Can you create a single word problem that ask for multiple factors?

Answer:

Approximately [tex]12.3\; {\rm N}[/tex] at approximately [tex]106^{\circ}[/tex].

Explanation:

Assume the two given directions are measured with respect to the positive [tex]x[/tex] axis.

If a vector of magnitude [tex]\| a\|[/tex] is at an angle of [tex]\theta[/tex] from the positive [tex]x[/tex] axis, this vector can be written in the component form as:

[tex]\begin{aligned}\| a\|\begin{bmatrix}\cos(\theta) \\ \sin(\theta)\end{bmatrix}\end{aligned}[/tex];

Or equivalently:

[tex]\begin{aligned}\begin{bmatrix}\|a\|\, \cos(\theta) \\ \|a\|\, \sin(\theta)\end{bmatrix}\end{aligned}[/tex].

For example, the [tex]7.6\; {\rm N}[/tex] force is a vector with magnitude [tex]7.6\; {\rm N}[/tex] at a direction of [tex]38^{\circ}[/tex] from the positive [tex]x[/tex] axis. This vector can be represented as:

[tex]\begin{aligned} 7.6\, \begin{bmatrix}\cos(38^{\circ}) \\ \sin(38^{\circ})\end{bmatrix} &= \begin{bmatrix}7.6\, \cos(38^{\circ}) \\ 7.6\, \sin(38^{\circ})\end{bmatrix} \approx \begin{bmatrix}5.9889 \\ 4.6790 \end{bmatrix}\end{aligned}[/tex].

Similarly, the [tex]11.8\; {\rm N}[/tex] vector can be represented as:

[tex]\begin{aligned}11.8\, \begin{bmatrix}\cos(143^{\circ}) \\ \sin(143^{\circ})\end{bmatrix} &= \begin{bmatrix}11.8\, \cos(143^{\circ}) \\ 11.8\, \sin(143^{\circ})\end{bmatrix} \approx \begin{bmatrix}-9.4239 \\ 7.1014 \end{bmatrix}\end{aligned}[/tex].

To find the sum of the two vectors, take the sum of each component separately:

[tex]\begin{aligned}& \begin{bmatrix}5.9889 \\ 4.6790 \end{bmatrix} + \begin{bmatrix}-9.4239 \\ 7.1014\end{bmatrix} \\ =\; & \begin{bmatrix}5.9889 + (-9.4239)\\ 4.6790 + 7.1014\end{bmatrix} \\ \approx\; & \begin{bmatrix}-3.4350 \\ 11.780\end{bmatrix} \end{aligned}[/tex].

Apply the Pythagorean Theorem to find the magnitude of this vector sum:

[tex]\displaystyle \sqrt{(-3.4350)^{2} + (11.780)^{2}} \approx 12.271[/tex].

Note that the first component ([tex]x[/tex]-component) of this vector is negative, such that this vector would point to the left of the vertical axis. Since the second component ([tex]y[/tex]-component) of this vector is positive, this vector would point above the horizontal axis. Hence, the direction of this vector (relative to the positive [tex]x\![/tex]-axis) would be an angle between [tex]90^{\circ}[/tex] and [tex]180^{\circ}[/tex].

Divide the [tex]x[/tex]-component of this vector by its magnitude to find the cosine of the angle between this vector and the positive [tex]x\![/tex]-axis. Apply the inverse cosine function to find this angle:

[tex]\begin{aligned}\arccos \left(\frac{-3.4350}{12.271}\right) \approx 106^{\circ}\end{aligned}[/tex].

a. The final angular speed of the disc after 18 seconds is 45 rad/s.

b. The disc goes through approximately 64.5 revolutions during this time period.

c. The linear speed of a point at the end of the disc after 18 seconds is 22.5 m/s.

a. The angular acceleration of the disc is constant at 2.5 [tex]rad/s^2[/tex].

Using the formula for angular velocity with constant angular acceleration, we have:

ωf = ωi + αt

Where:

ωi = initial angular velocity (0, since the disc starts from rest)

α = angular acceleration (2.5 [tex]rad/s^2[/tex])

t = time (18 s)

ωf = 0 + 2.5 × 18

ωf = 45 rad/s

Therefore, the final angular speed of the disc after 18 seconds is 45 rad/s.

b. To find the number of revolutions the disc goes through during this time period, we need to first find the total angle rotated by the disc. Using the formula for angular displacement with constant angular acceleration, we have:

θ = ωit + 1/2 α[tex]t^2[/tex]

Where:

ωi = initial angular velocity (0, since the disc starts from rest)

α = angular acceleration (2.5 [tex]rad/s^2[/tex])

t = time (18 s)

θ = 0 + 1/2 × 2.5 × [tex]18^2[/tex]

θ = 405 rad

One revolution is equal to 2π radians,

so the number of revolutions is given by:

N = θ / 2π

N = 405 / 2π

N ≈ 64.5 revolutions

Therefore, the disc goes through approximately 64.5 revolutions during this time period.

c. The linear speed of a point at the end of the disc is given by:

v = rω

Where:

r = radius of the disc (50 cm = 0.5 m)

ω = angular velocity (45 rad/s)

v = 0.5 × 45

v = 22.5 m/s

Therefore, the linear speed of a point at the end of the disc after 18 seconds is 22.5 m/s.

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Answer:

20,000 J

Explanation:

    Work = Force multiplied by Displacement

The work done on a object can only be calculated when the applied force is causing an object to move in the direction the force is being applied towards.

The given information:

Billy applies a form of 800N on a staller car and the total distance it was pushed was 25 meters.

To calculate the work done, substitute the given information into the formula for work.

Work = (800 N) × (25 m)

Work = 20,000 J

Note: Remember the SI unit for Work is Joules (J).

Option b is correct. If enough material from the accretion disk makes it onto the white dwarf then it will cause the white dwarf to collapse and produce a Type Ia supernova.

A white dwarf is a remnant of low or medium-mass stars that have stopped producing energy through nuclear fusion. White dwarfs are not planets; instead, they are the small cores of stars that have collapsed under the weight of their own gravity. They are the densest form of matter apart from black holes and neutron stars.

If a lot of material from the accretion disk makes it onto the white dwarf (before it can all fuse away), the material will accumulate on the surface of the white dwarf, increasing its mass.

The white dwarf will have a mass greater than the Chandrasekhar limit (1.4 solar masses). This can lead to a catastrophic event known as a Type Ia supernova, in which the white dwarf collapses and explodes. hence correct option is b.

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The balanced form of the given chemical equation is as follows: 2N₂ + 0₂ → 2N₂0.

A chemical equation in chemistry is a symbolic representation of a chemical reaction where reactants are represented on the left, and products on the right.

A chemical equation results in the formation of new substances called products from substances called reactants.

However, to obey the law of conservation of mass, the atoms of each element on both sides of the equation must be the same. This is referred to as a balanced chemical equation.

The balanced form of the reaction between nitrogen and oxygen gas is given above.

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According to the principles of quantum mechanics, the answer to the question, "Can one entangled particle be measured for momentum while the other entangled particle is measured for the position?" is no.

If you measure the position of one particle in an entangled pair, you are creating a definite outcome for that particle. By measuring the other particle's momentum, you are causing it to have a definite outcome. That, however, is incompatible with the fact that the two particles are entangled. Their correlation will be broken if this is done.

The position and momentum measurements are incompatible in quantum mechanics. If you want to measure the position of a particle, the uncertainty in the momentum of the particle must be large. Conversely, if you want to measure the momentum of a particle, the uncertainty in the position of the particle must be large.

Furthermore, measuring the position of a particle has a detrimental effect on the uncertainty in its momentum. Similarly, measuring the momentum of a particle has a detrimental effect on the uncertainty in its position. The measurement outcomes of two entangled particles are determined by correlations between them.

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The final speed of an electron accelerated through a potential difference V, starting from rest, is given by the expression [tex]v = 5.93 \times 10^7 \times \sqrt{V}[/tex], where v is in meters per second and V is in volts.

The kinetic energy gained by an electron accelerated through a potential difference V is given by:

K = eV

Where:

K is the kinetic energy gained by the electron (joules)

e is the charge of the electron ([tex]1.6 \times 10^{-19}[/tex]coulombs)

V is the potential difference across which the electron is accelerated (volts)

Since the electron was initially at rest, its initial kinetic energy was zero. Therefore, the final kinetic energy of the electron will be equal to the kinetic energy gained during acceleration:

K = eV

The final velocity of the electron can be calculated using the formula for kinetic energy:

K = (1/2)m[tex]v^2[/tex]

Where:

m is the mass of the electron[tex](9.11 \times 10^{-31} kg)[/tex]

v is the final velocity of the electron

Substituting the expression for K, we get:

eV = (1/2)m[tex]v^2[/tex]

Solving for v, we get:

v = √(2eV/m)

Substituting the values for e, V, and m, we get:

[tex]v =\sqrt{ [(2 \times 1.6 x 10^{-19} C \times V) / 9.11 \times 10^{-31} kg]}[/tex]

Simplifying this expression, we get:

[tex]v = 5.93 \times 10^7 \times \sqrt{V}[/tex]

Therefore, the final speed of an electron accelerated through a potential difference V, starting from rest, is given by the expression [tex]v = 5.93 \times 10^7 \times \sqrt{V}[/tex], where v is in meters per second and V is in volts.

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The aluminium wall measures about 0.273 centimetres in thickness.

Let's assume that the frequency of the ultrasound wave is denoted by f and the thickness of the aluminum wall is denoted by x. We know that the speed of the ultrasound wave in aluminum is greater than that in ethyl alcohol. Since the wavelength of the wave is constant, we can use the formula:

f1 x1 = f2 x2,

where f1 and f2 are the frequencies of the ultrasound wave in aluminum and ethyl alcohol, respectively, and x2 is the thickness of the alcohol.

We are given that the ratio of the number of cycles in the alcohol to that in the aluminum wall is 275. Therefore:

f2 = 275 f1.

We also know that the speed of the ultrasound wave in aluminum is approximately 5 times that in ethyl alcohol. Therefore:

x1 = 5 x2.

Substituting these values into the equation gives:

275 f1 x2 = f1 (5 x2),

which simplifies to:

x2 = (1/55) x1.

Finally, we substitute the length of the aluminum tank (15 cm) for x1 to get:

x2 = (15 cm) / 55 = 0.273 cm.

Therefore, the thickness of the aluminum wall is approximately 0.273 cm.

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(a) The magnitude of the force propelling the bobsled forward is 648 N. (b) The magnitude of the net force acting on the bobsled is 198 N.

Use Newton's second law of motion, which states that force equals mass times acceleration (F = ma). Rearranging the formula, we get F = ma, where F is the force, m is the mass, and a is the acceleration.

So, the force propelling the bobsled forward is,

F = ma = (270 kg)(2.4 m/s^2) = 648 N

The net force acting on the bobsled can be calculated by subtracting the forces resisting the motion from the force propelling the bobsled forward. So, the net force acting is,

Net force = Force propelling forward - Forces resisting motion

Net force = 648 N - 450 N

Net force = 198 N

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The coefficient of the kinetic friction of the sand paper would be = 0.5. That is option C.

To calculate the coefficient of the kinetic friction of the sand paper the slope of the sandpaper line is obtained. This is because slope of kinetic friction and normal force = coefficient of kinetic friction.

To calculate the slope = Y2 - Y1/ X2 - X1

Where Y2 = 3.3

Y 1 = 1.0

X2 = 6.9

X1 = 2

Slope = 3.3-1.0/6.9-2

= 2.3/4.9

= 0.5

Therefore the coefficient of the kinetic friction of the sand paper which is the slope of kinetic friction and normal force for the sandpaper line would be = 0.5.

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The kinetic energy decreases by 3movo^2

In an inelastic collision, kinetic energy is not conserved. Some of the initial kinetic energy of the system is converted into other forms of energy, such as heat, sound, or deformation energy, and is not available to do work on the system.

In fact, the total kinetic energy of the system usually decreases in an inelastic collision. This is because the objects involved in the collision stick together or deform upon impact, resulting in a loss of kinetic energy. The amount of energy lost depends on the specific properties of the objects and the nature of the collision.

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The object’s weight and area it presents, as well as air density.

The correct option is C.

Velocity may be defined as the rate that a thing travels in a certain direction. as the speed of a car driving north on a highway or the pace at which a rocket takes off. the proportion between the distance travelled in a simple machine by the point where the effort being applied to the distance moved in the same time by the place where the load is applied.

Galileo Galilei, an Italian physicist, is recognized with being the initial person to calculate speed by dividing it by the distance travelled and the time required. Galileo defined speed as the amount of distance travelled in a given amount of time.

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The complete question is -

Which of the following descriptions best describes all of the factors that need to be considered when determining an object’s terminal velocity?

A) The object’s weight, length, and width

B) Air density and the object’s drag coefficient

C) The object’s weight and area it presents, as well as air density

D) The object’s weight, length, width, and area it presents, as well as air density and the object’s drag coefficient

Using Ohm's law, we can find the current flowing in the circuit: I = V / R where I is the current, V is the voltage, and R is the resistance.

When a resistor of 25 ohms is connected to the battery, the terminal pd is 1.25 V. This means that the voltage drop across the internal resistance of the battery is: 1.5 V - 1.25 V = 0.25 V. Using Ohm's law, we can find the internal resistance of the battery: 0.25 V / I = R_internal. Substituting the given values, we get: R_internal = 0.25 V / (1.5 V / 25 ohm) = 4.17 ohm. The current flowing in the circuit is: I = 1.25 V / 25 ohm = 0.05 A. When the resistance is replaced by 10 ohms, the current flowing in the circuit is: I = 1.5 V / 35 ohm = 0.043 A. Using the same approach as before, the terminal pd can be calculated as: 1.5 V - 0.043 A * (R_internal + 10 ohm) = V_terminal. Substituting the value of R_internal, we get: V_terminal = 1.5 V - 0.043 A * (4.17 ohm + 10 ohm) = 1.34 V. Therefore, when the resistance is replaced by 10 ohms, the current flowing in the circuit is 0.043 A, the internal resistance of the battery is 4.17 ohm, and the terminal pd is 1.34 V.

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Speed before the tire popped must have been 35.8 m/s. To calculate your speed before the tire popped, we will use the equation vf = vi + at. In this equation, vf is the final velocity (0 m/s), vi is the initial velocity, a is the acceleration (deceleration in this case), and t is the time.

Since we know the diameter of the roundabout, the time it took to stop, and the acceleration is constant, we can calculate the initial velocity as:

vi = vf + at
vi = 0 m/s + (-1.125 m/s2) * 32 s
vi = -35.8 m/s

So, your speed before the tire popped must have been 35.8 m/s.

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Answer:

The speed of the object is increasing.

F = M a       as long as the magnitude of the acceleration is acting towards the right there will be an acceleration towards the right

I will give you an example to know how to do it, watch and learn.

Question:

The image of a candle flame placed at a distance of 30 cm from a mirror is formed on a screen placed in front of mirror at a distance of 60 cm from its pole. What is the nature of the mirror. Find its focal length. If the height of flame is 2.4 cm , find the height of image.

Given :-

u = - 30 cm

v = 60 cm

h = 2.4 cm

Solution :-

Using mirror formula,

1/f = 1/v - 1/u

⇒ 1/f = 1/60 - (1/- 30)

⇒ 1/f  = 1/60 + 1/30

⇒ 1/f = 3/60

⇒ 1/f = 1/20

⇒ f = 20 cm

Magnification, M = v/u = Height of image/height of object

⇒ v/u = 60/-30

⇒ v/u = h'/2.4

⇒ h' = - 60/30 × 2.4

⇒ h' = - 4.8 cm

Hence, The required height of the image is - 4.8 cm

The image formed by the mirror is inverted.

Now thats how you do it. get the idea?

Hope it helps :)

If you have a concave mirror. A candle is located 22 cm from the mirror. The image of the candle appears at a distance of 7.0 cm from the mirror. Then the focal length of the mirror is 5.31 cm.

To find the focal length of the concave mirror, we can use the mirror formula:

1/f = 1/u + 1/v

where:

f = focal length of the mirror

u = object distance (distance of the candle from the mirror)

v = image distance (distance of the candle's image from the mirror)

We are given that:

u = -22 cm (negative sign indicates that the object is in front of the mirror)

v = -7.0 cm (negative sign indicates that the image is formed behind the mirror)

Plugging in the values, we get:

1/f = 1/-22 + 1/-7.0

Simplifying, we get:

1/f = (-7.0 + (-22)) / (-22 × -7.0)

1/f = 29 / 154

f = 5.31 cm (rounded to two decimal places)

Therefore, the focal length of the concave mirror is 5.31 cm.

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The rock will be 10 meters from the ground level after 2.63 seconds when the rock is thrown upward with velocity of 11m/s .

When the rock is thrown upward with a velocity of 11 m/s from the top of the 44 m high cliff, it will take approximately 4.00 seconds for the rock to reach the top of its trajectory and start heading back down.

The velocity of the rock on its way back down will be 11 m/s in the opposite direction. After 2.63 seconds, the rock will have travelled a distance of 10 m from the ground level.

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The net gravitational force on b due to a and c is 5.338 x 10^-8 N.

The net gravitational force on b due to a and c can be calculated using the formula:

F = G (m1m2) / r^2

where;

First, let's calculate the gravitational force between a and b:

F1 = G (m1m2) / r^2

= 6.67 x 10^-11 * (10.0 x 10.0) / (0.50/2)^2

= 1.067 x 10^-7 N

Next, let's calculate the gravitational force between b and c:

F2 = G(m2m3) / r^2

= 6.67 x 10^-11 (10.0 x  15.0) / (0.50/2)^2

= 1.67 x 10^-7 N

The net gravitational force on b due to a and c is the vector sum of these two forces:

Fnet = F2 - F1

= 1.67 x 10^-7 N - 1.067 x 10^-7 N

= 5.338 x 10^-8 N

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Answer:

the magnitude of the car is

F=307.9N

Explanation:

The expression for the power in terms of force and velocity is as follows;

P=Fv

Here, P is the power, F is the force and v is the velocity.

Rearrange the above expression to get the value of the force.

F=\frac{P}{v}

Convert power from horsepower to watt.

P=75.0 hp

P= (75)(745.7) W

P= 55,927.5 W

Put P= 55,927.5 W and v= 18.2 meter per second in the above expression.

F=\frac{55,927.5}{18.2}

F= 3072.9 N

Therefore, the magnitude of the force is F= 3072.9 N.

Work is characterized as the resultant action when a force moves an object in the force's direction.

It is clear what the word "force" means. The terms "push" and "pull" are perfectly acceptable at this level to describe forces. An object does not have a force inside of it or within it. Another object applies a force to the first.

When two items come into contact with one another physically and interact, these kinds of forces are involved. Frictional, tensional, normal, air resistance, applied, and spring forces are examples of the several types of contact forces.

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Answer:

The answer is c

Explanation:

The third cup has the largest energy transfer

The right response is (c) Fn > Mg

When you are driving through a circular valley, the direction of the net force acting on you is constantly changing. At the bottom of the valley, your velocity vector is horizontal and your acceleration vector is pointing upwards.

According to Newton's second law, F = ma, where F is the net force, m is your mass, and a is your acceleration. Therefore, the net force acting on you is greater than your weight (Mg) and is equal to the sum of the normal force and the force of gravity.

Thus, the correct answer is (c) Fn > Mg. The normal force is greater than your weight to provide the additional force required to maintain the circular motion.

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The gravitational acceleration experienced by the spacecraft would be  13.33 m/s^2.

The maximum velocity the spacecraft can reach would be 1633.5 m/s.

The kinetic energy of the spacecraft would be KE = 1/2mv^2

The gravitational acceleration experienced by the spacecraft as it falls toward the planet's surface can be calculated using the formula

Thus:

g = (6.67 x 10^-11 N m^2/kg^2) * (4/3 * pi * (5000 km)^3 * 5500 kg/m^3) / (10000 km)^2 = 13.33 m/s^2.

The maximum velocity that the spacecraft can reach just before impacting the planet's surface can be calculated using the formula

The height from which the spacecraft falls is equal to the distance from the planet's surface to the spacecraft's initial position, which is 10,000 km - 5000 km = 5000 km.

Thus, v = sqrt(2 * 13.33 m/s^2 * 5,000,000 m) = 1633.5 m/s.

The kinetic energy of the spacecraft just before impacting the planet's surface can be calculated using the formula

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The minimum radius of the circle so that the acceleration at this point will not exceed 4.00 is 2304 m, and the apparent weight of the pilot at the lowest point of the pullout is 272.6 N.

The equation for centripetal acceleration is:

a = (v²)/r, where a is the centripetal acceleration, v is the velocity, and r is the radius of the circle.

The equation can be rearranged to solve for the radius of the circle,

r = (v²)/a.

Plugging in the given values, we get:

r = (96)² / 4.00g

r = 2304 m.

The equation for the apparent weight of the pilot is

[tex]w_{app}[/tex] = mg - m* [tex]a_{centripetal}[/tex], where [tex]w_{app}[/tex] is the apparent weight, m is the mass of the pilot, g is the acceleration due to gravity, and [tex]a_{centripetal}[/tex] is the centripetal acceleration.

Plugging in the given values, we get [tex]w_{app}[/tex] = (47.0)(9.8) - (47.0)(4) = 272.6 N.

Therefore, the minimum radius of the circle is 2304 m, and the apparent weight of the pilot is 272.6 N.

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According to the charge that is stored on the positive plate, the order is B, A, C, D, and E, from biggest to smallest.

The charge stored on the positive plate of a capacitor is given by Q = CV, where Q is the charge, C is the capacitance, and V is the voltage. Since the capacitors are connected in parallel, they all have the same voltage V. Therefore, the capacitor with the largest capacitance will have the largest charge stored on its positive plate.

Ranking the capacitors from largest to smallest based on their capacitances, we get:

B) A = 2 cm, C = 8 nF

A) A = 4 cm, C = 8 nF

C) A = 2 cm, C = 4 nF

D) A = 4 cm, C = 2 nF

E) A = 1 cm, C = 1 nF

Therefore, the ranking from largest to smallest based on the charge stored on the positive plate is: B, A, C, D, E.

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The car's displacement when sliding is 73.66 metres.

We can use the kinematic equation for displacement with constant acceleration to solve for the skidding displacement of the car:

d = vi * t + 0.5 * a * t^2

where d is the displacement, vi is the initial velocity, t is the time, and a is the acceleration.

First, we need to find the acceleration of the car. We can use the equation for average acceleration:

a = (vf - vi) / t

where vf is the final velocity (which is 0 since the car comes to a stop), vi is the initial velocity (28.5 m/s to the east), and t is the time (2.58 s).

a = (0 - 28.5 m/s) / 2.58 s

a = -11.05 m/s^2

The negative sign indicates that the acceleration is in the opposite direction to the initial velocity.

Now we can substitute the values into the first equation:

d = vi * t + 0.5 * a * t^2

d = (28.5 m/s) * (2.58 s) + 0.5 * (-11.05 m/s^2) * (2.58 s)^2

d = 73.66 m

Therefore, the skidding displacement of the car is 73.66 meters.

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Answer:

d. decomposer

Explanation:

they play a critical role in the flow of energythrough an ecosystem. They break apart dead organisms into simpler inorganic materials, making nutrients available to primary producers

The 46.4 kg wolf moving at a speed of 12.2 m/s has a kinetic energy of 3,456.98 J.

The amount of work done on an item and its acceleration following a moment of inertia caused by external forces are two aspects that affect the overall kinetic energy of an object.

The formula: gives the kinetic energy (KE) of an item.

KE = (1/2) × mass × velocity²

where velocity is measured in meters per second (m/s) and mass is measured in kilograms (kg).

Plugging in the following numbers will allow us to determine the wolf's kinetic energy:

KE = (1/2) × 46.4 kg × (12.2 m/s)²

= (1/2) × 46.4 kg × 148.84 m²/s²

= 3,456.98 joules (J)

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