what would the velocity of a bullet that strikes a tin can 350 meters away in 0.25 seconds

Answer:

a ave = ( v1x - v0x ) i/Δt  + v1y j/Δt

Explanation:

The acceleration of a body is the rate of change of the velocity of the  body

The correct equation and value for the average acceleration vector and magnitude of the acceleration of the car are as follows;

Part (a) The average acceleration vector is [tex]\overset \rightarrow a_{av} =\dfrac{(v_{1x} - v_{0x})}{\Delta t} }\mathbf{i} + \dfrac{v_{iy} }{\Delta t} \mathbf{j}[/tex]

Part (b) The magnitude of the cars acceleration is [tex]\mathbf{ 2.\overline{518} }[/tex] m/s²

The reason the above values are correct is as follows:

Question: The parts of the question that appears to be missing are;

Part (a); The vector expression for the average acceleration in the time periods

Part(b); Find the magnitude of the cars acceleration

Variables:

v₀ₓ = 31 m/s

v₁ₓ = 31 m/s

[tex]v_{1y}[/tex] = 6.8 m/s

Δt = 2.7 s

Solution:

Part (a) The average acceleration vector, [tex]\mathbf{\overset \rightarrow a_{av}}[/tex], is given as follows;

[tex]Average \ acceleration \ vector, \overset \rightarrow a_{av} = \mathbf{\dfrac{\overset \rightarrow v_2 - \overset \rightarrow v_1}{t_2 - t_1}} =\dfrac{\Delta \overset \rightarrow v}{\Delta t}[/tex]

The given parameters in the question;

v₀ = v₀ₓ i

v₁ = v₁ₓ i + [tex]v_{1y}[/tex]j

∴ v₁ - v₀ = v₁ₓ i + [tex]v_{1y}[/tex]j - v₀ₓ i

The average acceleration vector becomes;

[tex]\overset \rightarrow a_{av} = \mathbf{\dfrac{\overset \rightarrow v_1 - \overset \rightarrow v_0}{\Delta t}} =\dfrac{(v_{1x} - v_{0x})\mathbf{i} + v_{iy} \mathbf{j}}{\Delta t}[/tex]

Therefore;

[tex]\mathbf{The \ average \ acceleration \ vector} \overset \rightarrow a_{av} =\dfrac{(v_{1x} - v_{0x})}{\Delta t} }\mathbf{i} + \dfrac{v_{iy} }{\Delta t} \mathbf{j}[/tex]

Part (b) The magnitude of the car's acceleration is given by plugging values of the variables v₀ₓ, v₁ₓ, [tex]\mathbf{v_{1y}}[/tex], and Δt in the above equation as follows;

[tex]\overset \rightarrow a_{av} =\dfrac{(31 \, m/s - 31 \, m/s)\mathbf{i} + 6.8 \, m/s \mathbf{j}}{2.7 \, s} = 2.\overline{518} \ m/s^2 \ \mathbf{j}[/tex]

The magnitude of the cars acceleration, a = [tex]\sqrt {(2.\overline{518} \ m/s)^2 } = \mathbf{ 2.\overline{518} \ m/s^2}[/tex]

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Answer: no, it is an opinion and is not testable (a)

Explanation:

i just got this question on Study Island

The speed of light in glass [tex]1.97 \times 10^{8}\ \mathrm{m} / \mathrm{s}[/tex]

The speed of light in Ruby is [tex]1.75 \times 10^{8} \mathrm{m} / \mathrm{s}[/tex]

The refractive index of air with respect to glass​ is 0.666

Explanation:

The refractive index is the degree of diffraction of a light beam passing from one medium to another. It can also be defined as the ratio of the speed of light in an empty space to the speed of light in a material. The equation is given as

          [tex]\text {refractive index, n\ or } \mu=\frac{\text c}{\text {v}}[/tex]

Given data:

[tex]\mu_{\text {glass}}=1.52[/tex]

[tex]\mu_{r u b y}=1.71[/tex]

Velocity of light in vacuum, c = [tex]3 \times 10^{8} \mathrm{m} / \mathrm{s}[/tex]

We need to find velocity of glass, ruby and refractive index ratio of air and glass

To find velocity of glass,

[tex]1.52=\frac{3 \times 10^{8}}{\text {velocity of glass}}[/tex]

[tex]\text {velocity of glass}=\frac{3 \times 10^{8}}{1.52}=1.97 \times 10^{8} \mathrm{m} / \mathrm{s}[/tex]

To find velocity of ruby,

[tex]1.71=\frac{3 \times 10^{8}}{\text {velocity of Ruby}}[/tex]

[tex]\text {velocity of Ruby}=\frac{3 \times 10^{8}}{1.71}=1.75 \times 10^{8}\ \mathrm{m} / \mathrm{s}[/tex]

To calculate the refractive index of air with respect to glass:   =  [tex]\frac{\mathrm{n}_{\text {air}}}{\mathrm{n}_{\text {glass}}}[/tex]

We know, the value of the refractive index of air is 1

The value of the refractive index of glass is 1.5

So, the ratio of them should be [tex]\frac{1}{1.5}=0.666[/tex]

Answer:

1.47 km

Explanation:

When the pilot hangs freely in the seat and does not push against the  seat belt, his centripetal acceleration would counter balance gravitational acceleration g = 9.81m/s2 = a

We can calculate the radius of the loop using velocity v = 120m/s and a

[tex]a = \frac{v^2}{r}[/tex]

[tex]r = \frac{v^2}{a} = \frac{120^2}{9.81} = 1467.89 m[/tex] or 1.46 km

The radius of the plane's loop is approximately 1469.4 meters. This is determined by equating the centripetal force and gravitational force at the top of the loop and solving for radius.

The question is about determining the radius of a plane's loop while considering the gravitational force and centripetal acceleration. At the top of the loop, the pilot is not pushed against the belt, which means the gravitational force is providing the necessary centripetal force. We can use the equation of motion for circular motion to solve the problem.

Given that the mass (m) of the pilot is 75 kg and he is travelling with a speed (v) of 120 m/s, and the acceleration due to gravity (g) is approximately 9.8 m/s². Centripetal force (mv²/r) is equal to the gravitational force (mg), hence we can equate mv²/r= mg. The unknown here is r (radius), which we can solve for by rearranging the equation to: r = v²/g. Plugging in the given values gives r = (120 m/s)² / 9.8 m/s² = approximately 1469.4 meters.

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Answer:D

Explanation:

The standard deviation of a set of data tell you how much each data point differs, on average, from the mean value of the set. The correct option is D.

A standard deviation is a measure of how far apart the data is from the mean. A low standard deviation indicates that data is clustered around the mean, whereas a high standard deviation indicates that data is more spread out.

When data is distributed, standard deviation is important because it aids in understanding the measurements. The higher the standard deviation, the more evenly distributed the data is.

To summarize continuous data, the standard deviation is used in conjunction with the mean.

Furthermore, like the mean, the standard deviation is normally only appropriate when the continuous data is not significantly skewed or has outliers.

Thus, the correct option is D.

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A) A concave mirror forming a larger, virtual image

Explanation:

The figure is missing; see attachment.

There are two types of mirror:

The image formed by a mirror can also be of two types:

In the figure of this problem (see attachment), we see that:

- The mirror reflects the light from the object inward --> so it is a concave mirror

- The image is formed on the other side of the mirror --> it is a virtual image

So the correct option is

A) A concave mirror forming a larger, virtual image

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Answer:

Explanation:

Your description corresponds to the picture attached.

In that model, the spheres represent atoms or molecules (is the same) of a substace. You can call them particles.

The particles tightly packed inside the cylinder of the left represent a substance in solid state whose particles are in a fix position and cannot move freely.

The particles randomly distributed throughout the cylinder on the right model a substance is gas state, where the particles occupy the whole space, moving freely.

Thus, the image depicts the change of a substance from solid state to gaseus phase. Such change is defined as sublimation.

Therefor, the answer is the third choice of your list: sublimation.

The change observed is the process of sublimation in the model. The correct answer is (c) sublimation.

In that model, the spheres represent atoms or molecules (the same) of a substance. You can call them particles.

The particles tightly packed inside the cylinder on the left represent a substance in a solid state whose particles are in a fixed position and cannot move freely.

The particles are randomly distributed throughout the cylinder on the right model a substance is a gas state, where the particles occupy the whole space, moving freely.

Thus, the image depicts the change of a substance from a solid state to the gaseous phase. Such change is defined as sublimation.

Therefore, the answer is the third choice of your list sublimation. The correct answer is (c).

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Explanation:

The initial speed of train = 24 km/hr = 24 x 1000/3600 = 20/3 m/sec

The final speed of train =  8 km/hr = 8 x 1000/3600 = 20/9 m/sec

The relation of motion

v = u + a x t

final velocity = initial velocity + acceleration x time

20/9 = 20/3 - 2 x t   where t is time

Because the acceleration is negative

2 t =  20/3 - 20/9 = 40/9   or  t = 20/9 sec = 2.2 sec

The time taken to decrease the speed from 24 km/hr to 8 km/hr is 2.2 sec approx

Answer:

2 seconds

Explanation:

The frequency of a wave is related to its wavelength and  speed by the equation

[tex]f=\frac{v}{\lambda}[/tex]

where

f is the frequency

v is the speed of the wave

[tex]\lambda[/tex] is the wavelength

For the wave in this problem,

v = 2 m/s

[tex]\lambda=8 m[/tex]

So the frequency is

[tex]f=\frac{2}{8}=0.25 Hz[/tex]

The period of a wave is equal to the reciprocal of the frequency, so for this wave:

[tex]T=\frac{1}{f}=\frac{1}{0.25}=4 s[/tex]

This means that the wave takes 4 seconds to complete one full cycle.

Therefore, the time taken for the wave to go from a point with displacement +A to a point with displacement -A is half the period, therefore for this wave:

[tex]t=\frac{T}{2}=\frac{4}{2}=2 s[/tex]

The time taken by the wave to travel the vertical  displacement from the point on the rope to -A is 2 seconds

Given to us:

wavelength λ = 8 m,

Velocity v = 2 m/s,

The frequency of a wave is given by:

[tex]frequency=\dfrac{Velocity}{wavelength}\\f=\dfrac{V}{\lambda}\\\\f=\dfrac{2}{8}\\\\f= 0.25\ \rm Hz[/tex]

Therefore, the frequency of the wave is 0.25 Hz.

The period of a wave is equal to the reciprocal of the frequency,

[tex]{\rm period\ of\ time}(T),\\T=\dfrac{1}{f}\\T=\dfrac{1}{0.25}\\\\T=4\ sec[/tex]

Therefore, It takes 4 seconds to complete one full cycle.

Hence, the time taken by the wave to travel the vertical  displacement from the point on the rope to -A is 2 seconds as its is the half distance which is needed to be traveled by the wave.  

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Answer:

Areas of equal pressure.

Explanation:

The line making a circle means equal pressure.

Final answer:

The lines around a low-pressure area on a weather map are isobars, indicating areas of equal pressure crucial for predicting weather conditions.

Explanation:

The lines making a circle around the low-pressure area indicate areas of equal pressure, also known as isobars. These isobars connect places with the same atmospheric pressure measurements, typically in millibars. On a weather map, isobars form almost circular shapes around low-pressure centers, like cyclones, and indicate areas where the pressure decreases towards the center.

Understanding these pressure patterns is essential for meteorologists to describe and predict weather, as they directly affect weather conditions. For instance, the approach of a low-pressure system often brings cloudiness, winds, and precipitation.

Answer: 2.17 s

Explanation:

The described situation is related to projectile motion (also known as parabolic motion). So, this kind of motion has a vertical component and a horizontal component; however, in this case we will only need the equation related to the horizontal displacement [tex]x[/tex]:

[tex]x=V_{o}cos \theta t[/tex]

Where:

[tex]x=45 m[/tex] is the arrow's horizontal displacement

[tex]V_{o}=800 m/s[/tex] is the arrow's initial velocity

[tex]\theta=75\°[/tex] is the angle

[tex]t[/tex] is the time the arrow is in the air

Isolating [tex]t[/tex]:

[tex]t=\frac{x}{V_{o}cos \theta}[/tex]

Solving with the given data:

[tex]t=\frac{45 m}{800 m/s cos(75\°)}[/tex]

[tex]t=2.17 s[/tex] This is the time the arrow is in the air

Answer:

the initial conditions

Explanation:

The rest of the answers are

the duration of seasons on Earth

turn left toward the coast, turn right and head out to sea (in that order)

a warm, dry air mass moving over an area.

The two models assimilate data differently using different equations.

changes in ocean currents

In a model ensemble system, meteorologists change  the initial conditions each time they run a simulation of the same model.

Ensemble modelling is a process in which multiple diverse models are created to predict an outcome, either by employing a variety of modelling algorithms or by employing a variety of training data sets. The ensemble model then aggregates each base model's prediction, yielding a single final prediction for the unseen data.

The goal of using ensemble models is to reduce prediction generalization error. When the ensemble approach is used, the prediction error of the model decreases as long as the base models are diverse and independent. In making a prediction, the approach seeks the wisdom of the crowds.

Hence, in a model ensemble system, meteorologists change  the initial conditions each time they run a simulation of the same model. Option(c) is correct.

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The answer is B. metalloids

(boron, silicon, germanium, arsenic, antimony, tellurium, astatine, and polonium)

Final answer:

Elements along the stair step line of the periodic table are metalloids, with properties between those of metals and nonmetals. Metals are to the left and are conductive and malleable, while nonmetals are to the right and are typically poor conductors. Atomic radii decrease across a period and increase down a group. Option b

Explanation:

Elements that lie along the stair step line of the periodic table are known as metalloids. These elements exhibit properties that are intermediate between those of metals and nonmetals. Metals are typically found to the left of the metalloids, and they are generally malleable, shiny, and good conductors of heat and electricity.

On the other hand, nonmetals are located to the right of the metalloids and typically have opposite properties, such as being poor conductors of heat and electricity. The atomic radii of elements tend to decrease from left to right across a period because of the increasing positive charge in the nucleus, which pulls electrons closer. In contrast, atomic radii generally increase as you move down a group due to the addition of energy levels.

Answer:

Therefore the new temperature of the water is 91.67°C

Explanation:

Specific heat of water = 4.186 joule /gram °C

The equation to calculate change of temperature

Q=s×m×ΔT

Q = the amount of heat = 30,000 J

s= Specific heat of water = 4.186 joule /gram °C

m = mass of the water = volume ×density=(100×1)gram =100 gram

ΔT = the change of temperature = (T-20)

Therefore,

30000= 4.186×100×(T-20)

⇔(T-20)= 71.67

⇔T = 71.67+20

⇔T = 91.67

Therefore the new temperature of the water is 91.67°C

ANSWER :

(A) AT RIGHT ANGLES TO THE DIRECTION THE WAVE TRAVELS.

EXPLANATION :

TRANSVERSE WAVES IS THAT IN WHICH THE PARTICLES VIBRATE WITH AN UP-AND-DOWN MOTION. THE PARTICLES IN A TRANSVERSE WAVE MOVE ACROSS OR PERPENDICULAR TO THE DIRECTION THAT THE WAVE IS TRAVELING OR AT RIGHT ANGLES TO THE DIRECTION THE WAVE TRAVELS.

Answer:

The answer is A

Explanation:

If it goes 80km/h on a flat highway than it is not going any faster or slower.

When a  car moves at 80 kilometers / hour on a flat, straight highway then the car would not accelerate, therefore the correct answer is option A.

The rate of change of the velocity with respect to time is known as the acceleration of the object.

As per the second option when the car slows from 80 km/h to 35 km/h, then it would accelerate with negative acceleration.

When the car turns in the corner car would accelerate because there is a change in the velocity of the motion.

Similarly in the last option when a car speeds up from 35 km/h to

80 km/h, then it would generate acceleration because there is a change in the velocity with respect to the time.

The first option is the tye only case when the car would not accelerate because there is no change in the velocity of the car, thus the correct answer is option A.

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Answer:

according to the method of their formation

Explanation:

Explanation:

The gravitational force of attraction on the surface of earth F = G M m/R²

Here G = gravitational constant = 6.67 x 10⁻¹¹

M = mass of the earth and m = mass of the body on the surface of earth .

R = radius of earth

In this question

mass of earth = 6 x 10²⁴ kg  and its radius = 6 x 10⁶ m

The values are substituted in the above equation

F = 6.67 x 10⁻¹¹ x 6 x 10²⁴ x 5 / ( 6 x 10⁶ )² =  49 N

The mass will be attracted by 49 N of force .

In scientific discourse, a law is generally considered a descriptive generalization about how some aspect of the natural world behaves under stated circumstances. A theory, on the other hand, is a well-substantiated explanation of some aspect of the natural world that incorporates facts, laws, inferences, and tested hypotheses. The principal difference is that a law describes what happens and a theory explains why it happens.

Laws are accepted as fact because they are simple, true statements about how things occur in nature, usually summed up in a mathematical formula. They are typically based on empirical evidence from observations and experiments. For example, the Law of Gravity describes the attraction between two objects but doesn’t explain the mechanism. Theories, however, go through rigorous testing and are only sustained after consistent empirical support. They aim to provide the most reasonable explanation based on the evidence at hand. Consider the Theory of Evolution by Natural Selection - it explains the mechanisms behind the changes in species over time. Unlike a law, a theory can be adjusted or discarded if new evidence presents itself that doesn't align with the current theory. This flexibility is why theories, despite being well-supported, are not accepted as unchanging facts, but rather as the best explanations we have based on current knowledge.

Answer:

Mechanical advantage of the ramp = [tex]\frac{980}{650} = 1.51[/tex]

Efficiency of the ramp = [tex]\frac{Actual\hspace{0.1cm} work\hspace{0.1cm} done}{Work}[/tex] = [tex]\frac{100\times 9.8\times 3}{650\times 5} = \frac{2940}{3250} = 0.9046 = 90.46%[/tex]

Explanation:

i) Mechanical advantage of the ramp = [tex]\frac{980}{650} = 1.51[/tex]

ii) Efficiency of the ramp = [tex]\frac{Actual\hspace{0.1cm} work\hspace{0.1cm} done}{Work}[/tex] = [tex]\frac{100\times 9.8\times 3}{650\times 5} = \frac{2940}{3250} = 0.9046 = 90.46%[/tex]

The mechanical advantage and the efficiency of the ramp are respectively;

330 N and 90%

I have drawn an image of the force diagram on the crate and attached it.

Applying Newton's second law to the force diagram attached, we have;

F_fric + F + N + mg = 0

Projecting forces gives us;

In the x-direction;

F = F_fric + mg*sin α

In the y-direction;

N - mg*cos α = 0

Also;

F_fric = μmg*cos α

Thus;

F = (μmg*cos α) + (mg*sin α)

Mechanical advantage is;

ΔF = mg - F

ΔF = mg - mg((μ cos α) + (sin α))

Since the ramp is 3 m high and 5 m long, then by trigonometric ratios;

(sin α) = 3/5

cos α = 4/5

But we are given that F is 650 N.

Thus;

ΔF = (100 × 9.8) - 650

ΔF = 330 N

Efficiency of the ramp is;

η = (mgh/Fl) × 100%

η = (100 × 9.8 × 3/(650 × 5)) × 100%

η ≈ 90%

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C) By altering the length of the pendulum

Explanation:

The period of a simple pendulum is given by the equation

[tex]T=2\pi \sqrt{\frac{L}{g}}[/tex]

where

L is the length of the pendulum

g is the acceleration due to gravity

In this problem, we are asked which adjustmenet can be done to speed up or slow down the pendulum clock: that means, which adjustment can be done in order to change the period of the pendulum.

From the equation above, we notice that the period of a pendulum depends only on its length (and the acceleration of gravity). Therefore, its period can be changed only by changing the length of the pendulum. And so, the only correct answer is

C) By altering the length of the pendulum

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Answer:

B

Explanation:

When a beam of light hits glass straight on it passes right through it. But the whites that make up the light actually get sloped down by the glass. And only go back to their normal speed when they come out the other side. That slowing down is what causes white light to split into a rainbow of color whenever it hits glass on an angle. it happens because glass slows some colors of light more than others and because slowing down on an angle causes them to slightly bend. All colors get bend somewhere in between. The reason that different colors get split is because they all have different wavelengths. The longest being red and violet being the shortest. The longer the wavelengths, the slower it is.  

Different wavelengths of visible light refract at different angles when passing from air to glass.

Refraction is the bending of light (it also happens with sound, water and other waves) as it passes from one transparent substance into another. This bending by refraction makes it possible for us to have lenses, magnifying glasses, prisms and rainbows.

When a beam of light hits glass straight on it passes right through it. But the whites that make up the light actually get sloped down by the glass. And only go back to their normal speed when they come out the other side.

That slowing down is what causes white light to split into a rainbow of color whenever it hits glass on an angle. it happens because glass slows some colors of light more than others and because slowing down on an angle causes them to slightly bend.

All colors get bend somewhere in between. The reason that different colors get split is because they all have different wavelengths. The longest being red and violet being the shortest. The longer the wavelengths, the slower it is.  

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Explanation:

Let us assume , an Object is thrown with initial Velocity u m/s and angle of θ above the horizontal level. The horizontal and vertical velocities are (x,y)

vₓ = v₀cos θ

[tex]v_{y}[/tex] = v₀ sinθ

now, the time when the object reaches the maximum height can be calculated from

[tex]v_{y}[/tex] = v₀ sinθ - at₀ = 0

t₀ = v₀ sinθ/a

thus, the total time in air is two times higher ; t = 2t₀ = 2 (v₀ sinθ) /a

the maximum distance can be calculated from this equation

X = vₓ t= v₀ cos  θ x 2 (v₀ sinθ) /a

it implies x is inversely proportional to a.

we know the acceleration on the Moon is 1/6 th of Earth.the ratio between between maximal distance on the moon and on the earth is 6.

Increase

Explanation:

Naomi increasing the pressure on a solution of liquid and gas in a closed container will increase the amount of gas held in her solution.

Increase in pressure increases the solubility of gases in a solution.

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Increasing the pressure on a solution of liquid and gas in a closed container will increase the amount of gas held in the solution.

Increasing the pressure on a solution of liquid and gas in a closed container will increase the amount of gas held in the solution. This is because an increase in pressure will result in more collisions between gas particles and the container walls, leading to a greater force being exerted on the walls. As a result, the pressure inside the container increases.

Answer:

The answer is B (has greater mass)

The real car has more momentum because it has greater mass.

The correct answer is B. The real car has greater mass.

Momentum is defined as the product of an object's mass and its velocity. In this case, both the real car and the toy car are moving at the same speed of 10 km/h. However, since the real car has greater mass, it will have a greater momentum.

For example, let's say the real car has a mass of 1000 kg and the toy car has a mass of 100 kg. The momentum of the real car would be 1000 kg × (10 km/h) = 10,000 kg km/h, while the momentum of the toy car would be 100 kg × (10 km/h) = 1000 kg km/h. Therefore, the real car has more momentum than the toy car.

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Explanation:

Correct.  Air has an index of refraction of approximately 1, and the angle of incidence is 35°.  The substance has an unknown index of refraction n, and the angle of refraction is 25°.

1 sin 35° = n sin 25°

n = 1.36

Answer:

                                     1             2               3          4            5

 New force ( N )           1.25      0.4166      48      175         150

Explanation:

We know that ,

Force ( f ) ∝ distance ( d )

1 )

initial distance =40 m

initial force = 5 N

F ∝ d

F = k d     ( k = proportionality constant )

5 = k * 40

k = (1/8)

new distance = 10 m

new force = ( 1/8 ) * 10 = 1.25 N

2)

d = 72 m

F = 2.5 N

k = 2.5/72

new distance = 12 m

new force = ( 2.5/72 ) * 12 = 0.4166 N

3)

d = 12 m

F = 8 N

k = 2/3

new distance = 72 m

new force = ( 2/3 ) *72 =  48 N

4 )

d = 6 m

F = 25 N

k = 25/6

new distance = 42 m

new force = ( 25/6)*42  = 175 N

5)

d = 10 m

F = 50 N

k = 5

new distance = 30 m

new force = 5 * 30 = 150 N

Since she is testing where the plant would grow best, the type, height and amount of water does not help the original question. Only moving the plants will help her determine where to plant the basil plants. Option B. the location of the plants

Answer: C. the height of the plants

Explanation: