Distinguish between the following natural science and social science

Answers

Answer 1

Anthropology is a social science that deals with the history of man. ... This is the main difference between social science and natural science. Sciences such as logic, mathematics, and statistics are called as formal sciences and they too are different from natural sciences.

Answer 2
Natural sciences are studies of the natural world.This generally involves life forms, but also geology and weather. the occur naturally and are physically observable . it is quantitative study ( referring to quantities and measurable characteristics).

Social Studies are the study of interactions between life forms , most commonly focusing on the dynamic interface between people , their societies, or their cultures. These are not observable as physical objects but are instead a study of behaviors and action. It is a qualitative study, as in the examination of qualities.

Related Questions

A resource (like the Sun) that essentially never "runs out" is said to be _____.

A. reusable
B. recyclable
C. inexhaustible
D. nonrenewable

asap please

Answers

the answer youre looking for is (C

________ fuel is a renewable alternative to petroleum fuels that is made through either biologically or chemically driven production in a process called gasification.

Answers

Gasoline fuel is a renewable alternative to petroleum fuels that is made through either biologically or chemically driven production in a process called gasification.

Answer:

Hydrogen fuel is a renewable alternative to petroleum fuels that is made through either biologically or chemically driven production in a process called gasification.

Just before snapping backup in the air, my speed is 50m/s. What is my kinetic energy just before snapping back up

Answers

Kinetic energy of anything is (1/2) (mass) (speed)² .

Your kinetic energy just before you snap back up (? ?) is

(1/2) (your mass in kilograms) (50 m/s)² =

(1/2) (your mass in kilograms) (2,500 m²/s²) =

(1,250 x your mass in kilograms) .  The unit is Joules.

What is the mass of a car that is going 2m/s2 and then hits a tree with a force of 6000N

Answers

Given that force applied due to tree on car is 6000 N

and during the stop the acceleration is given as 2 m/s^2.

So here we can say that As per Newton's II law

[tex]F = m*a[/tex]

here F = force on car = 6000 N

a = acceleration of car = 2 m/s^2

now we can plug in all values above in the given equation

[tex]6000 = 2*m[/tex]

[tex]m = 3000 kg[/tex]

So here the mass of the car will be 3000 kg

Final answer:

The mass of the car is 3000 kg.

Explanation:

To calculate the mass of the car, we can use Newton's second law of motion: F = ma.

In this case, the force exerted on the car is 6000 N and the acceleration is 2 m/s².

So, using the formula F = ma, we can rearrange it to solve for mass (m). Therefore, m = F/a = 6000 N / 2 m/s² = 3000 kg.

The colors of pigments is it a) are cyan,yellow,and magenta b) are the same as the secondary c) combine in equal amounts to provide black or d) all of the above


Answers

The answer would be A or D. The most appropriate answer would be D. Hope I helped :)

How much work does an elephant do while moving a circus wagon 20 meters with a pulling force of 200n

Answers

Given:

s(distance)= 20 meters

F(force)=200N

Now we know that

work done= Force applied x distance

Substituting the given values in the above formula we get

Work done= 20 x 200= 4000J

Final answer:

The work done by an elephant while moving a circus wagon 20 meters with a pulling force of 200N is calculated using the formula: Work = Force x Distance. Plugging the values into the formula gives us 4000 Joules.

Explanation:

The work done by the elephant pulling the circus wagon can be calculated using the formula for work, which is Work = Force x Distance. In this situation, the Force applied by the elephant is 200N and the Distance moved by the wagon is 20 meters.

So, the Work done would be: 200N x 20m = 4000 Joules.

This means the work done by the elephant is 4000 Joules.

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What did Rutherford’s model of the atom include that Thomson’s model did not have?

Answers

Rutherford tested Thomson'shypothesis by devising his "gold foil" experiment. Rutherford was forced to discard the Plum Pudding modeland reasoned that the only way the alpha particles could be deflected backwards was if most of the mass in an atom was concentrated in a nucleus.

Answer:

Nucluas

Explanation:

What is the least functional sense at birth?

Answers

I think its either sight or its your hands/sensory limbs because it takes babie a while to figure out how to use their hands. i would say speech but it is not a sense. hope this helps!

Final answer:

The least functional sense at birth is vision. Newborn babies have limited visual acuity and are unable to see clearly or focus on objects that are far away. Their vision gradually improves as they grow older.

Explanation:

The least functional sense at birth is vision. Newborn babies have limited visual acuity and are unable to see clearly or focus on objects that are far away. Their visual system is still developing, and it takes a few months for them to develop better visual skills.

Babies are born with the ability to hear, taste, and touch, but their vision is less developed at birth. They can detect light and motion, but their vision gradually improves as they grow older. By about 6 months of age, most babies have developed the ability to see more clearly.

During the early stages of development, babies rely on their other senses, such as touch and hearing, to explore and interact with the world. These senses are more functional at birth compared to vision.

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I NEED HELP IS URGENT PLEASE!!!
Which of the following statements applies to the motion of a ball rising and then falling in free fall?

I. The ball has constant acceleration as it moves upward.

II. The ball has constant acceleration at the top of its path.

III. The ball has constant acceleration as it moves downward.

a.

I only

b.

III only

c.

I and III

d.

I, II, and III

 

Answers

D.  For any projectile motion, there is a constant downwards acceleration due to gravity at all instances.  This not to be confused with velocity, which changes due to gravity at every moment along the object's path.

Who is faster: someone traveling a mile a minute or someone traveling 20 m/s.?

Answers

speed of first one is given as

[tex]v_1 = 1 mile \: in \: 1 min[/tex]

we also know that

1 mile = 1609 meter

also for time of motion

t = 1 min = 60 s

so in SI units the speed is given as

[tex]v = \frac{1609}{60}[/tex]

[tex]v = 26.82 m/s[/tex]

so 1 mile/min = 26.82 m/s

So here we will say that 1 mile per min is more speed than 20 m/s as we can see that 1 mile / min is 26.82 m/s in SI units after its conversion

Final answer:

Someone traveling at a mile a minute (26.67 m/s) is faster than someone traveling at 20 meters per second.

Explanation:

To determine who is faster between someone traveling a mile a minute and someone traveling at 20 meters per second, we need to convert one of the rates so that both are in the same units. First, let's convert a mile a minute to meters per second. Since one mile is equivalent to 1600 meters, and one minute is equivalent to 60 seconds, if you travel a mile in a minute, you're traveling 1600 meters in 60 seconds. Thus, the conversion is 1600 meters / 60 seconds = 26.67 meters per second.

Now, we compare:

A mile a minute = 26.67 m/s

Someone traveling at 20 m/s

It's clear that 26.67 m/s is faster than 20 m/s. Therefore, someone traveling a mile a minute is faster than someone traveling at 20 m/s.

A father lifts a toddler 1.5m up in the air. The child gains 187.5J of gravitational potential energy as a result. What is the mass of the toddler? (Assume that the gravitational field strength is 10N/kg.)

Answers

Answer:

Mass of toddler = 12.5 kg

Explanation:

 The potential energy of a body is given by the expression, PE = mgh, where m is the mass of the body, g is the acceleration due to gravity value and h is the height of the body.

 Potential energy = 187.5 J

 Height = 1.5 m

 Substituting

     187.5 = m * 10 * 1.5

     m = 12.5 kg

So mass of toddler = 12.5 kg

PLEASE HELP!! When a box rests on a round sheet of wood on the ground, it exerts an average pressure p on the wood. If the wood is replaced by a sheet that has half the diameter of the original piece, what is the new average pressure? I think the answer is 4p but I don't know why.

Answers

The new average pressure will be four times the original pressure when the wood is replaced by a sheet with half the diameter, i.e p' = 4p.

The pressure exerted by an object is given by the force applied divided by the area over which it is distributed.

The formula for pressure (p) is (p = F/A).

If the box exerts a pressure (p) on the original round sheet of wood, and the wood is replaced by a sheet with half the diameter, the new area will be (1/4) of the original (since area is proportional to the square of the diameter).

Therefore, the new pressure (p') can be expressed as:

p' = F ÷ (1/4)A = 4p

So, the new average pressure will be four times the original pressure when the wood is replaced by a sheet with half the diameter.

Eric decided to go for a walk from his home. He headed 6 meters east and x meters north. The angle formed by the displacement vector and the horizontal vector is 37°. What is the length of the displacement vector?

Answers

Answer:

 Length of displacement vector = 7.51 m

Explanation:

 Consider east as positive X axis and North as positive Y axis.

 Eric headed 6 meters east, Displacement = 6 i

 Then he headed X meters north, Displacement = X j

 Total displacement = 6 i + X j

  Angle it makes with horizontal axis, θ = tan⁻¹(X/6) = 37°

  X/6 = tan 37

   X = 4.52 m

Total displacement = 6 i + 4.52 j

Magnitude = [tex]\sqrt{6^2+4.52^2} =7.51m[/tex]

 Length of displacement vector = 7.51 m

The answer is A. 7.5.

Alex, who has a mass of 100 kg, is skateboarding at
9.0 m/s when he smacks into a brick wall and comes
to a dead stop in 0.2 s.
a. Show that his deceleration is 45 m/sz.
b. Show that the force ofimpact is 4500 N. (Ouch!)

Answers

Part a)

acceleration is defined as rate of change in velocity

so we can write

[tex]a = \frac{v_f - v_i}{t}[/tex]

here we know that

finally it will stop so vf = 0

initial speed is given as 9m/s

and the time to stop is 0.2 s

[tex]a = \frac{0 - 9}{0.2}[/tex]

[tex]a = -45 m/s^2[/tex]

Part b)

Now by 2nd law of Newton

[tex]F = ma[/tex]

given that

m = 100 kg

a = 45 m/s^2

so now using above equation

[tex]F = 100 * 45[/tex]

[tex]F = 4500 N[/tex]

so it will exert 4500 N force to stop

A. The deceleration of Alex is 45 m/s²

B. The force of impact is 4500 N

A. How to determine the deceleration

From the question given above, the following data were obtained:

Initial velocity (u) = 9 m/sFinal velocity (v) = 0 m/sTime (t) = 0.2 sDeceleration (a) =?

a = (v – u) / t

a = (0 – 9) / 0.2

a = –9 / 0.2

a = –45 m/s²

The, negative sign indicate that the Alex is coming to rest.

B. How to determine the force Deceleration (a) = 45 m/s²Mass (m) = 100 KgForce (F) =?

F = ma

F = 100 × 45

F = 4500 N

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Calculate how much energy is needed to get a typical car with a mass of 1500 kg up to a speed of 40 mph ignoring friction or any other losses or inefficiencies. Show all work, and give your answer in kWh.

Answers

m = mass of the car = 1500 kg

we know that 1 mph = 0.45 m/s

hence

v = speed gained by the car = 40 mph = 40 x 0.45 m/s = 18 m/s

since the car is gaining speed here , hence the energy need is same as the kinetic energy gained by the car

kinetic energy is given as

KE = (0.5) m v²                     where m = mass , v = speed

inserting the above values in the formula

KE = (0.5) (1500) (18)²

KE = 2.43 x 10⁵ J

we know that , 1 J = 2.78 x 10⁻⁷ kwh

hence

KE = (2.43 x 10⁵) (2.78 x 10⁻⁷)

KE = 0.068 kwh

hence the energy needed is 0.068 kwh

What moon phase occurs 3-4 days after a waning gibbous?

Answers

The "waning gibbous" begins immediately after the Full Moon and lasts about a week.

At the end of the week, the moon is no longer gibbous, but it's still waning.  At the instant it's exactly half-illuminated, it's called "Third Quarter", and then it continuous to wane for another week.

So 3 to 4 days after the END of the waning gibbous phase, it's a Waning Crescent. It still has another 3 to 4 days of waning to go, before it wanes away to nothing and we have the next New Moon.

The waning gibbous phase is the phase between the full and last quarter moon late at night or in the early morning . The waning crescent is the phase that occurs 3-4 days later a waning gibbous.

What is waning gibbous ?

The waning gibbous phase is the phase between the full and last quarter moon late at night or in the early morning.

The waning gibbous phase moon appears more than half-lighted but less than the full moon. A full sunset is a time when the full moon rises. The rising time of the waning gibbous moon is late at night.

It looks red like a  full moon when it’s near the horizon.

To learn more about the waning gibbous refer to the link ;

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what force does a window washer want acting on him when he is trying to keep the same position

Answers

Answer

The force he applies on himself is balanced force.

Explanation: Balanced force means the net forces applied on himself will be zero. Which is forces applied on right side will be equal to left side forces. And upward forces will be equal to downward forces. According to first law of motion, an object in rest can never be in motion except some force is exerted on it to do so. Hence if force on window washer will be balanced force ( Net force = 0 ), then there will be no motion and he will be in same position.

Answer:a balanced force

Explanation:

A racing car whose mass is 1.2 X 10^3 kg is travelling at 8.9 m/s. It stops with a constant deceleration in a distance of 1.8X10^1 m. What force must the brakes apply to the car if the friction in the car’s engine is 1.8 X 10^3 N.

Answers

given that initial speed of the car is

[tex]v_i = 8.9 m/s[/tex]

now after travelling the distance d = 1.8 * 10^1 m the car will stop

so here we can use kinematics to find the acceleration of car

[tex]v_f^2 - v_i^2 = 2 a d[/tex]

[tex]0 - 8.9^2 = 2 a d[/tex]

here we have

[tex]- 79.21 = 2*(18)*a[/tex]

[tex]a = -2.2 m/s^2[/tex]

net force applied due to brakes of car is given by Newton's II law

[tex]F = ma[/tex]

here we have

mass = 1.2 * 10^3 kg

[tex]F_{net} = 1.2 * 10^3 * 2.2[/tex]

[tex]F_{net} = 2.64 * 10^3 N[/tex]

now we can say

[tex]F_{net} = F_1 + F_2[/tex]

[tex]2.64 * 10^3 = 1.8 * 10^3 + F_2[/tex]

[tex]F_2 = 8.4 * 10^2 N[/tex]

So the force applied due to brakes is given as above

Starting from rest, the Road Runner accelerates at 3 m/s for ten seconds. What is the final velocity of the Road Runner?

Answers

Answer

The answer to this question is [tex]30 ms^{-1}[/tex]

Explanation

As we know that accelartion is the rate of change of velocity. So, it can be write as

[tex]a = (V_f -V_i) /t[/tex]

where

[tex]V_f[/tex] is the final velocity

[tex]V_i[/tex] is the initial velocity

t is the time

a is the accelartion

as we konw

[tex]a = 3 ms^{-2}[/tex]

t = 10 s

From rest So,

[tex]V_i[/tex] = 0

[tex]V_f[/tex] = ?

Putting values

[tex]3 = (V_f - 0)/10[/tex]

[tex]3 * 10 = V_f[/tex]

[tex]30 = V_f[/tex]

[tex]V_f = 30 ms^{-1}[/tex]

So, the right answe is [tex]30 ms^{-1}[/tex]

(3 m/s²) x (10 s) = 30 m/s

His speed at the end of 10 sec is 30 m/s.  We can't describe his velocity, because we have no information about the direction he's moving.

A certain metal has a coefficient of linear expansion of 2.00 × 10-5 K-1. It has been kept in a laboratory oven at
325°C for a long time. It is now removed from the oven and placed in a freezer at ‐145°C. After it has reached
freezer temperature, the percent change in its density during this process is closest to
A) +2.90%.
B) ‐2.90%.
C) +2.74%.
D) ‐2.74%.
E) It is not possible to tell without knowing the mass and original volume of the metal.

Answers

Hi, the answer is A) +2.90%.

A: +2.90% is the answer

a race car accelerates uniformly from 18.5m/s to 46.1m/s in 2.4 seconds. determine the acceleration of the car and the distance traveled

Answers

The car's (average) acceleration would be

[tex]a=\dfrac{46.1\,\frac{\mathrm m}{\mathrm s}-18.5\,\frac{\mathrm m}{\mathrm s}}{2.4\,\mathrm s}=11.5\,\dfrac{\mathrm m}{\mathrm s^2}[/tex]

The car's position over time would be given by

[tex]x=v_0t+\dfrac12at^2[/tex]

so that after 2.4 seconds, the car will have traveled a distance of

[tex]x=\left(18.5\,\dfrac{\mathrm m}{\mathrm s}\right)(2.4\,\mathrm s)+\dfrac12\left(11.5\,\dfrac{\mathrm m}{\mathrm s^2}\right)(2.4\,\mathrm s)^2[/tex]

[tex]\implies x=77.5\,\mathrm m[/tex]

Hello!

A race car accelerates uniformly from 18.5 m/s to 46.1 m/s in 2.47 seconds. Determine the acceleration of the car and the distance traveled.

* Determine the acceleration of the car....

We have the following data:

V (final velocity) = 46.1 m/s

Vo (initial velocity) = 18.5 m/s

ΔV  (speed interval)  = V - Vo → ΔV  = 46.1 - 18.5 → ΔV  = 27.6 m/s

ΔT (time interval) = 2.4 s

a (average acceleration) = ? (in m/s²)

Formula:

[tex]\boxed{a = \dfrac{\Delta{V}}{\Delta{T^}}}[/tex]

Solving:  

[tex]a = \dfrac{\Delta{V}}{\Delta{T^}}[/tex]

[tex]a = \dfrac{27.6\:\dfrac{m}{s}}{2.4\:s}[/tex]

[tex]\boxed{\boxed{a \approx 11.5\:m/s^2}}\longleftarrow(acceleration)\:\:\:\:\:\:\bf\green{\checkmark}[/tex]

* The distance traveled ?

We have the following data:

Vi (initial velocity) = 18.5 m/s

t (time) = 2.47 s

a (average acceleration) = 11.5 m/s²

d (distance interval) = ? (in m)

By the formula of the space of the Uniformly Varied Movement, it is:

[tex]d = v_i * t + \dfrac{a*t^{2}}{2}[/tex]

[tex]d = 18.5 * 2.4 + \dfrac{11.5*(2.4)^{2}}{2}[/tex]

[tex]d = 44.4 + \dfrac{11.5*5.76}{2}[/tex]

[tex]d = 44.4 + \dfrac{66.24}{2}[/tex]

[tex]d = 44.4 + 33.12[/tex]

[tex]\boxed{\boxed{d = 77.52\:m}}\longleftarrow(distance)\:\:\:\:\:\:\bf\green{\checkmark}[/tex]

________________________________  

[tex]\bf\red{I\:Hope\:this\:helps,\:greetings ...\:Dexteright02!}[/tex]

Cereal plants gain chemical potential energy as they grow. Which form of energy is converted to create the chemical potential energy? A. gravitational potential energy B. kinetic energy C. light energy D. thermal energy

Answers

Answer:

C. light energy

Explanation:

In all these plants the energy is converted from the photosynthesis process. As per this photosynthesis phenomenon plants get energy by the light received from the sun.

This will help to make the plants to grow and make fruits in the plant.

in this word photosynthesis we can see it is combination of photo + synthesis

which clearly means that this energy synthesis is with the help of photons received from the sun.

These photons are light photons

So here correct answer will be

C. light energy

Answer:

light energy

Explanation:

what gas is most abundant greenhouse gas ? a) ozone b) chlorofluorocarbon c) carbon dioxide d) methane e) water vapor

Answers

i believe the answer is water vapor

hope this helps


Answer:

WATER VAPOR

Explanation:

I got a 100% on my test

A 32.5-kg rock is traveling at a constant velocity through space. Then a force of 140 N is exerted on the rock. What acceleration does the force produce?

3.31 m/s^2
2.32m/s^2
4.31 m/s^2
45.5 m/s^2
10.7 m/s^2

Answers

As per Newton's II law we can say force applied on an object is product of mass and acceleration

[tex]F = ma[/tex]

given that

Force = 140 N

mass = 32.5 kg

now we can use above formula

[tex]140 = 32.5* a[/tex]

[tex]a = \frac{140}{32.5}[/tex]

[tex]a = 4.31 m/s^2[/tex]

so its acceleration must be 4.31 m/s^2

A velocity vs. time graph for an object is shown.


Which best describes the acceleration of the object?

constant and positive
constant and negative
changing and positive
changing and negative

Answers

Answer:

The correct answer is constant and positive

Explanation:

The velocity is changing with respect to time at constant rate and we know that the change in velocity is known as acceleration so a constant change in velocity with respect to time will give us a constant acceleration. Similarly the velocity is gradually increasing that is why we will take the acceleration as positive .


Answer: constant and positive

Explanation:

Acceleration is the rate of change of velocity. It can be measured in meter per second square.

[tex]a = \frac{dv}{dt}[/tex]

It can be measured from the slope of velocity - time graph.

In the given velocity vs. time graph, the slope is a straight line in the first quadrant. This means the acceleration is uniform (constant) and positive.

Acceleration from the given graph is:

a = change in velocity /time interval = (5-0)m/s/(5-0)s = 1 m/s².

When a 60 g (=0.06 kg) tennis ball is served by a newly invented machine, it accelerates from zero to 50 m/s. The ball experiences a constant acceleration due to the impact with the racket over a distance of 0.5 m. What is the

Answers

here tennis ball is accelerated from initial speed zero to final speed 50 m/s

In this accelerated motion the distance moved by the ball is 0.5 m

So here we can use kinematics to find the acceleration of the ball during this distance

[tex]v_f^2 - v_i^2 = 2 a d[/tex]

here given that

vf = 50 m/s

vi = 0

d = 0.5 m

[tex]50^2 - 0 = 2*a*0.5[/tex]

[tex]2500 m/s^2 = a[/tex]

now if we have acceleration during its motion so we can find the applied force by using Newton's II law

[tex]F = ma[/tex]

[tex]F = 0.06*2500[/tex]

[tex]F = 150 N[/tex]

now the applied force will be 150 N on the ball by racket

NEED ANSWER NOW PLZ WILL MARK BRAINLIEST

Why is diffusion important to cells?

A. it permits the sorting of water molecules from solute molecules, such as sugar.

B. it regulates salt content in the cell, preventing bloating and shriveling.

C. it helps maintain the balance of materials needed for survival, such as oxygen and water.

D. The back and forth movement creates extra energy as ADP is transformed into ATP.

WILL MARK BRAINLIEST

Answers

I'm like 89% sure that the answer is C.

it is the process by which important molecules enter the body cells and waste products are removed from cells.  is why it is important because your body kills off the stuff that's  not supposed to be in it and makes sure all the good cells are  where they're supposed to be

60 g of vinegar was used in a chemical reaction with baking soda. The total mass of the products is 140 g. What was the mass of the baking soda

Answers

The mass of the baking soda was 80 g

Answer: the mass is 80g

Explanation: In a solution of 140g, we knot that there are 60g of vinegar, the only other component in the solution is baking soda.

Now we want to find the mass of the baking soda in the solution.

Because there are only two components in the solution, if we remove the 60g of vinegar, the residue mass is the mass of the baking soda.

then we need to calculate:

Mass = 140g - 60g = 80g

So the mass of baking soda in the solution is 80g.

The average mass of 1 baking soda compound is 84 amu After it reacts with 1 vinegar molecule the total mass of the product is 144 amu What is the mass of the one vinegar molecule
A 60 amu
B 84 amu
C 144 amu
D 228 amu

Answers

I think its 60. I think you would subtract 144-84 to get the mass of the vinegar molecule.

Answer:

m = 60 amu

Explanation:

As we know that total mass is always conserved

So here we know that compound is of mass 84 amu initially

after reaction with vinegar molecule the total mass is given as

[tex]M_{total} = M + m[/tex]

here we know that

[tex]M = 84 amu[/tex]

so we will have

[tex]M_{total} = 144 amu[/tex]

so we have

[tex]144 = 84 + m[/tex]

[tex]m = 60 amu[/tex]

What’s the kinetic energy of the roller coaster at the top and bottom of the hill? Use . A kiddie roller coaster car has a mass 100 kilograms. At the top of a hill, it’s moving at a speed of 3 meters/second. After reaching the bottom of the hill, its speed doubles. The car’s kinetic energy at the bottom is its kinetic energy at the top. The car has joules of kinetic energy at the bottom of the hill.

Answers

The kinetic energy of the roller coaster at the bottom of the hill is 1800 joules, which is indeed twice the kinetic energy at the top of the hill (450 joules). This confirms the statement that the car has joules of kinetic energy at the bottom of the hill, which is twice its kinetic energy at the top.

The kinetic energy of the roller coaster at the bottom of the hill is twice its kinetic energy at the top of the hill.

To find the kinetic energy (KE) of the roller coaster, we use the formula:

[tex]\[ KE = \frac{1}{2}mv^2 \][/tex]

where [tex]\( m \)[/tex] is the mass of the object and [tex]\( v \)[/tex] is its velocity.

Given that the mass [tex]\( m \)[/tex] of the roller coaster car is 100 kilograms, and its speed [tex]\( v \)[/tex] at the top of the hill is 3 meters/second, we can calculate the kinetic energy at the top of the hill as follows:

[tex]\[ KE_{top} = \frac{1}{2} \times 100 \text{ kg} \times (3 \text{ m/s})^2 \] \[ KE_{top} = \frac{1}{2} \times 100 \text{ kg} \times 9 \text{ m}^2/\text{s}^2 \] \[ KE_{top} = 50 \text{ kg} \times 9 \text{ m}^2/\text{s}^2 \] \[ KE_{top} = 450 \text{ J} \][/tex]

Since the speed of the roller coaster car doubles at the bottom of the hill, its new speed [tex]\( v_{bottom} \)[/tex] is:

[tex]\[ v_{bottom} = 2 \times 3 \text{ m/s} = 6 \text{ m/s} \][/tex]

The kinetic energy at the bottom of the hill is:

[tex]\[ KE_{bottom} = \frac{1}{2} \times 100 \text{ kg} \times (6 \text{ m/s})^2 \] \[ KE_{bottom} = \frac{1}{2} \times 100 \text{ kg} \times 36 \text{ m}^2/\text{s}^2 \] \[ KE_{bottom} = 50 \text{ kg} \times 36 \text{ m}^2/\text{s}^2 \] \[ KE_{bottom} = 1800 \text{ J} \][/tex]

Therefore, the kinetic energy of the roller coaster at the bottom of the hill is 1800 joules, which is indeed twice the kinetic energy at the top of the hill (450 joules). This confirms the statement that the car has joules of kinetic energy at the bottom of the hill, which is twice its kinetic energy at the top.

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