the millersburg ferry (m=13000.0 kg loaded) puts its engines in full reverse and stops in 65 seconds. if the speed before braking was 2.0 m/s, what was the braking force supplied by the propellers? solve using impulse and momentum.

Answer:

The answer you're looking for is B.

In polar view of the Milky Way, you can see the spiral arms and the dense collection of stars that make up core of the galaxy. The entire galaxy is rotating in a clockwise direction. As to classification, the Milky Way is a SBc barred spiral galaxy. And that red dot above the Orion Arm is the location of the Solar System.

Our solar system belongs to the Milky Way galaxy and the Milky Way galaxy is classified as a spiral galaxy. The correct option is B.

A galaxy is a vast, gravitationally bound system of stars, interstellar gas, dust, and dark matter. Galaxies can range in size from dwarf galaxies with just a few million stars to giant galaxies with hundreds of billions of stars.

Galaxies come in a variety of shapes and sizes, including spiral galaxies, elliptical galaxies, and irregular galaxies.

Spiral galaxies, such as our own Milky Way, have a flat, rotating disk with spiral arms and a central bulge.

Elliptical galaxies are more rounded and typically have fewer young stars and more old stars.

Irregular galaxies have irregular shapes and can be the result of interactions or mergers between galaxies.

Galaxies are the basic building blocks of the universe, and the study of galaxies and their properties is a fundamental part of astronomy and astrophysics. By studying the properties of galaxies, scientists can learn about the structure and evolution of the universe, as well as the nature of dark matter and dark energy.

Here in the question,

The Milky Way galaxy is a large, barred spiral galaxy that is estimated to contain between 100 and 400 billion stars, as well as a variety of other celestial objects. It is estimated to have a diameter of around 100,000 light-years and a thickness of around 1,000 light-years.

The Milky Way galaxy contains a number of distinct components, including a central bulge, a disk of gas and dust where most of the star formation occurs, and a halo that surrounds the galaxy and contains old stars and globular clusters. The galaxy also contains a number of smaller satellite galaxies, including the Large and Small Magellanic Clouds.

In addition to stars, the Milky Way contains a variety of other celestial objects, including planets, asteroids, comets, and interstellar gas and dust. It is also believed to contain a significant amount of dark matter, which is thought to make up approximately 85% of the total mass of the galaxy.

Therefore, The Milky Way galaxy is classified as a spiral galaxy.

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Explanation:

6. Force = mass × acceleration

F = m Δv / Δt

F = (0.155 kg) (50.0 m/s − (-44.0 m/s)) / (0.00450 s)

F = 3240 N

7. Force = mass × acceleration

F = m Δv / Δt

75 N = (180 kg) (2.0 m/s − 0 m/s) / Δt

Δt = 4.8 s

To find how long it takes for a basketball to roll down a 3.5m incline at an angle of 80.6°, calculate the component of gravitational acceleration along the incline and use the kinematic equation for motion. The basketball takes approximately 0.85 seconds to roll down the incline.

The question deals with the motion of a basketball rolling down an incline. The key to solving this problem is to use the concepts of rotational motion together with Newton's laws of motion. Given the incline angle is 80.6° to the horizontal and the acceleration due to gravity is 9.81 m/s2, we can determine the component of gravitational acceleration that acts along the slope. This component is g sin(θ), with θ representing the angle, which causes the acceleration of the ball down the slope.

Since the basketball is a spherical shell it has a moment of inertia I = 2/3 m r2, where m is the mass and r is the radius of the sphere. However, without the mass of the basketball, we'll approach this by determining the translational acceleration a = g sin(θ), using the formula for the acceleration of an object down an incline. Knowing the distance (s = 3.5 m) it rolls without slipping, and starting from rest, we can use the kinematic equation s = 1/2 a t2 to solve for t, the time taken.

Calculating the acceleration component: a = 9.81 * sin(80.6°) = 9.67 m/s2. Then, we use the equation 3.5 = 1/2 * 9.67 * t2 to find t. Solving for t yields approximately 0.85 seconds.

Using rotational and translational motion principles, the basketball takes approximately 0.85 seconds to roll without slipping down the 80.6-degree incline.

To determine the time it takes for the basketball to roll without slipping down the incline, consider both rotational and translational motion.

Step 1: Calculate the effective radius of the basketball on the incline:

R_eff = (D/2) * sin(theta), given the diameter D of the basketball (47 cm) and the incline angle (theta) of 80.6 degrees.

Step 2: Calculate the linear acceleration down the incline:

a = g * sin(theta), given the acceleration due to gravity (g) as 9.81 m/s².

Step 3: Use the kinematic equation for linear motion to find the time (t):

t = sqrt(2h/a), given the height (h) the basketball descends down the incline is 3.5 m.

Step 4: Substitute the values into the equation and solve for t:

R_eff = (0.47/2) * sin(80.6 degrees) ≈ 0.235 m,

a = 9.81 * sin(80.6 degrees) ≈ 9.7 m/s²,

t = sqrt(2 * 3.5 / 9.7) ≈ sqrt(7 / 9.7) ≈ sqrt(0.7216) ≈ 0.85 s.

So, it will take approximately 0.85 seconds for the basketball to roll without slipping down the incline.

The 1st example is NOT a longitudinal wave

Explanation:

Waves are periodic disturbance of the space that travel carrying energy but not matter.

Depending on their vibration, waves are classified into two types:

In  this problem we have four options given:

Therefore, the only wave which is not longitudinal is the one in the 1st picture.

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Longitudinal waves are those where the displacement of the medium is along the direction of the wave's propagation, such as sound waves. An example that does not fit into this category is light waves, which are transverse waves, having their oscillations perpendicular to the direction of the wave's movement.

Longitudinal waves are waves in which the displacement of the medium is in the same direction, or opposite direction, to the direction of propagation of the wave. Examples are sound waves and seismic P-waves. However, an example of a wave that is not longitudinal would be light waves.

Light waves are transverse waves. This means that their oscillations are perpendicular to the direction of energy transfer. Unlike longitudinal waves, which contain compressions and rarefactions, transverse waves have peaks and troughs.

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Answer:

54 g

Explanation:

Mass is conserved.  Mass of reactants = mass of products.

24 g + 96 g = 66 g + x

x = 54 g

The testing perspective centers on measuring intelligence with tests, specifically analytical intelligence when examining data trends. Creative is not one of Gardner's Multiple Intelligences, and IQ tests' validity is contested due to potential bias.

The correct answer to the student's question is the testing perspective, which focuses on measuring the amount of intelligence a person has by using intelligence tests.

When examining data for trends, the type of intelligence primarily used is analytical intelligence. Analytical intelligence is the ability to analyze, evaluate, judge, or compare and contrast information.

Among Gardner's Multiple Intelligences, creative is not one of the identified categories; instead, Gardner's intelligences include modalities such as spatial, linguistic, and musical intelligences.

Intelligence can be a broad concept and varies from person to person. Practical intelligence, or street smarts, is related to real-world problem-solving and can be distinct from what traditional IQ tests measure. The IQ test attempts to measure intelligence but has been subject to debate regarding its validity and the scope of abilities it assesses.

Conflict theorists argue that IQ tests may be biased because they may not give children with learning disabilities a fair chance to demonstrate their true intelligence, thereby limiting the understanding of each individual's unique capabilities.

Final answer:

The testing perspective focuses on measuring intelligence with intelligence tests, specifically referred to as the 'testing' perspective. This falls under the study of cognitive psychology, which examines human thinking and the various aspects of intelligence, including analytical ability and the debate over the validity of IQ tests.  So the correct option is C.

Explanation:

The testing perspective focuses on measuring the amount of intelligence a person has by using intelligence tests. The correct answer is C. Testing. This relates to the domain of psychology where the quantification of human intelligence is often conducted through various assessments that aim to gauge different abilities in the areas of problem-solving, reasoning, memory, and other cognitive functions.

When it comes to examining data to identify trends, the type of intelligence predominantly used is analytical intelligence. Analytical intelligence refers to the ability to analyze, evaluate, judge, compare, and contrast information. In Howard Gardner's Multiple Intelligences theory, creative intelligence, while important for some types of problem-solving and innovation, is not listed as one of Gardner’s Multiple Intelligences. His theory includes types of intelligence such as spatial, linguistic, and musical, among others.

Cognitive psychology is the branch that focuses on human thinking. Questions around what intelligence is, how it varies from person to person, and whether or not 'street smarts' are a kind of intelligence, all fall under the study of cognitive psychology. Intelligence Quotient (IQ) tests aim to measure intellectual capabilities, but their validity and the extent to which they truly capture an individual's varied intelligence is a topic of ongoing debate.

We're adding two vectors here.  The first is 300 Newtons to the right, which we can write as (300, 0), meaning 300 to the right, 0 up.

The second is 300 at let's say a 45 degree angle down.  For the components we have an isosceles right triangle with hypotenuse 300, so the components are both magnitude 300/√2 = 150√2.  So we can write this vector (150√2, -150√2), the negative sign because it points down in the y direction.

Adding is componentwise.  The resulting force is (300+150√2, -150√2).

That has square magnitude

r² = (300+150√2)² + (-150√2)² = 150² ( (2+√2)² + (√2)² )

= 150²( (6 + 4√2) + 2)

= 300²(2+√2)

so

r = 300 √(2+√2) Newtons

That's the answer; I'm not sure if your class expects a calculator approximation, which is 554.3 Newtons.

For energy producing reactions they need Hydrogen atoms, heat, and pressure for the experiments.

Explanation:

The initial step of the Hydrogen combination process: a core of Deuterium (2H) is shaped from two protons with the discharge of an antielectron and a neutrino. In the fundamental Hydrogen combination cycle, four Hydrogen cores (protons) meet up to make a Helium core.

An atomic combination response is characterized as the response wherein at least two lighter cores consolidate together to shape heavier cores with the arrival of high measures of vitality.

Combination can possibly give the sort of baseload vitality expected to give power to our urban communities and our enterprises. Maintainability: Fusion powers are generally accessible and almost limitless.

The braking distance is given by [tex]s=\frac{-u^2}{2a}[/tex]

Explanation:

When the driver of a car hits the pedal of the brakes, the car starts decelerating until it stops. Assuming the deceleration is constant, then the motion is a uniformly accelerated motion, so we can use the following suvat equation:

[tex]v^2-u^2=2as[/tex]

where

u is the initial speed of the car

v is the final speed of the car, which is zero because the car comes to rest:

v = 0

a is the acceleration of the car

s is the distance travelled by the car during the deceleration, so it is the braking distance

Therefore, re-arranging the equation for s, we find an expression for the braking distance:

[tex]s=\frac{-u^2}{2a}[/tex]

Note that the sign of [tex]a[/tex] is negative since the car is decelerating, therefore the final sign of [tex]s[/tex] is positive.

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The correct answer is; False.

Further Explanation:

Ash does not remain in the atmosphere for years after an eruption. It only takes a few days or at the most a few weeks for all of the ash to leave the atmosphere. It has little impact on the climate or global temperatures.

When a volcano erupts there are three things that the volcano puts out, they are;

The one thing that does have an effect on the global temperatures of an eruption is the volcanic aerosols. These aerosols, when released, reflect the solar radiation back to space.

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The momentum of the coupled cars is 0.16 kg m/s

Explanation:

We can solve this problem by using the law of conservation of momentum: in absence of external forces, the total momentum of the two cars must be conserved before and after they couple together.

Mathematically, this can be written as

[tex]p_i = p_f\\m_1 u_1 + m_2 u_2 = p_f[/tex]  

where:  

[tex]m_1 = m_2 = 0.04 kg[/tex] is the mass of the two cars

[tex]u_1 =4 m/s[/tex] is the initial velocity of the first car

[tex]u_2=0[/tex] is the initial velocity of the second car, which is at rest

[tex]p_f[/tex] ithe momentum of the coupled cars, after the collision

By re-arranging the equation and substituting the values that we have, we find the final momentum:

[tex]p_f = m_1 u_1 + m_2 u_2 = (0.04)(4)+0=0.16 kg m/s[/tex]

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The momentum of the coupled toy cars after the collision is 0.16 kg·m/s.

In this problem, we are dealing with the conservation of momentum.

To find the momentum of the coupled cars, we first need to calculate the initial momentum of the moving car and then use the conservation of momentum principle to find the final momentum of the system.

Initial momentum of the moving car:

where

    p = 0.04 kg * 4 m/s

    p = 0.16 kg·m/s
Since the car is stationary, its initial momentum is 0 kg·m/s.

Add the momentum of both cars:

After collision, the cars couple together and move as a single object with a combined mass

Using the conservation of momentum principle, the total momentum before and after the collision remains the same. Thus:

The momentum of the coupled cars after the collision is 0.16 kg·m/s.

Answer:

8.85m/s

Explanation:

v=√2gh

v=√2×9.8×4

v=8.85m/s

The watermelon be moving as it strikes the ground below  8.85m/s.

The formula that is used to find the velocity in this case is:  

[tex]v=\sqrt{2gh} \\\\v=\sqrt{2*9.8*4}\\\\v=8.85m/s[/tex]

Thus, the velocity will be 8.85 m/s.

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Using the equation v = u + at, the final velocity of the police car after maintaining an acceleration of 5 m/s^2 for 30 seconds is found to be 200 meters per second.

To determine the final velocity of a police car that accelerates from a given speed, we can use the formula for final velocity, which is derived from the equations of motion under constant acceleration. The formula we will use is v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

In this case, the initial velocity u is 50 meters per second, the acceleration a is 5 m/s2, and the time t is 30 seconds. Plugging these values into the formula:

v = 50 m/s + (5 m/s2 × 30 s)

Calculating this, we get:

v = 50 m/s + 150 m/s = 200 m/s

Therefore, the final velocity of the police car after maintaining the acceleration for 30 seconds will be 200 meters per second.

Answer:

OK...   lets go the mathematical terms of magic is science and that the world is round ,GOD created everything Jesus died for us on the cross ,the big bang theory is something  scientist believe if you are a christian then you know that is a lie and if you are a REDNECK then fishing and hunting is life and REDNECK think city people SUCK BUTT that is life.

Explanation:

Quantum units in physics generally end with the suffix "on" because they are named after famous scientists who made significant contributions to the field.

In quantum mechanics, many units end with the suffix "on" because they are named after famous scientists who made significant contributions to the field. For example, the unit "electron" is named after J.J. Thomson, the physicist who discovered the electron. Similarly, the unit "photon" is named after Albert Einstein, who proposed the concept of light particles.

By using these named units, scientists can refer to specific quantities and entities in a concise and standardized manner. It helps in clear communication and facilitates research in the field of quantum mechanics.

Some examples of units in quantum mechanics that end with "on" include electron, photon, neutron, positron, and graviton.

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Answer:

Answer: Both move with constant speed.

Explanation:

Constant Speed Motion

When an object moves in such a way that it travels the same distances at the same times, we can say its speed is constant. For example, if it travels x=10 m in t=2 seconds and later it travels x=20 m in t=4 seconds, its speed is constant and equal to v=5 m/s. The relation between the variables x,t, and v is

x=v.t

Note that the relation between x and t is v, a constant value, thus the graph x-t is a line.

The question describes two graphs, for Object A and Object B respectively, and both of the descriptions correspond to lines. We don't have much information about the characteristics of the lines, but we can be sure, according to the definitions stated above, that both objects are traveling at a constant speed.

Answer: Both move with constant speed.

Answer:

C

Explanation:

Yes it is C

Answer:

In contrast, wind turbines produce no greenhouse gases when generating electricity. We should note that both noise and visual pollution are environmental disadvantages of wind turbines. However, these factors don't have a negative impact on the earth, water table or the quality of the air we breathe.

The shortest wavelength of visible light = violet light

Energy that can be felt as heat but not seen = infrared

Short, invisible rays that can cause eye damage = ultraviolet

Visible light with the longest wavelength = red light

Explanation:

Electromagnetic waves are waves consisting of oscillations of the electric and the magnetic field, occurring in a plane perpendicular to the direction of motion the wave.

They are the only type of waves able to travel without a medium, and they are transverse in nature.

All electromagnetic waves travel in a vacuum at the speed of light, which value is:

[tex]c=3.0\cdot 10^8 m/s[/tex]

Electromagnetic waves are classified into 7 different classes, depending on their wavelength/frequency, and they have different properties. From shortest to longest wavelength (and from highest to lowest frequency), they are:

Gamma rays

X rays

Ultraviolet

Visible light

Infrared radiation

Microwaves

Radio waves

Moreover, the visible light of the spectrum is further divided into different colors, according to how our eye perceive them; from shortest to longest wavelength:

violet

blue

green

yellow

orange

red

Therefore, we have:

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The types of energy described are associated with specific wavelengths and frequencies in the electromagnetic spectrum, where violet is the shortest visible wavelength, infrared is felt as heat, ultraviolet rays can cause eye damage, and red has the longest visible wavelength.

The question pertains to the electromagnetic spectrum and types of energy associated with different wavelengths and frequencies of light.

These energy types represent various parts of the electromagnetic spectrum, with red light having the longest wavelength and least energy, and violet having the shortest wavelength and most energy. Infrared is typically experienced as heat, while ultraviolet rays, shorter still than violet, carry enough energy to potentially cause harm to biological tissues, like eye damage.

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Carpet tends to produce differences in static electricity more than that of hardwood or tile floors because there's a release of negative charges which are called electrons to the person's body.

In such a case, when an individual shuffle their feet across a carpet, there will be a transfer of electrons unto the person and this then brings a static charge on the skin of the person.

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Answer:

-40,000 N

Explanation:

First, use the kinematics equation v(f) = v(i) + at.  Final velocity is 0, initial is 8, and time is 0.2 seconds.  Solving for a, you get -40 m/s^2.  Then, use Newton’s second law, F=ma, to find the force.  F = (1000)(-40) = -40,000 N.

Final answer:

The force exerted on a car with a mass of 1,000 kg, which is brought to rest from an initial velocity of 8 m/s over a time span of 0.2 s, is calculated to be 40,000 N in the direction opposite to the car's initial motion.

Explanation:

To calculate the force exerted on a 1,000 kg car that is brought to rest from an initial velocity of 8 m/s over a time span of 0.2 s, we can apply the concept of impulse and momentum. The impulse exerted on the car can be found using the formula:

Impulse = Change in Momentum = Force × Time

The change in momentum is equal to the final momentum minus the initial momentum. Since the car is brought to rest, its final momentum is 0, and the initial momentum is the product of the mass and the initial velocity. Therefore, we have:

Change in Momentum = 0 - (Mass × Initial Velocity)

Change in Momentum = 0 - (1,000 kg × 8 m/s)

Change in Momentum = -8,000 kg·m/s

The impulse exerted on the car is also the product of the force exerted and the time interval:

Force × Time = Change in Momentum

Force × 0.2 s = -8,000 kg·m/s

Force = -8,000 kg·m/s / 0.2 s

Force = -40,000 N

The negative sign indicates that the force is acting in the opposite direction of the car's initial motion. Therefore, the force exerted on the car is 40,000 N in the direction opposite to the car's initial motion.

Answer:

An Anvil?

Explanation:

I cant answer the question properly mate, ill edit this answer to the correct one if you add details

Answer:

7.75m/s or [tex]2\sqrt{15}m/s[/tex]

Explanation:

m = 1.5kg

u= 10m/s

s = 2m

a = [tex]10m/s^{2}[/tex]

v = ?

acceleration due to gravity is negative when an object is going up because the force of gravity reduces the speed of the object

using the formula ;

[tex]v^{2} = u^{2} - 2as[/tex] since the object is moving upwards (negative acceleration)

= 100 - 2(10)(2)

100 - 40

[tex]v^{2}[/tex] = 60

v = [tex]\sqrt{60}[/tex]

= 7.75m/s

Velocity is a vector quantity. The value of the final velocity for the given ball is 7.75 m/s.

[tex]v^2= u^2 +2as[/tex]

Where,

[tex]v[/tex] - final velocity

[tex]u[/tex]- initial  velocity = 10m/s

[tex]a[/tex] - acceleration = [tex]10 \rm \ m/s^2[/tex]

[tex]s[/tex] - speed =2 cm

Put the values in the equation,

[tex]v^2 = 100 - 2(10)(2)\\\\v = \sqrt {100-40}\\\\v = 7.75\rm \ m/s[/tex]

Therefore, the value of the final velocity for the given ball is 7.75 m/s.

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Case d) has the strongest gravitational force

Explanation:

The magnitude of the gravitational force between two objects is given by the equation:

[tex]F=G\frac{m_1 m_2}{r^2}[/tex]

where :

[tex]G=6.67\cdot 10^{-11} m^3 kg^{-1}s^{-2}[/tex] is the gravitational constant

m1, m2 are the masses of the two objects

r is the separation between the objects

a) For this pair of objects:

m1 = 10 kg

m2 = 2 kg

r = 30 km = 30,000 m

So the gravitational force is

[tex]F=(6.67\cdot 10^{-11})\frac{(10)(2)}{30000^2}=1.48\cdot 10^{-18}N[/tex]

b) For this pair of objects:

m1 = 10 kg

m2 = 10 kg

r = 30 km = 30,000 m

So the gravitational force is

[tex]F=(6.67\cdot 10^{-11})\frac{(10)(10)}{30000^2}=7.41\cdot 10^{-18}N[/tex]

c) For this pair of objects:

m1 = 2 kg

m2 = 2 kg

r = 10 km = 10,000 m

So the gravitational force is

[tex]F=(6.67\cdot 10^{-11})\frac{(2)(2)}{10000^2}=1.33\cdot 10^{-17}N[/tex]

d) For this pair of objects:

m1 = 10 kg

m2 = 10 kg

r = 10 km = 10,000 m

So the gravitational force is

[tex]F=(6.67\cdot 10^{-11})\frac{(10)(10)}{10000^2}=6.67\cdot 10^{-17}N[/tex]

Therefore, the  strongest gravitational force is in case d).

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Explanation:

Newton's first law of motion states: "an object in motion stays in motion, and an object at rest stays at rest, until acted upon by an unbalanced force."

When you're riding in a vehicle, your body is moving forward.  When the vehicle slows or turns, your body's inertia continues to move you forward.  The seatbelt is the unbalanced force that pushes you back into your seat.  Without it, you would slide off your seat.

Since there is a tendency for motion to continue in accordance to Newtons laws, a passenger that is not wearing a seat belt may be pushed out of the windscreen.

According to Newtons laws of motion, a  body will continue in its state of rest or uniform motion unless it is acted upon by an external, unbalanced force.  This means that force is the reason why motion starts or uniform motion is changed.

If a car is suddenly applies its brakes, the uniform motion of the car is disturbed and there is a tendency for the motion to continue according to Newtons first law hence the passengers moves forward. This is the reason why wearing a seat belt is important. The seat belt protects the passengers from being pushed out of the windscreen.

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CHARLES'S LAW

At a constant pressure, the volume of a given amount of gas is directly proportional to its absolute temperature.

Answer:

Directly propotional

Explanation:

Charles law states that volume of a fixed mass of a given is directly propotional to its absolute temperature

And

V∞ T

Answer: The speed of the beach ball would be 2.0 m/s

Explanation:

Answer:

2.0 m/s

Explanation:

Explanation:

Wave

It is the periodic disturbance in a medium.

Types of Wave

There are two types of wave in general depending upon their propagation through a substance.

• Mechanical  

• Electromagnetic  

Mechanical Wave

It is the kind of wave which needs medium to travel. For example: Sound Wave  

That means sound can be heard only whenever there is presence of certain substance like water, glass, air etc .It can’t be heard in vacuum no matter how loud is the sound.

Electromagnetic Wave

Is that which can travel through medium as well as through vacuum. For example: Light  

But unlike sound, light can be seen through a substance or in vacuum. That is the reason it is referred as electromagnetic wave.

Answer:

An eraser top.

Explanation:

it is small enough to fit into that category

Answer: mechanical pencils

Explanation:

The final speed of the rock is 19.8 m/s

Explanation:

We can solve this problem by using the law of conservation of energy: the total mechanical energy of the rock (the sum of potential energy + kinetic energy) must be conserved during the fall. Therefore we can write:

[tex]U_i +K_i = U_f + K_f[/tex]

where :

[tex]U_i[/tex] is the initial potential energy, at the top

[tex]K_i[/tex] is the initial kinetic energy, at the top

[tex]U_f[/tex] is the final potential energy, at the bottom

[tex]K_f[/tex] is the final kinetic energy, at the bottom

We can rewrite the equation as:

[tex]mgh_i + \frac{1}{2}mu^2 = mgh_f + \frac{1}{2}mv^2[/tex]

where:

m = 5 kg is the mass of the rock

[tex]g=9.8 m/s^2[/tex] is the acceleration of gravity

[tex]h_i = 20 m[/tex] is the initial height  of the rock

u = 0 is the initial speed

[tex]h_f = 0[/tex] since the rock falls to the ground

v is the final speed

And solving for v, we find the final speed:

[tex]v=\sqrt{2gh_i}=\sqrt{2(9.8)(20)}=19.8 m/s[/tex]

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