal to the energy density multiplied by the wave velocity. Usually measured in watts per square meter. Intensity depends on wave strength and amplitude.

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Answer: Fg = 265.68 N

Explanation:

Fg = m * g

m = Fg / g

m = 1607.2 N / 9.8 m/s^2

m = 164 kg

Fg = m * g

Fg = 164 kg * 1.62 m/s^2

Fg = 265.68 N

The motion of the free electron sea causes the electrical conduction.

Metals that are near to one another have valence electrons that do not only remain on their own atom but also easily migrate throughout the entire metal complex. They seem to be floating through an sea of electrons, like a solitary water molecule floating freely in the sea. For this reason, it is often referred to as the electron sea model.

These atoms become positively charged cations because each metal atom is free to move around. These cations resemble a positively charged island because they are encircled by a sea of negatively charged electrons. Because of these free-moving electrons, metal is a good conductor of electricity.

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Elliptical galaxies most likely to be found in the central regions

Galaxies with an elliptical form are known as elliptical galaxies. Since an ellipse has an oval shape, these galaxies also have an oval shape. Elliptical galaxies are those with little to no gas and dust. The elliptical galaxies are the most abundant type of galaxies. Elliptical galaxies are most likely to be found in the central regions of galaxy clusters. Galaxy clusters are large groups of galaxies that are bound together by gravity and are some of the largest structures in the universe.

Elliptical galaxies are characterized by a lack of distinct features, such as spiral arms or a visible nucleus. These galaxies are thought to have formed through the merger of smaller galaxies and are generally found in high-density environments such as the centres of galaxy clusters. They are less common on the outskirts of galaxy clusters and are rarely found in small clusters or in between larger clusters.

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Work done on a 1500kg elevator by its cable to lift it 40m at a constant speed is 592000N.

The work done by a force is calculated as the product of the force(F) and the displacement of the object on which the force is acted.

Work done = F×d

downward forces are weight of lift and frictional force

upward force is only tension of string.

T = Frictional force + Mg

Mg = 1500× 9.8 = 14700N

given frictional force is 100N

So, Tension in string = (100+ 14700) N

= 14800N

work done by tension in lifting = tension force ×

displacement of lift

= 14800 × 40

= 592000N.

hence, work done on a 1500 kg elevator by its cable to lift it 40m at a constant speed is 592000N.

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The moment of inertia is measured in units of mass times squared distance, such as kgm2. The rotational kinetic energy of an item in rotation about an axis is K = 12I2.

Moment of inertia divided by half equals rotational kinetic energy (angular speed). Where 0 0 is the starting angular velocity, = 0 + t (constant) and = 0 + t (constant). The equation is the same as the linear version, with the exception that the angular equivalents of the linear variables. It is necessary to specify the moment of inertia in relation to a selected axis of rotation. The moment of inertia for a point mass is equal to the mass times the square of the distance perpendicular to the rotation axis, or I = mr2.

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Top-Down: Gas and dark matter collided, causing the gas to star-form. merging of spiral galaxies whose gas has already turned into stars (bottom-up) is the way how the elliptical galaxy formation was happened.

spiral galaxies evolved from bottom-up, and elliptical galaxies from a mix of top-down and bottom-up. There is extremely little raw material for the creation of new stars in elliptical galaxies, in contrast to spiral galaxies, which contain abundant stores of the dust and gas that support star formation. When two spiral galaxies collide, they change from their recognized form into the less organized elliptical galaxies. These old galaxies are considered to be powered by a supermassive black hole. These gas- and dust-eating giants may contribute to the elliptical galaxies' slower development.

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The resistance of the resistor is 1.8Ω

Consider the voltage across the inductor 4 sec after the switch is closed is V(4)

The voltage across the inductor 4 sec after the switch is closed is 80%  of its maximum value, i.e., V(4)=0.8[tex]V_{0}[/tex]

Consider the expression for the voltage across the RL circuit.

V(t)=[tex]V_{0}e-\frac{t}{T}[/tex]

Where [tex]V_{0}[/tex] is the maximum voltage, t is the time, V(t) is the voltage at time

t and T is the time constant.

Substitute the values of ,[tex]V_{0}[/tex], V(t) and t in the above expression.

[tex]$$\begin{aligned}0.8 \mathrm{~V}_0 & =\mathrm{V}_0 \times \mathrm{e}^{-\frac{4}{\tau}} \\0.8 & =\mathrm{e}^{-\frac{4}{\tau}} \\\frac{1}{0.8} & =\mathrm{e}^{\frac{4}{\tau}}\end{aligned}$$[/tex]

Take natural log on both the sides.

[tex]$$\ln \left(\frac{1}{0.8}\right)=\frac{4}{\tau}$$[/tex]

Rearrange the above expression.

[tex]$$\begin{aligned}\tau & =\frac{4}{\ln \left(\frac{1}{0.8}\right)} \\& =17.9 \mathrm{~s}\end{aligned}$$[/tex]

Now consider the expression for time constant.

[tex]$$\tau=\frac{\mathrm{L}}{\mathrm{R}}$$[/tex]

Where R is the inductance and L is the resistance.

Rearrange the above expression.

R = [tex]\frac{L}{T}[/tex]

Substitute the values of T and L in the above expression.

[tex]R=\frac{34}{17.9}\\ R=1.8[/tex]Ω.

Therefore, the resistance of resistor is 1.8Ω

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To establish a geosynchronous orbit at a distance of 8.6 105 m, the spacecraft must orbit the planet in the same period as the planet's rotation.

This means that the spacecraft must complete one orbit every T = 31 hours. The orbital period is related to the orbital radius by the equation T2 = 4π2R3/GM, where G is the gravitational constant and M is the mass of the planet.

Substituting in the values for T and R into this equation, we can solve for GM: GM = 4π2(8.6 105 m)3/T2 = 2.08 1017 m3/s2.

The spacecraft must then use its thrusters to adjust its speed and position until it enters an orbit with a period of 31 hours and a radius of 8.6 105 m. It can achieve this by using a combination of delta-v maneuvers to adjust its speed and trajectory. The first maneuver will be a prograde burn to increase the spacecraft's speed until it enters an orbit that is slightly more distant than the desired orbit. The spacecraft will then use a series of impulsive maneuvers to adjust its trajectory until it is in an orbit with the desired radius. Finally, the spacecraft will use a retrograde burn to reduce its speed until it reaches the desired orbital period.

Once the spacecraft has completed all of these maneuvers, it will be in a geosynchronous orbit at a distance of 8.6 105 m from the planet's surface.

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You're in a boat with a big rock, in a swimming pool. You toss the rock overboard. Level of water will increase as of the mass of big rock to the level of the water in the pool.

The buoyancy of any floating object partially or totally submerged in a fluid can be computed thanks to Archimedes' principle. The weight of the thing alone exerts a downward mass on it. The upward or buoyant force acting on the object is what is meant by the aforementioned Archimedes' principle. The difference between the buoyant force and the object's weight is therefore the net force acting on it. In the event that this net force is positive, the item will rise; in the event that it is negative, the object will sink; and in the event that it is zero, the object will be neutrally buoyant, remaining stationary. Simply said, when a body is partially or entirely submerged in a fluid, the Archimedes' principle applies. Consider a cuboid submerged in a fluid, with its top and bottom facing in the direction of gravity, which is considered to be constant throughout the length of the cube. Each face of the fluid will experience a normal force, but only the normal forces on the top and bottom will result in buoyancy. The height directly affects the pressure difference between the top and bottom faces (difference in depth of submersion). A net force on the cuboid is created by multiplying the pressure difference by the area of a face.

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Answer:

To calculate the work done by the electrostatic field in moving a charge from one point to another, you can use the formula:

work = charge * (final potential - initial potential)

In this case, the charge is 2 coulombs, the initial potential is 20V, and the final potential is -5V. Plugging these values into the formula, we get:

work = 2 coulombs * (20V - (-5V))

= 2 coulombs * (25V)

= 50 Joules

Therefore, the work done by the electrostatic field in moving the charge from one point to another is 50 Joules.

pushed to the right = 300 newtons

pushed to the left = 400 newtons

[tex]400-300=100[/tex]

[tex]\fbox{100 Newtons to the left}[/tex]

A negative object so it takes in the charge object and nothing will happen until something else would touch it.

Electric charge is the property of a material that makes it feel a force when subjected to an electromagnetic field. Protons and electrons most typically carry positive and negative charges, which are the two forms of electric charges.

The basis of the SI system of physical units is the coulomb It is referred to as C. A coulomb is the unit of power that a one-ampere current can carry in one second.

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The net force acting on the cart is 2 N in left direction.

The definition of force in physics is: The push or pull on a massed object changes its velocity.

An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude. Newton is the SI unit of force.

Jimi is pushing a large cart at work toward the left side of the store using 10N of force.

Jonah pushed the cart with 8 N of force toward the right side of the store.

Hence, the net force acting on the cart in left direction = ( 10 N - 8 N) = 2 N.

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When we calculate a function's average rate of change over a certain interval, we are computing the average number of units that the function moves up or down per unit along the xx-axis.

Given the function and interval of interest (f(x)f(x) and [x ₁,x₂]), [x\s​₁,x₂ ]), our first step is to compute the value of our function at both ends of the interval. Then we plug those numbers and the interval's ends into our algorithm to calculate the average rate of change.

The average rate of change formula is

{x₂-x₁}

x f = x₂ x 1 f(x₂ )

​​within the interval [x₁,x ₂][x ₁,x ₂ ].

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In an experiment with n = 14 and preal = 0.10, then the power using a = 0.012 tail will be 0.997

Power is the capacity to shape or direct events, other people's behavior, or both. It is the ability to decide what to do and then do it. It might be either physical—like power—or mental—like wisdom. Power may also be social, political, or economic. It can be employed constructively, such as to effect change and defend human rights, or destructively, such as to repress and exert control. Power may be utilized to both bring about and stop change. Politics, economics, and culture all exhibit it since it is an essential component of all social relations.

N = 14

Mean, mu=0.10,

s=sqrt [0.10(1-0.10)/14]=0.08,

cumulative probability, 0.003,

Power=1-0.003=0.997

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If a = a1, a2, a3 and b = b1, b2, b3 . Then [tex]& \vec{a} \times \vec{b}=(-1)(\vec{b} \times \vec{a})[/tex] Or [tex]& \vec{a} \times \vec{b}=-\vec{b} \times \vec{a}[/tex]

As per the details share in the above question are as bellow,

The provided data are follow,

The product of two or more integers that remain the same, regardless of the sequence in which they are multiplied, is referred to as the commutative property formula for multiplication. The commutative property formula for multiplication is (A x B) = (B x A).

Let us consider, Let a = a1, a2, a3

And b=b1, b2, b3

We have the property that a × b = − b × a.

Then a × b = __ = (−1) __ =− b × a.

[tex]& \vec{a}=a_1 i+a_2 j+a_3 k \\ \vec{b}=b_1 i+b_2 j+b_3 k[/tex]

Then,

[tex]$$\vec{a} \vec{x} \vec{b}=\left|\begin{array}{ccc}i & j & k \\a_1 & a_2 & a_3 \\b_1 & b_2 & b_3\end{array}\right|$$[/tex]

[tex]$$=i\left(a_2 b_3-a_3 b_2\right)+j\left(a_3 b_1-a_1 b_3\right)+k\left(a_1 b_2-a_2 b_1\right)$$[/tex]

So further we get,

[tex]& =i\left(b_2 a_3-a_2 b_3\right)+j\left(a_1 b_3-a_3 b_1\right)+k\left(a_2 b_1-a_1 b_2\right) \\& =-\left[i\left(a_2 b_3-a_3 b_2\right)+j\left(a_3 b_1-a_1 b_3\right)+k\left(a_1 b_2-a_2 b_1\right)\right.[/tex]

So, we get,

[tex]\vec{a} \times \vec{b}=\left[i\left(a_2 b_3-a_3 b_2\right)+j\left(a_3 b_1-a_1 b_3\right)+k\left(a_1 b_2-a_2 b_1\right)\right.[/tex]

We get,

[tex]& \vec{b} \times \vec{a}=-[\vec{a} \times \vec{b}][/tex]

Or [tex]& -\vec{b} \times \vec{a}=\vec{a} \times \vec{b}[/tex]

Then,

[tex]& \vec{a} \times \vec{b}=(-1)(\vec{b} \times \vec{a})[/tex]

Or [tex]& \vec{a} \times \vec{b}=-\vec{b} \times \vec{a}[/tex]

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They are so distant that the parallax is too small to be measured since parallax varies inversely with distance.

Parallaxes can be measured accurately out to distances of approximately 100 light-years. The nearest galaxies are about 50,000 to 80,000 light-years from the Sun. Therefore, there is no perceptible change in the apparent position of any galaxy as we view it from opposite sides of Earth's orbit.

Because of the influences of the Earth's atmosphere, it is highly challenging to estimate parallax angles of less than 0.01 arcsec from Earth. Due to this, telescopes on Earth can only measure the distances to stars that are 1/0.01 or 100 parsecs distant.

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If a ball is thrown at an initial horizontal velocity of 3.6 meters per second off of a cliff that is 19.6 meters high, it will land 35.28 meters away from the cliff.

The vectoral expression of a particle and object's motion with respect towards time is called its velocity. The recognized unit for measuring magnitude of velocity is indeed the meters per second (m/s), which is frequently referred to as speed. Velocity is the rate at which an object's position is changing as perceived from a particular point of view and so as measured by a certain unit of time. It refers to the direction speed of the an object in motion.

Average speed is calculated by dividing a quantity by the time required to obtain that quantity. Speed in the SI is expressed in m / sec. The average speed (S) is calculated using the equation S = d/t, where d is the entire distance traveled and t denotes the total time. One can determine an object's beginning velocity by dividing the time it took the thing to go a specific distance by the total distance.

D = (1/2) gt2 where g = 9.8 m/s2

It takes time to descend the 19.6-meter cliff.

19.6 = 1/2(9.8)t2

19.6/4.9 = t2

Square root 90.4 = about 9.8 sec.

3.6 m/s x 9.8 sec = 35.28 m

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The current north of the wire fliws upwards as of the electric current straight upward.

The proper-hand thumb rule suggests the path of the magnetic area for a recognise path of the modern-day. If the thumb of the proper-hand factors alongside the path of modern-day then the curled arms of that hand offers the path of the magnetic area because of the modern-day.

The path of the magnetic area is perpendicular to the twine and is withinside the path the arms of your proper hand might curl in case you wrapped them across the twine together along with your thumb withinside the path of the modern-day.A vertical twine wearing a modern-day withinside the upward path is located in a horizontal magnetic area directed toward north.

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91.66 A is the amount of current flowing through a light bulb with a resistance of 1.2 when it is connected to a 110 volt power source.

current (I) = V/R

= 110 volt / 1.2 ohm

= 91.666666666667 ampere (A)

ions (atoms that have acquired or lost one or more electrons), holes, or subatomic charged particles such as electrons with a negative charge or protons with a positive charge make up electric current (electron deficiencies that may be thought of as positive particles).

Electrons serve as the charge carriers in a wire, and the amount of charge moving through any point of the wire in a given amount of time is measured as electric current. In direct current, the direction of the electric charges is not regularly reversed, although it is in alternating current. In many situations, the flow of positive charge is assumed to be in the same direction as the current in electric circuits.

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The Sun's surface emits as a black body its surface temperature is [tex]$5.78 \times 10^3 \mathrm{~K}$[/tex].

The sun's surface area is,

A 3D object's surface area is the entire area that all of its faces cover. If we need to figure out how much paint is needed to paint a cube, for example, we may use the cube's surface area. It is consistently expressed in square units.

[tex]A=4 \pi r^2[/tex]

The sun's radius, r, is indicated here.

Substitute [tex]$6.96 \times 10^8 \mathrm{~m}$[/tex] for r.

[tex]A & =4 \pi\left(6.96 \times 10^8 \mathrm{~m}\right)^2 \\& =6.09 \times 10^{18} \mathrm{~m}^2[/tex]

The radiated power is, according to Stefan's law

Energy that emanates from an origin and moves through space at the speed of light is referred to as radiation. This radiation has wave-like qualities and is accompanied by an electric field and a magnetic field.

[tex]P & =\sigma A e T^4 \\T^4 & =\frac{P}{\sigma A e} \\T & =\left(\frac{P}{\sigma A e}\right)^{\frac{1}{4}}[/tex]

Substitute [tex]$6.09 \times 10^{18} \mathrm{~m}^2$[/tex] for A,

[tex]5.67 \times 10^{-8} \mathrm{~W} / \mathrm{m}^2. \mathrm{K}^4$[/tex] .  for [tex]$\sigma$[/tex],

and [tex]$3.85 \times 10^{26} \mathrm{~W}$[/tex] for P.

[tex]T & =\left(\frac{3.85 \times 10^{26} \mathrm{~W}}{\left(5.67 \times 10^{-8} \mathrm{~W} / \mathrm{m}^2 \cdot \mathrm{K}^4\right)\left(6.09 \times 10^{18} \mathrm{~m}^2\right)(1)}\right)^{\frac{1}{4}} \\& =\left(1.12 \times 10^{15} \mathrm{~K}^4\right)^{\frac{1}{4}} \\& =5.78 \times 10^3 \mathrm{~K}[/tex]

The temperature is [tex]$5.78 \times 10^3 \mathrm{~K}$[/tex].

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Note:- The correct question would be as follow,

The radius of our Sun is [tex]$6.96 \times 10^8 \mathrm{~m}$[/tex], and its total power output is [tex]$3.85 \times 10^{26} \mathrm{~W}$[/tex]. (a) Assuming the Sun's surface emits as a black body, calculate its surface temperature.

There is a transverse sinusoidal wave on a string that flows in a straightforward harmonic fashion and has an angular frequency that matches the wave. (Chose c.)

An energetic disturbance called a wave moves from one place to another. Every time a wave moves, energy is changed, regardless of the change. The substance through which a wave passes is known as the medium. Back and forth oscillations occur repeatedly in that medium.

A wave is a disruption or variation that progressively moves energy from one location in a medium to another. It could manifest as an elastomeric deformation or a shift in pressure, magnetic or electric field strength, electric potential, or temperature.

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Electric flux through the surface is [tex]1.5 Nm^2/C[/tex].

As per the detail share in the above question are as bellow,

Given an area A with a unit normal vector n, the electric flow through that region is given by Φ = E.(An) = |E|Acosθ

Where angle between vectors E and n =θ .

Also Magnitude of E = |E|

When the magnitude of n is |n| = 1

The normal n and the electric field vector E make an angle of,

θ = 90 - 30 = 60 degrees,

Therefore magnitude of,

|E| = 300N/C

And A= 0.1 x 0.1 = 0.01 m.

Thus,

Φ = |E|Acosθ

Substitute the value in above equation we get,

=300 x 0.01 x cos(60)

=3 x 0.5

[tex]= 1.5 Nm^2/C[/tex]

Electric flux=Φ=[tex]1.5 Nm^2/C[/tex]

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Note : The correct question would be as follow,

what is the electric flux through the surface shown in the figure? assume that e=300n/c.

The definite integral of this function 60f(x)dx is given by \int{0}^{6} f(x)dx = 18∫06f(x)dx=18.

A definite integral describes the area of a function within the interval formed by the bounds of the definite integral. This means that we can find the definite integral for this problem simply by finding the area of the function.

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The pear will not hit the fish where he eyes the fish in the water.

Please note that fish in the water will not be the same as what our eyes see. Where the location of the position will be different because it follows the refraction of light obtained so that it can be concluded that the position of the fish is not the actual position. The fish swims forward and the shooter looks at the water from above as if the fish is looking up.

This event is caused by the process of refraction of light. Refraction is the deflection of the direction of propagation of light when it enters a medium of different densities.

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The kinetic energy of another body having three times the mass of the given object will be 108 J

Kinetic energy-In physics, the kinetic energy of an object is the energy  it has due to  motion. It is defined as the work required to accelerate a body from a given mass from rest to a specified speed.

The kinetic energy of a body is given by [tex]K.E= \frac{1}{2}Mv^{2}[/tex] (first equation)

Given K.E= 36J

Now the mass of second body is m=3M

also the second body is moving with the same speed v

So kinetic energy of second body K.E₂= [tex]\frac{1}{2}mv^{2} =\frac{1}{2}(3M)v^{2}[/tex]=36×3

=108J (from first equation)

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