The center of mass of a pitched baseball of radius 4.66 cm moves at 38.7 m/s. The ball spins about an axis through its center of mass with an angular speed of 62.9 rad/s. Treat the baseball as if it is a solid sphere rotating about its center (I = [tex]\frac{2}{5}[/tex]MR²).
Calculate the ratio of the rotational energy to the translational kinetic energy.

Answers

Answer 1

The ratio of rotational energy to the translational kinetic energy is 1:435.

What is the  rotational energy of the ball?

The rotational energy of the ball is calculated as follows;

E = ¹/₂Iω²

where;

I is the moment of inertia of the ballω is the angular speed of the ball

I = ²/₅MR²

I = ²/₅ x (0.0466)²(M)

I = 8.69 x 10⁻⁴ M

E =  ¹/₂Iω²

E =  ¹/₂(8.69 x 10⁻⁴ M)(62.9)²

E = 1.72 M

The translational kinetic energy of the ball is calculated as follows;

E = ¹/₂Mv²

E = ¹/₂ (38.7)²M

E = 748.85 M

Ratio of rotational energy to the translational kinetic energy is calculated as;

R = ( 1.72 M ) / ( 748.85 )

R = 1 : 435

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Related Questions

Gretchen runs the first 4. 0 km of a race at 5. 0 m/s. Then a stiff wind comes up, so she runs the last 1. 0 km at only 4. 0 m/s.

Answers

Answer: Answer: The constant speed is 4.76 m/s

What is Velocity ?

-- Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time.

- It is vector quantity.

-- SI unit is M/s.

Determination of the time taken for first 4 Km

Distance = 4 Km = 4 × 1000 = 4000 m

Speed = 5 m/s

Time 1 =?

Time 1 = distance / speed

Time 1 = 4000 / 5

Time 1 = 800 s

Determination of the time taken for the last 1 Km

Distance = 1 Km = 1 × 1000 = 1000 m

Speed = 4 m/s

Time 2 =?

Time 2 = distance / speed

Time 2 = 1000 / 4

Time 2 = 250 s

Determination of the constant speed

Total distance = 4000 + 1000 = 5000 m

Total time = 800 + 250 = 1050 s

Constant speed =?

Constant speed = Total distance / total time

Constant speed = 5000 / 1050

Constant speed = 4.76 m/s

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What is the expression for momentum Mcq?.

Answers

p = m v . The equation demonstrates because momentum is directly related to an object's motion (m) and velocity (v).

In the actual world, what is momentum?

Almost every action that involves motion has momentum. It is an important tenet of physics. In athletics, the term "momentum" is frequently used. For instance, if a team is moving forward and trying to stop, it will be difficult.

How do you define momentum?

singular nouns Momenta, plural for momentums. force or rate of motion; impulse, as of a tangible thing or sequence of events: Going downward, the automobile picked up speed.

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A lever with an effort arm of 10 meters and a load arm of 2 meters is used to lift an object weighing 220 newtons to a height of 4 meters. if 400 joules of work is done, how much force must have been applied?

Answers

If 400 joules of work is done, 100 newtons force much have been applied.

In order to calculate the force required to lift an object weighing 220 newtons to a height of 4 meters with a lever having an effort arm of 10 meters and a load arm of 2 meters, we must first determine the amount of work done.

Since 400 joules of work was done, we can use the formula Work = Force x Distance to calculate the force required.

In this case, the distance is 4 meters, so the equation becomes

400 = Force x 4.

By dividing 400 by 4 we can determine that the force required is 100 newtons.

Therefore, in order to lift the object weighing 220 newtons to a height of 4 meters with a lever having an effort arm of 10 meters and a load arm of 2 meters, 100 newtons of force must have been applied.

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When the value of g at the surface of the earth is 9. 8 m/s2 then what will be the value of g at a place 480 km above the surface of the earth radius of the earth 6400 km?.

Answers

The value of g at a place 480 km above the surface of the earth will be 8.49 m/s². If the value of g at the surface of the earth is 9.8 m/s².

Acceleration due to gravity of the earth is mathematically defined as

g = GM/R²......(1)

Where G is the universal gravitational constant, M is the mass of the earth, and R is the radius of the earth or the distance of the object on which the acceleration due to gravity of the earth is to calculate.

R = 6400 km

h = 480 km

g₁ =  GM/(R+h)²......(2)

On dividing the equation (2) by equation (1)

g₁/g = R²/(R+h)²

g₁ = gR²/(R+h)²

g₁ = 9.81 × (6400)²/(6400+480)²

g₁ = 8.49 m/s²

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What happens to the value of potential energy and kinetic energy as the coaster is moving throughout the entire coaster ride do not consider air resistance or friction?.

Answers

As the roller coaster is moving throughout the whole coaster ride ignoring air resistance or friction, then the value of potential energy is highest at the top point and the value of kinetic energy is maximum at the bottom point.

Air resistance can affect a roller coaster as it is in the air, and it provides a force that is countering the movement of the roller coaster.  However, with no air resistance,  the roller coaster has a maximum quantity of potential energy and no kinetic energy at the top. As the roller coaster begins moving down to the bottom, its gravitational potential energy starts decreasing and the kinetic energy starts increasing. And at the bottom, kinetic energy is highest while there is no potential energy.

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What is the condition for two vectors A and B to be parallel?.

Answers

Two vectors A and B are parallel if they have the same direction, opposite direction, or are proportional.

The vectors have the same direction: If vector A and vector B point in the same direction, they are parallel. This means that the angle between the two vectors is 0 degrees.

The vectors are of opposite directions: If vector A and vector B point in opposite directions, they are also parallel. This indicates that there is a 180° angle between the two vectors.

The vectors are proportional: if two vectors are parallel, the ratio of their magnitudes is a constant, which means that A = k B, where k is a constant.

It's important to note that vectors can also be anti-parallel, which means they are pointing in opposite directions, but they are not parallel as they are not in the same direction.

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What do you predict the 3 main sources of electrical energy generation to be 40 years from now? Why?

Answers

Three main sources of electrical energy generation 40 years from now would predictably be:

Renewable energy Nuclear energy Natural gas

Which electrical energy sources might be around in 40 years ?

Renewable energy which includes sources such as solar, wind, geothermal, and hydroelectric power, which are considered to be sustainable and have low environmental impact. As concerns about climate change and the need to reduce carbon emissions continue to grow, it is likely that renewable energy sources will play an increasingly important role in meeting energy needs.

Nuclear power plants are a reliable and low-carbon source of energy, but have a lot of concerns regarding safety, waste and proliferation. Natural gas is considered a transition fuel, as it emits less carbon dioxide than coal, but more than renewable energy sources.

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What is F Gm1m2 d2?.

Answers

The gravitational force which try pulls two objects with masses m1 and m2 apart over a certain distance is represented by the equation F = G[tex]m_{1} *m_{2}[/tex]/d^2. G, which represents the universal gravitational constant.

The product of each object's individual mass determines the gravitational force between them. The square of one object's mass determines how much gravity will pull on the other. If their mass is raised by a factor of two, the gravitational force between the two objects is quadrupled.

The formula F = G[tex]m_{1} *m_{2}[/tex]/d^2 describes the dimensions of G as the gravitational force that pulls two objects with point masses of m1 and m2 toward one another, and r represents the distance between them.

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How much is 1 mole exactly?.

Answers

The mole, often known as mol, is a SI unit that counts the particles in a given substance. 6.0221*10^23 atoms, or other fundamental building blocks like molecules, make up one mole.

A substance's mole is equivalent to 6.022 x 10^23 of that material (such as atoms, molecules, or ions). The term "Avogadro's number" or "Avogadro's constant" refers to the number 6.0221*10^23. To convert between mass and the quantity of particles, use the mole concept.

The ratio between the atomic mass unit and gram mass unit sizes affects the number in a mole, or Avogadro's number. One mole of hydrogen atoms weighs about one gram, compared to the mass of one hydrogen atom, which is roughly one unit.

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what is the wavelength of a beam of light having a frequency of 6 × 10^17 hz?

Answers

The wavelength of the of a beam of light having a frequency of 6 × 10^17 hz is 5*10^(-8)m or 50nm.

Data given as per the question:

Frequency of the wavelength: 6 × 10^17 hz

As we know that,

Speed of light = Frequency × wavelength

Speed of light (c)=3×[tex]10^{8}[/tex] m/s.

Frequency (f)=6×10[tex]10^{14}[/tex] Hz (given)

Wavelength (λ)=?

As per the formula,

λ= [tex]\frac{c}{f}[/tex]

= 5*10^(-8)m or 50nm

The wavelength of light can be defined as the distance between the two successive crests or troughs of the light wave. It is actually denoted by the Greek letter lambda (λ). Hence, the distance between either one crest or trough of one wave and the next wave is known as wavelength.

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A crane is used to lift a steel beam on a building site. The crane does 250 kJ of work against gravity
in order to lift the steel beam a vertical distance of 20 m. Calculate the weight of the steel beam.

Answers

The weight of the steel beam is 126.53 kg

What is gravity?

Gravity is a force that attracts two objects with mass towards each other. The strength of the gravitational force between two objects depends on their masses and the distance between them.

The force of gravity is described by Newton's law of universal gravitation, which states that the force between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them.

We can use the equation

W = mgh to find the weight of the steel beam where W is workM is mass G is acceleration due to gravity H is height.

W = mgh

m = W / (g * h) = 250 kJ / (9.8 m/s^2 * 20 m) = 126.53 kg

Therefore, The weight of the steel beam is 126.53 kg.

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A ball falls from a tall bridge. The ball has a mass of 0.15 kg. The air density is 1.225 kg/m³. The ball's surface area is
0.0026 m². The ball's coefficient of drag is 0.007. What is the ball's terminal velocity? (1 point)
O 164 m/s
O 30.4 m/s
O 402 m/s
O 363 m/s

Answers

Answer:

Gravity and Air Resistance Quick Check

Explanation:

1)It stops accelerating.

2)The greater the object’s surface area, the more air resistance it encounters.

3)Vt=2w/dACd

4)363 m/s

5)a typical meteorite’s weight, surface area, and coefficient of drag; air density close to Earth

This is for gaca people other people might not have this so relook at it to make sure or u will get a low grade

who discovered cosmic microwave background radiation?

Answers

Answer: Robert Wilson and Arno Penzias

Explanation:

What do sound energy and thermal energy have in common?

Answers

Answer: Answer below :)

Explanation:

What do sound energy, radiant energy, and thermal energy all have in common? answer choices They're all forms of kinetic energy

the stem of a meat thermometer shall be constructed of

Answers

The stem of meat thermometer shall be constructed of stainless steel.

What kind of meat thermometer is ideal?

An instant-read thermometer is a more popular type that you can quickly use to determine whether food is done by inserting it into it for a short period of time. A probe thermometer is another kind; it is made to stay inside the meat throughout cooking.

Still, it can get as cold as -58 to as hot as 572 degrees Fahrenheit. We used this thermometer to check the temperature of our meats, and we discovered that it was just as accurate—if not more—and quicker. Even though the price is higher, the product's high quality and prolonged battery life make it worthwhile.

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A change in the magnetic field surrounding the conductor induces a voltage in the conductor. this induced voltage is known as ___.

Answers

A change in the magnetic field surrounding a conductor induces a voltage in the conductor. This induced voltage is called self-induction.

A changing magnetic field induces an additional emf or voltage in a conductor. This induction of additional voltage is called self-induction because it is induced in the conductor itself. A coil of wire induces a current when it is placed in a changing magnetic field. Something creates an electric field around the wire, forcing a charge around it. (Early charges cannot become magnetic because they are not moving).  Electromagnetic induction is the process by which an electric current is induced by a changing magnetic field.

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How to find total distance traveled from position function?

Answers

Total distance traveled from position function is found by:

Differentiating the position function to get velocity function.Integrating the velocity function under proper limits.

Example : Find the total distance traveled for a particle traveling in a horizontal motion from t = 0 to t = 5 seconds according to the position function:

                                          s(t) = 8t^2 – 4t.

Step 1: Find the velocity function. The velocity function is the derivative of the position function. So, to find the velocity function you need to differentiate s(t) = 4t^2 – 2t, using the power rule and derivative of a constant rule:

                                                v(t) = 16t – 4

Step 2: Set the velocity function to zero, then solve, to find where the velocity function changes direction:

v(t) = 16t – 4 = 0

16t – 4 (+ 4) = 0 (+ 4)

16t(/16) = 4 (/16)

t = 4/16 = 1/4

Step 3: Solve the position function for the starting and ending interval values (which are 0 and 5, according to the question), and any t-values you found in step 2:

s(0) = 8(0)^2 – 4(0) = 0.

s(1/4) = 8(¼)^2 – 4(1/4) = -½

s(5) = 8(5)^2 – 4(5) = 180.

Step 4: Find the distance traveled between each point. These are vectors, so we have to use absolute values to find the distance:

Between 0 and -½, distance = |-½ – 0| = ½ & Between -½ and 180, distance = |180 – (-½)| = 180½

Step 5: Add your values from Step 4 together to find the total distance traveled.

                                            ½ + 180 ½ = 181

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What is K in a vector?.

Answers

A plane wave's wave vector, also known as the k vector, is a vector that, at least in the case of isotropic optical material, points in the wave's direction of propagation. It always faces away from the wavefronts.

The x, y, and z-axes' respective vectors are three significant unit vectors that are frequently employed. The unit vectors in the x, y, and z axes are I j, and k respectively.

The unit vector in the x axis' direction is the unit vector. Three perpendicular axes will serve as the vector v's markers in the three-dimensional plane (x, y, z-axis). In mathematics, I stands in for the unit vector along the x-axis.

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What is probability sampling Mcq?.

Answers

Probability sampling is a method of selecting a sample from a population in which each member of the population has a known, non-zero probability of being selected for the sample.

This means that every individual in the population has an equal chance of being selected for the sample. The purpose of probability sampling is to ensure that the sample is representative of the population from which it is drawn, and that the results of the study are used for generalization.

Random sampling is one of the examples. Simple random sampling, each member of the population has an equal probability of being selected for the sample. For example, if you wanted to conduct a survey of 100 people to determine their opinions on a certain topic, you could use simple random sampling to select 100 people from a list of all eligible participants. You would randomly select 100 names from the list and survey those individuals.

Another example is stratified sampling. In stratified sampling, the population is divided into subgroups, or strata, and a random sample is taken from each stratum. This can be useful if the population is heterogeneous, and you want to ensure that the sample is representative of different subgroups within the population. For example, if you wanted to survey the opinions of men and women on a certain topic, you could divide the population into two strata (men and women) and take a random sample of 50 men and 50 women.

Probability sampling is important because it allows for generalization of findings to the population, and it allows for estimation of sampling error.

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Particles q1 = -66.3 UC, q2 = +108 uC, and
93 = -43.2 uC are in a line. Particles q1 and q2 are
separated by 0.550 m and particles q2 and q3 are
separated by 0.550 m. What is the net force on
particle q2?

Answers

The sum total of all forces which are acting on an object is known as the net force. A mass can accelerate due to the net force.

What is net force?

The net force can be defined as the vector sum of all the forces which act upon an object. It is the sum of all the forces, taking into account the fact that a force is a vector and two forces of equal magnitude and opposite direction will cancel out each other.

Here, r₁₂ = 0.550m and r₂₃ = 0.550m. Then the distance from the first charge to the third one will be:

r₁₃ = r₁₂ + r₂₃ = 0.550 + 0.550 = 1.1m

According to the Coulomb's law, the net force on particle q₂ will be equal to the sum of the forces on particle q₂ from the particle q₁ and q₃.

F₃+ = F₁₃ +F₂₃ = q₁q₂/r²₁₃ + k q₃q₂/r²₂₃

Where, k = 9 × 10⁹ N m²/C²

Substituting numerical values, we obtain:

F₃ = 9 × 10⁹ (-66.3 × 10⁻⁶)(-43.2 × 9 × 10⁻⁶)/ 1.45² + 9 × 10⁹ × 108 × 10⁻⁶ (-43.2 × 10⁻⁶) / 0.550²

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Answer: -74.12

Explanation:

Credit to the comment above! this answer works for Acellus! :D

Particles q1 = -66.3 UC, q2 = +108 uC, and
93 = -43.2 uC are in a line. Particles q1 and q2 are
separated by 0.550 m and particles q2 and q3 are
separated by 0.550 m. What is the net force on
particle q2?

Answers

The sum total of all forces which are acting on an object is known as the net force. A mass can accelerate due to the net force.

What is net force?

The sum total of all the forces which are acting on an object is known as the net force. A mass that can accelerate due to net force on an object. Whether a body is at rest or in motion, it is a subject to another force. When there are a lot of forces which are acting on a system, the term net force is used to denote it.

Here, r₁₂ = 0.550m r₂₃ = 0.550m. Then the distance from the first charge to the third one will be:

r₁₃ = r₁₂ + r₂₃ = 0.550 + 0.550 = 1.1m

According to the Coulomb's law, the net force on particle q₂ will be equal to the sum of the forces on particle q₂ from the particle q₁ and q₃.

F₃+ = F₁₃ +F₂₃ = q₁q₂/r²₁₃ + k q₃q₂/r²₂₃

Where, k = 9 × 10⁹ N m²/C²

Substituting numerical values, we obtain:

F₃ = 9 × 10⁹ (-66.3 × 10⁻⁶)(-43.2 × 9 × 10⁻⁶)/ 1.45² + 9 × 10⁹ × 108 × 10⁻⁶ (-43.2 × 10⁻⁶) / 0.550²

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A man walk at a velocity of 3 m per econd before accelerating at a rate of 2 m quare for 4 what i hi velocity at end of the 4

Answers

Answer: Velocity of the particle is 11m/s.

What is velocity ?

-- Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time

-- Velocity is vector quantity.

-- Standard unit for the measurement is Metre/Second .

In this question we have given.

Initial velocity = 3m/s

Acceleration = 2m/s^2

We ned to find the velocity after 4 sec.

In this module we use

which is V = U + at

here :; V= 3 + 4× 2

V = 3 + 8.

V = 11 m/s .

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What is SI unit of frequency Mcq?.

Answers

The hertz (Hz) is the SI frequency unit named after the German physicist Heinrich Hertz; one hertz means that an event occurs once every second.

What is frequency?

The frequency of a repeating event is the number of occurrences per unit of time. It is distinct from angular frequency and is sometimes referred to as temporal frequency. The unit of frequency is hertz, which equals one event per second. The number of waves that pass through a fixed point in a given amount of time is described by frequency. So, if a wave takes half a second to pass, the frequency is 2 per second. The frequency is 100 per hour if it takes 1/100 of an hour.

Here,

The hertz (Hz) is the SI unit of frequency, named after the German physicist Heinrich Hertz; one hertz means that an event occurs once every second.

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is copper a good conductor of heat

Answers

Yes, copper is a good conductor of heat.

Copper is a good conductor of heat along with silver, aluminum etc.  What makes copper a good conductor of heat is that it has free electrons moving inside it. The electrons can move freely through it which makes transfer of heat and its dissipation faster. The free electrons makes the conduction of heat and electricity possible. These electrons are called conduction electrons.

That's why copper is used in many cooking utensils, fuses and as a heat sink in electrical appliances. It is a good conductor of electricity also.

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classify each statement as an example of adhesion, cohesion, or surface tension.

Answers

Examples of adhesion are option A and C, cohesion are option B and E, and surface tension are option D and F.

Adhesion refers to the tendency of dissimilar particles or surfaces to cling to one another. Water molecules that cling to plant cell wall and water molecules that cling to the side of a beaker are examples of adhesion. Cohesion refers to the tendency of similar or identical particles or surfaces to cling to one another.  Water molecules attracted to each other, or a drop of water spilled on a table forms a drop on the table, rather than spreading out over the surface are examples of cohesion.

Surface tension refers to the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension enables objects with a higher density than water to float on a water surface without becoming even partly submerged. A sewing needle floats when it is placed gently on top of water in a bucket, or a water strider runs across a pond without breaking the surface are examples of surface tension.

Note: The question is incomplete.  The complete question probably is: Classify each statement as an example of adhesion, cohesion, or surface tension. A) Water molecules cling to the side of a beaker. B) A drop of water spilled on a table forms a drop on the table, rather than spreading out over the surface. C) Water molecules cling to plant cell wall D) A water strider runs across a pond without breaking the surface. E) Water molecules are attracted to each other F) A sewing needle floats when it is placed gently on top of water in a bucket.

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Each statement can be classified as follows:

Adhesion: Water molecules cling to plant cell wall, Water molecules cling to the side of a beaker.

Cohesion: Water molecules are attracted to each other, A drop of water spilled on a table forms a drop on the table, rather than spreading out over the surface.

Surface tension: A sewing needle floats when it is placed gently on top of water in a bucket, A water strider runs across a pond without breaking the surface.

Adhesion, cohesion, and surface tension are three important properties of liquids that affect their behavior.

Adhesion is the attractive force between two different substances, such as the attraction between a liquid and a solid surface.

Cohesion is the attractive force between molecules of the same substance, such as the attraction between liquid molecules.

Finally, surface tension is the property of a liquid that allows it to resist an external force, such as the surface of a liquid appearing as if it is stretched. Together, these three properties help explain the behavior of liquids, such as how they move, flow, and interact with other materials.

Although a part of your question is missing, you might be referring to this question:

Classify each statement as an example of adhesion, cohesion, or surface tension. A) Water molecules cling to the side of a beaker. B) A drop of water spilled on a table forms a drop on the table, rather than spreading out over the surface. C) Water molecules cling to plant cell wall D) A water strider runs across a pond without breaking the surface. E) Water molecules are attracted to each other F) A sewing needle floats when it is placed gently on top of water in a bucket.

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What is ballistic examples?.

Answers

A ballistic issue is when a projectile moves unevenly through a resistant material, such as air. Any missile, spacecraft, or aero plane are all considered "rockets," as are certain other objects.

Ballistics is a branch of mechanics that studies the projectile's launch, flight, behaviour, and effects. the art or science of making and accelerating projectiles to achieve a desired performance, especially projectiles like bullets, unguided bombs, rockets, or the like. Cartridges are made utilising the ballistics scientific theory by a weapons engineer or armourer, commonly known as a "ballistician." Any rocket-powered missile, spacecraft, aeroplane, or other type of vehicle is referred to as a "rocket." The word "ballistics" comes from a Greek verb that means "to toss."

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How long does a Ferris wheel go around?.

Answers

The longest Ferris wheel go around is 48 hours, 8 minutes and 25 seconds. This is recorded by Guinness World Records that break by An employee of Chicago's Navy Pier. The normal trip took around 15-20 minutes in three or four round where each round took 3 minutes.

What is Ferris wheel?

A Ferris wheel or a Giant Wheel or an observation wheel define as an amusement ride that made of a rotating upright wheel which has multiple passenger-carrying instrument that normally called as passenger cars,  gondolas, capsules, cabins, tubs, or pods attached to the rim in such a way that as the wheel turns, they are usually stay upright by gravity.

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Where does the energy for the water cycle come from?

Answers

Answer: Answer below :)

Explanation:

Water & Energy Cycle

When energy from the Sun reaches the Earth, it warms the atmosphere, land, and ocean and evaporates water. The movement of water from the ocean to the atmosphere to the land and back to the ocean—the water cycle—is fueled by energy from the Sun.

Changes in the energy cycle will ripple into the water cycle. As greenhouses gases retain more energy in the Earth system, the extra energy enhances the water cycle. An enhanced water cycle means more extreme weather events, particularly floods and droughts.

A worker moves a table, sliding it across the level floor a distance of 3.0 m using a force of 45 N. Calculate the work done by the worker.

Answers

Answer:

135 J

Explanation:

Let's take a look at the formula for Work, W=Fd, F being force (N) and d being distance (m). We are given the force and distance so plugging it into the formula, W=45N(3.0m), we get 135 J of work.

Hope this helps!

What is the angle between the vector A 3i 4j K and B =- 4i 4j 4k?.

Answers

The angle between the vectors A and B is arccos(0.5) equal to 60 degree

The angle between two vectors can be found using the dot product, which is a measure of the similarity between the two vectors. The dot product is calculated by multiplying the corresponding components of the two vectors and then summing the results. In this case, the dot product of vectors A and B is (3 ×-4) + (44) + (k4k)

= -12 + 16 + 0 = 4.

The dot product is related to the angle between the two vectors by the following equation:

cos∅ = A × B / (A × B)

Where theta is the angle between the two vectors, A . B is the dot product of the two vectors, and A and B are the magnitudes (lengths) of the vectors. To find the angle you need to find the inverse cosine of this value.

Using the dot product formula,

= A . B / (A × B) = 4 / (3^2 + 4^2 + k^2) * (-4^2 + 4^2 + 4^2) = 0.5.

Then, taking the inverse cosine of 0.5 gives an angle of arccos(0.5) = 60 degrees between the vectors A and B.

To learn more about vectors

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