1. How many correct experiments do we need to disprove a theory? How many do we need to prove a theory? Explain.

2. A guidebook describes the rate of climb of a mountain trail as 120 meters per kilometer. How can you express this as a number with no units?

Answers

Answer 1
1.  You can never prove a theory. All theories and laws and scientific knowledge in general is provisional. If your theory is inconsistent with an experiment (and you are sure the experiment is correct), your theory needs to be pitched or modified.

2. change the meters to kilometers; 

120 m/km = .12 km/km = .12 

or the kilometers to meters; 

120 m/km = 120 m/1000m = .12 

This sounds like its telling you how far you climb vertically (.12 km) for every 1 km that you walk along the slanted, winding trail. 

The unitless number ".12" is usefull because now you can think of the rate of climb in any units you want. So you rise vertcally .12 miles for every mile you walk the trail, or you rise .12 ft for every foot you walk the trail, etc.
Answer 2

Disproving a theory requires just one contradicting experiment while proving a theory involves numerous supporting experiments. The mountain trail's rate of climb, 120 meters per kilometer, is expressed as a dimensionless number 0.12 after dividing meters by kilometers. Theory validation is based on predictive success and scientific acceptance, whereas a model's validity can be more limited in scope.

Understanding Theory Validation and Rate Expression

In the context of scientific theories, disproving a theory typically requires only one definitive experiment that provides evidence contradicting the theory's predictions. In stark contrast, proving a theory is a more complex process. A theory cannot be proven in an absolute sense; it can only be supported by a preponderance of evidence. This involves numerous experiments that consistently validate the theory's predictions.

When expressing the rate of climb of a mountain trail, which is described as 120 meters per kilometer, we are dealing with a simple ratio. To express this as a dimensionless number, we divide the number of meters by the number of kilometers, understanding that 1 kilometer equals 1000 meters. The resulting figure is 0.12, which is the gradient or incline of the trail without any units.

The validity of a theory is determined by how well it predicts and explains phenomena in the natural world. Theories are considered more valid if they have been thoroughly tested and widely accepted in the scientific community. For a model to be considered valid, it doesn't need to be universally applicable; it must effectively represent the phenomena for which it was designed. In contrast, a theory is generally expected to have wider applicability.


Related Questions

A visitor to the observation deck of a skyscraper manages to drop a penny over the edge. As the penny falls faster, the force due to air resistance increases. How does this affect the acceleration of the penny?
a. The acceleration decreases b. The acceleration remains constant and not zero (my answer)
c. The acceleration remains zero d. The acceleration increases.

Answers

Final answer:

The acceleration of the penny decreases as the air resistance increases because the net force acting on it reduces until it reaches terminal velocity, where acceleration becomes zero. So the answer to the question is a.

Explanation:

When a penny is dropped from an observation deck of a skyscraper, initially it accelerates due to gravity. As it gains speed, the force of air resistance increases. This air resistance force acts in the opposite direction to the penny's motion, therefore, as the air resistance increases, it will reduce the net force acting on the penny. According to Newton's second law, acceleration results from forces acting on an object divided by its mass. When the upward air resistance force equals the downward gravitational force, the net force becomes zero, and the penny no longer accelerates and reaches terminal velocity.

Therefore, as the air resistance increases while the penny falls, the acceleration of the penny decreases until it hits terminal velocity, where the acceleration will be zero. So the answer to the question is a. The acceleration decreases.

A heavy crate rests on the bed of a flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to accelerate? ...?

Answers

Explanation:

A heavy crate rests on the bed of a flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. Due to the frictional force, the crate accelerates.

The force of friction is an opposing force. The force of friction depends on the coefficient of friction and the normal force acting on the object. The frictional force is of two types i.e sliding friction, static friction.

So, the frictional force causes the crate to accelerate.

PLEASE HELP!!!! Scientists launch a rocket, and they monitor its acceleration and the force exerted by its engines. As the rocket gets higher, the monitors show that the acceleration of the rocket is increasing but the force exerted stays the same. How do Newton’s laws explain why the scientists could expect this to happen?

The total force stays the same, but the action force is increasing as the reaction decreases.
The mass of the rocket decreases as fuel is burned, so the acceleration increases.
The inertia of the rocket increases, which reduces the force needed to change its speed.
The reaction force is increasing as fuel is burned, which causes a greater acceleration.

Answers

The force exerted is constant because the mass of the rocket decreases as fuel is burned, so the acceleration increases.

What is the relationship between force mass and acceleration?

The relationship between force, mass, and acceleration is given by Newton's second law and stated mathematically as follows:

Force = mass × acceleration

As the rocket accelerates, fuel is burnt and the mass of the rocket reduces. Thus, the force exerted remains constant.

Therefore, the mass of the rocket decreases as fuel is burned, so the acceleration increases.

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Answer:

b

Explanation:

Which tools would be use to find an irregularly shaped object’s mass and volume?

Answers

Scales for weight
Any beaker to measure the volume of liquid displaced

What accounts for an increase in the temperature of a gas that is kept at constant volume ?

Answers

Energy has been added as heat to the gas. Hope that helps.

The correct answer to the question is : By increasing the pressure.

EXPLANATION:

Before answering this question, first we have to understand Gay lussac's law.

As per Gay lussac's law, the pressure of a gas increases or decreases by 1/273 th of its pressure at zero degree celsius; for every 1 degree celsius rise or fall of temperature at constant volume

In a simple way, the pressure is directly proportional to absolute temperature.

Mathematically P ∝ T.       [ P = pressure and T = temperature]

Hence, increase in pressure at constant volume may increase its temperature.

A woman exerts a horizontal force of 1 pounds on a box as she pushes it up a ramp that is 2 feet long and inclined at an angle of 30 degrees above the horizontal. Find the work done on the box in ft -lbs.
...?

Answers

work done = force times distance the force parallel to the slope of the ramp 1 * cos 30 degrees work done = cos 30 * 2 ft lbs

If an object has a mass of 38 kg, what is its approximate weight on earth?

Answers

38*10=380 N
To be more exact, 38 should be multiplied by 9.8 instead of 10.

Which of the following was NOT an outcome of Bacon's rebellion?

A. A more direct focus on the "Indian Problem"

B. A more focused plain to isolate black slaves from white servants

C. More people where in support of armed expantion to nNative Americans' territory

D. A reformed land policy for thse living in Virgina

Answers

Answer: D

Explanation: I took the test

A reformed land policy for these living in Virgina is not an outcome of Bacon's rebellion. Hence, option D is correct.

What Bacon's rebellion?

A local conflict with the Doeg Indians on the Potomac River served as the catalyst for Bacon's Rebellion, which was waged between 1676 and 1677. The Indians started assaulting the Virginia frontier after being pursued north by Virginia militiamen, who also assaulted the Susquehannock, who were otherwise uninvolved.

The General Assembly was persuaded to approve a scheme by the governor, Sir William Berkeley, that would have isolated the Susquehannock while enlisting Indian allies on Virginia's side. Others saw the Susquehannock War as a chance to launch a general Indian war that would result in the capture of Indian slaves and lands, as well as the expression of widespread anti-Indian feeling.

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One end of a rope is fastened to a boat and the other end is wound around a windlass located on a dock at a point 4m above the level of the boat. If the boat is drifting away from the dock at the rate of 2m/min, how fast is the rope unwinding at the instant when the length of the rope is 5m? ...?

Answers

it seems that you need to solve this using phytagoras

x^2 + 4^2   = D^2

2xx'    =  yy'

y'    = xx'/y

y' = 3x2/5

= 6/5

hope this helps

A 2.44 x 10^3 kg car requires 5.3 kJ of work to move from rest to some final speed. During this time, the car moves 27.4 m.
Neglecting friction, find
a) the final speed
b) the net horizontal force exerted on the car

Answers

Final answer:

The final speed of the car is 8.16 m/s and the net horizontal force exerted on the car is 2976.8 N.

Explanation:

To find the final speed of the car, we can use the work-energy principle. The work done on an object is equal to the change in its kinetic energy. Since the car starts from rest, its initial kinetic energy is zero, and the work done on the car is equal to its final kinetic energy.

Given that the car requires 5.3 kJ of work and has a mass of 2.44 x 10^3 kg, we can calculate the final kinetic energy using the equation:

Kinetic Energy = (1/2) * mass * velocity^2

By rearranging the equation, we can solve for the final velocity:

velocity = sqrt(2 * work / mass)

Substituting the values, we get:

velocity = sqrt(2 * 5300 / 2440) = 8.16 m/s

To find the net horizontal force exerted on the car, we can use Newton's second law, which states that force is equal to mass times acceleration. Since there is no vertical motion, the net force in the horizontal direction is equal to the mass times the acceleration.

Given that the mass of the car is 2.44 x 10^3 kg and the final velocity is 8.16 m/s, we can calculate the net horizontal force using the equation:

Force = mass * acceleration

Since the car starts from rest, the initial velocity is zero. Therefore, the acceleration is equal to the final velocity divided by the time taken to reach the final velocity. Given that the car moves 27.4 m, we can calculate the acceleration using the equation:

acceleration = velocity^2 / (2 * distance)

Substituting the values, we get:

acceleration = (8.16^2) / (2 * 27.4) = 1.22 m/s^2

Finally, we can calculate the net horizontal force:

Force = (2.44 x 10^3) * 1.22 = 2976.8 N

An artificial satellite circles Earth in a circular orbit at a location where the acceleration due to gravity is 9.00 m/s2. Determine the orbital period of the satellite.

Answers

 g = GMe/Re^2, where Re = Radius of earth (6360km), G = 6.67x10^-11 Nm^2/kg^2, and Me = Mass of earth. On the earth's surface, g = 9.81 m/s^2, so the radius of your orbit is:


R = Re * sqrt (9.81 m/s^2 / 9.00 m/s^2) = 6640km 

here, the speed of the satellite is:

v = sqrt(R*9.00m/s^2) = 7730 m/s 

  the time it would take the satellite to complete one full rotation is:

T = 2*pi*R/v = 5397 s * 1h/3600s = 1.50 h 

Hope it help i know it's long and may be confusing but if you have any more questions regarding this topic just hmu!  :)
Final answer:

The orbital period of a satellite depends on the radius of its orbit and the acceleration due to gravity. The mass of the satellite does not affect its orbital period. The calculation assumes a circular orbit and a uniform gravitational field.

Explanation:

The orbital period of an artificial satellite is the time it takes the satellite to complete one full orbit around the Earth. Using the given acceleration due to gravity (9.00 m/s2) and the formula for the period of an orbit, we can solve for the satellite's orbital period. The formula for the period (T) of an orbit is derived from the formula for the speed of an orbit: V_orbit = 2πr/T. This formula shows that the orbital speed is equal to the circumference of the orbit divided by the orbital period. By substituting this into the centripetal acceleration equation (a = V²/r), it can be rearranged to get the period of orbit.

The mass is cancelled out in these equations, so the mass of the satellite does not affect the orbital period or speed. Therefore, any satellite at the same altitude will have the same orbital period, regardless of its mass.

A crucial point to remember is that this calculation assumes a circular orbit, which simplifies the calculation. In reality, orbits may not always be perfectly circular. This also ignores the effect of the Earth's nonuniform gravitational field and assumes that the only force acting on the satellite is the Earth's gravity.

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Two masses, each weighing 1.0 × 103 kilograms and moving with the same speed of 12.5 meters/second, are approaching each other. They have a head-on collision and bounce off away from each other. Assuming this is a perfectly elastic collision, what will be the approximate kinetic energy of the system after the collision?
A. 1.6 × 105 joules
B. 2.5 × 105 joules
C. 1.2 × 103 joules
D. 2.5 × 103 joules ...?

Answers

Answer:

A.  1.6 × 105 joules

Final answer:

The total kinetic energy remains the same in a perfectly elastic collision. Since the two identical masses have identical speeds initially, their joined kinetic energies will be 1.6 × 10⁵ joules after the collision, same as before.

Explanation:

In a perfectly elastic collision, both momentum and kinetic energy are conserved. Since the two masses are identical and approach each other with the same speed, they will bounce back with the same speed after the collision, assuming no external forces act on the system. The kinetic energy of the system before the collision can be calculated using the formula KE = 0.5 × m × v² for each mass and then adding the two values together.

For each mass, KE = 0.5 × 1.0 × 10³ kg × (12.5 m/s)². Calculating this we get KE = 0.5 × 1.0 × 10³ × 156.25 = 78,125 Joules. Since there are two masses, the total kinetic energy would be 2 × 78,125 J = 156,250 Joules.

Immediately after collision, because it is perfectly elastic, the same amount of kinetic energy will be present. Therefore, the approximate kinetic energy of the system after the collision will be 1.6 × 10⁵ joules.

what is the half life of a radioactive isotope that decreased to one-fourth its original amount in 100 year

Answers

two times 100 years = 200 years is half life

Final answer:

The half-life of a radioactive isotope that decreases to one-fourth its original amount in 100 years is 50 years, as this duration represents two half-lives.

Explanation:

The half-life of a radioactive isotope is the time required for half the atoms of a radioactive sample to decay. If a radioactive isotope decreases to one-fourth of its original amount after 100 years, it means that two half-lives have passed (since one half-life leaves us with half the original amount, and another half-life would then leave us with one-fourth). Therefore, the half-life is 50 years. This exemplifies an exponential decay process, typical for radioactive substances.

Which statements describe characteristics of most metals? Check all that apply.
A They can be formed into wires.
B They are shiny.
C They are liquid at room temperature.
D They are good conductors.
can be easily shaped by hammering or pounding.

Answers

The answer is:

A. They can be formed into wires.

B.They are shiny.

D. They are good conductors

E.can be easily shaped by hammering or pounding.

The explanation:

Let's see the characteristics of the most metals:

1) the most metals can be hit by a hammer and form a thin sheets without breaking and this called malleability.

for example: Aluminium and copper

2) They can form into a very thin wires and this called ductility

for example: silvar , Aluminium and copper.

3) The metal can conduct the heat and the electricity very easy and quick, this mean that the meals are good conductor for the heat and electricity.

4)The metals like gold can be used at jewellery because it is very shiny.

5) and answer C is wrong because most metals are solid at room temperature.

Answer:

Option A, B, D and E are the characteristics of Metal

Explanation:

Some of the common characteristics of most of the metals are -

a) Most of the metal have lustrous surface which means they glitter in the presence of light for example - Iron, copper etc.

b) All metals are malleable which means they can be molded into different shape on beating for example copper can be converted into copper wire, jug, plates etc.

c) All metals are good carrier of charge and thus they are good conductors. These metals have valence shells electron which are free to move with a small force. Good metal conductors are copper , iron etc

d) Most of the metal are solid at room temperature.

If a plane can travel 450 miles per hour with the wind and 410 miles per hour against the wind, find the speed of the plane without a wind and speed of the wind?

Answers

The speed of the plane through the air is 430 mph, and you described a day when the wind was blowing at 20 mph.
Assuming that Rp = speed of the plane and Rw = speed of the wind

450 = Rp + Rw

410  = Rp - Rw

(add both equations)

860 = 2Rp

Rp = 430

Hope this helps

What is Darwin's theory of the origin of species?

Answers

While Darwin's Theory of Evolution is a relatively young archetype, the evolutionary worldview itself is as old as antiquity. Ancient Greek philosophers such as Anaximander postulated the development of life from non-life and the evolutionary descent of man from animal. Charles Darwin simply brought something new to the old philosophy -- a plausible mechanism called "natural selection." Natural selection acts to preserve and accumulate minor advantageous genetic mutations. Suppose a member of a species developed a functional advantage (it grew wings and learned to fly). Its offspring would inherit that advantage and pass it on to their offspring. The inferior (disadvantaged) members of the same species would gradually die out, leaving only the superior (advantaged) members of the species. Natural selection is the preservation of a functional advantage that enables a species to compete better in the wild. Natural selection is the naturalistic equivalent to domestic breeding. Over the centuries, human breeders have produced dramatic changes in domestic animal populations by selecting individuals to breed. Breeders eliminate undesirable traits gradually over time. Similarly, natural selection eliminates inferior species gradually over time.
Well... Darwin is a character in the amazing world of gum ball and in the episode, he was a magic fish who has connection with gumball and magical stuff happens... JUST SEE THE EPISODE ITS CALLED DARWINS ORIGINS!!!

As you rise upwards in the atmosphere, air pressure
a. increases.
b. decreases.
c. doesn't change.
d. first increases, then decreases.

Answers

As you rise upwards in the atmosphere, air pressure "Decreases"

So, option B is your answer.

Hope this helps!

Answer:

B

Explanation:

As altitude rises, air pressure drops. In other words, if the indicated altitude is high, the air pressure is low. This happens for two reasons. The first reason is gravity. Earth's gravity pulls air as close to the surface as possible. The second reason is density. As altitude increases, the amount of gas molecules in the air decreases—the air becomes less dense than air nearer to sea level. This is what meteorologists and mountaineers mean by "thin air." Thin air exerts less pressure than air at a lower altitude.

(:

byeeeee

The sound produced by touching each button on a touch-tone phone is described by y = sin 2πlt + sin 2πht where l and h are the low and high frequencies (cycles per seconD. in the figure shown.

Use a calculator to find the graph of the sound emitted by touching the 4 key in a [0, 0.01, 0.001] by [-2, 2, 1] viewing rectangle.

Answers

Your graph is attached.

It kinda looks to me like ' D ' is the choice,
but I'm pretty tired, so you oughta check it.

Is it true that a conductor is a material that doesn't allow electrons to flow through it easily?

Answers

False, what you described is an insulator.
A conductor WILL allow electrons to flow through it easily.

Two cars leave an intersection at the same time. One is headed south at a constant speed of 40 miles per hour, the other is headed west at a constant speed of 30 miles per hour (see the figure). Express the distance d between the cars as a function of the time t. (Hint: At t = 0 the cars leave the intersection.)

d(t)= ...?

Answers

I got into a mess of trouble when I reached the part where it says
"(see the figure)".  But I think I was able to get enough out of the
rest of the question to answer it.

One car is headed south, and the other car is headed west.
So the cars are driving on the legs of a right triangle, and the
hypotenuse is always the line between the cars.

First car:  Distance from the starting point after 't' hours = 40 t miles.

Second car:  Distance from the starting point after 't' hours = 30 t miles.

         Distance between the cars

      = hypotenuse of the right triangle

     =  √(one leg² + other leg²)

     =  √[ (40t miles)² + (30t miles)² ]

     =  √ (1600t² miles² + 900t² miles²)

     = √   2500 t² miles²

      d(t) = 50 t miles . 

The cars are 50 miles apart after 1 hour, 100 miles apart after 2 hours,
150 miles after 3 hours, 200 miles after 4 hours, . . . , etc.

Final answer:

The distance between the two cars can be expressed as a function of time using the Pythagorean theorem. At t = 0, the cars are 2 km apart, and as time progresses, their distances increase.

Explanation:

The distance between the two cars can be expressed as a function of time using the Pythagorean theorem. Let's consider the time t as the independent variable. At t = 0, both cars leave the intersection, so the distance between them is initially given by:

[tex]d(0) = \sqrt{((2 km)^2 + (0 km)^2)} = \sqrt{(4 km^2)} = 2 km[/tex]

As time progresses, the car headed south travels at a speed of 40 mph, which means its distance from the starting point increases by 40t miles. Similarly, the car headed west travels at a speed of 30 mph, increasing its distance from the starting point by 30t miles.

Using the Pythagorean theorem again, we can find the distance d between the two cars as a function of time:

[tex]d(t) = \sqrt{((40t)^2 + (30t)^2)[/tex]

A 1700kg rhino charges at a speed of 50.0km/h. What is the magnitude of the average force needed to bring the rhino to a stop in 0.50s?

Answers

Force (N) = mass (kg) x velocity (m/s) / time (s)

Sound waves travel through air in a pattern of squeezing in and spreading out.
True
False

Answers

Sound waves DO travel through air in a pattern of squeezing in and spreading out. This is the case for all waves - they all oscillate.
I think that statement is True
Sound waves are always longitudinal waves in a gas, and are always alternating pressure in air

hope this helps

In an experiment performed in a space station, a force of 60n causes an object to have an acceleration equal to 4m/s s .what is the objects mass?

Answers

We Know, F = m*a
Here, F = 60N
a = 4 m/s²

Substitute their values in the equation,
60 = m*4
m = 60/4
m = 15

So, your final answer & the mass of the object would be 15 Kg

Hope this helps!

In an experiment performed in a space station, a force of 60 Newtons  causes an object to have an acceleration equal to 4 meters/second², then the mass of the object would be 15 kilograms,

What is Newton's second law?

Newton's Second Law states that The resultant force acting on an object is proportional to the rate of change of momentum.

F = mass ×acceleration

As given in the problem In an experiment performed in a space station, a force of 60 Newtons  causes an object to have an acceleration equal to 4 meters/second²,

mass = force /acceleration

         = 60 Newtons/ 4 meters/second²

         = 15 kilograms

Thus, the mass of the object would be 15 kilograms

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which nervous system consist of the brain and spine

Answers

The CNS (Central Nervous System) consists of the brain and spinal cord.

Enter a one- or two-word answer that correctly completes the following statement.

If the constant force is applied for a fixed interval of time , then the _____ of the particle will increase by an amount at.

Answers

In my view it looks like this: If the constant force is applied for a fixed interval of time , then the time and velocity of the particle will increase by an amount at.

What does it mean that a form of energy might take more energy to harness than it provides? Are renewable resources always renewable, or can they become non-renewable? Why aren't renewable resources used for everything that we use energy for? Explain.

Answers

Final answer:

Energy that costs more to harness than it provides indicates an energy deficit in the transformation and conversion process. Renewable resources can potentially become non-renewable if their consumption surpasses replenishment. The use of renewable resources is not ubiquitous due to cost, geographical, and technological limitations.

Explanation:

When a form of energy takes more energy to harness than it provides, it means that the energy input required to extract or convert the energy is greater than the energy output made available for use. This is a significant factor in evaluating the efficiency of energy sources and plays into the concept of energy transformation and conversion.

Renewable resources, by definition, are replenished naturally over short time scales relative to the lifetime of human civilization. However, the ability to renew does not equate to infinite availability if consumption rates surpass replenishing rates. Thus, although inherently renewable, they may de facto become non-renewable.

While renewable energy resources offer numerous benefits, including lower emissions and a reduced dependence on fossil fuels, they are not used for everything due to several factors. These include cost, geographical limitations, and technology constraints. For instance, the initial costs of renewable energy systems can be high, and not all locations receive enough sunlight or wind to be effective. Additionally, technology has not advanced to a level where renewable energy can fully replace non-renewable sources in all uses.

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Harnessing some energy sources can be inefficient if the energy input exceeds the output. Renewable resources can sometimes become non-renewable if consumed faster than they are replenished. Challenges like intermittency, energy density, infrastructure costs, and location dependency limit the use of renewable energy for all purposes.

When it is said that a form of energy might take more energy to harness than it provides, it means the energy input required to extract, process, and deliver the energy is greater than the usable energy output gained. This scenario is inefficient and often not sustainable.

Renewable resources are typically those that can be naturally replenished within a human lifespan. Examples include solar, wind, and biomass energy. However, they can become non-renewable if their rate of consumption exceeds the rate at which they are replenished, or if environmental conditions change drastically, making them less viable.

There are several reasons why renewable energy sources are not used for all energy needs:

Intermittency: Sources like solar and wind are not always available since they depend on weather and time of day.Energy Density: Renewable energy often has a lower energy density compared to fossil fuels, meaning more space and materials are needed to produce the same amount of energy.Infrastructure Costs: Transforming existing infrastructure to adapt to renewable energy can be costly and complex.Location Dependency: Some regions are more suited to certain types of renewable energy than others, making it impractical or inefficient in some areas.

While renewable resources offer many advantages, including lower environmental impact and sustainability, technical and logistical challenges must be addressed for them to replace non-renewable sources completely.

An electric clothes dryer has a resistance of 16ohms. it draws 15 A of a current. what is the voltage, in volts, of the wall outlet that it is plugged into?

Answers

The answer is 240 volts :)
the answer is 240 volts

A medieval prince trapped in a castle wraps a message around a rock and throws it from the top of the castle with an initial velocity of 12m/s[42 degrees of above the horizontal]. The rock lands just on the far side of the castle's moat, at a level 9.5m below the initial level. Determine the rock's time of flight. ...?

Answers

Vertically we can say 
Vertical acceleration = - g 
Vertical velocity = u sinѲ - gt [Ѳ = 42; u = 12 m/s] 
Vertical displacement = u sinѲt - (1/2) g t^2 + 9.5 

When the rock hits the ground, its vertical displacement will be zero. So we can say.. 

u sinѲt - (1/2) g t^2 + 9.5 = 0 
I'll rearrange this .... 

- (1/2) g t^2 + u sinѲt + 9.5 = 0 

Can you see that we now have a quadratic in t? 

Using the well known formula 

t = [ - u sinѲ ± √( u^2 sin^2Ѳ - 4(( - (1/2)g * 9.5))] / (- g) 

t = [- u sinѲ ± √( u^2 sin^2Ѳ + 19g)] / (-g) 

t = [- 8.03 ± √(250.86)] / (-9.81) 

t = [- 8.03 ± 15.84] / (-9.81) 

t = (- 8.03 + 15.84) / (-9.81) or t = (-8.03 - 15.84) / (-9.81) 

t = - 0.8 or t = 2.43 

Well, a negative time has no meaning so 
t = 2.43 seconds. 

The rock's time of flight is approximately 2.85 seconds. This is determined by solving a quadratic equation derived from the vertical motion kinematic equation. The initial vertical velocity component and gravitational acceleration are key to finding the solution.

To determine the time of flight of the rock, we need to analyze its vertical motion. The initial vertical velocity is given by:

               V₀y = 12 m/s * sin(42°)

               Solving for V₀y, we get approximately 8.02 m/s.

Using the kinematic equation for vertical motion,

               y = V₀yt + 0.5 * a * t²

where y is the displacement (−9.5 m, since the rock falls below its original level), a is the acceleration due to gravity (−9.8 m/s²), and V₀y is the initial vertical velocity.

Substituting the values, we get:

               -9.5 = 8.02t - 4.9t²

Rearranging and solving the quadratic equation:

               4.9t²- 8.02t - 9.5 = 0

Using the quadratic formula where a = 4.9, b = -8.02, and c = -9.5:

               [tex]t= \frac{8.02 \pm \\\sqrt{(8.02^{2} - 4(4.9)(-9.5))}} {(2(4.9))}[/tex]

               t ≈ 2.85 s

Therefore, the rock's time of flight is approximately 2.85 seconds.

Ultraviolet light emits a total of 2.5 × 10^–17 J of light at a wavelength of 9.8 × 10^–7 m. How many photons does this correspond to?

Answers

Final answer:

To find the number of photons, we first calculate the energy of one photon using Planck's equation and then divide the total energy by this value. With the given wavelength, the energy per photon is 2.03 × 10⁻¹⁹ J, leading to approximately 1.23 × 10² photons for the total energy emitted.

Explanation:

To calculate the number of photons emitted at a given wavelength, we use the energy of a single photon and divide the total energy by this value. The energy (E) of a photon is related to its wavelength (λ) by the equation E = hc/λ, where h is Planck's constant (6.63 × 10⁻³⁴ J·s) and c is the speed of light (3.00 × 10⁸ m/s). Given a wavelength of 9.8 × 10⁻⁷ m, the energy per photon can be calculated. Then, the total number of photons is total energy / energy per photon.

First, we find the energy of one photon:

Energy per photon (E) = (6.63 × 10⁻³⁴ J·s) × (3.00 × 10⁸ m/s) / (9.8 × 10⁻⁷ m)E = 2.03 × 10⁻¹⁹ J per photon

Next, we use the total energy to find the number of photons:

Number of photons = Total energy / Energy per photonNumber of photons = (2.5 × 10⁻¹⁷ J) / (2.03 × 10⁻¹⁹ J)Number of photons ≈ 1.23 × 10² photons

Final answer:

To find the number of photons that correspond to 2.5 × 10⁻¹⁷ J of ultraviolet light at a wavelength of 9.8 × 10⁻· m, first calculate the energy per photon using Planck's formula, then divide the total energy by this value, resulting in approximately 1.23 × 10² photons.

Explanation:

To calculate the number of photons corresponding to 2.5 × 10⁻¹⁷ J of ultraviolet light at a wavelength of 9.8 × 10⁻· m, we must first determine the energy per photon using the formula E = hc/λ, where E is the photon energy, h is Planck's constant (6.626 × 10⁻4 J·s), c is the speed of light in a vacuum (3 × 10⁸ m/s), and λ is the wavelength of the light.

First, we calculate the energy per photon:

E = (6.626 × 10⁻4 J·s)(3 × 10⁸ m/s) / (9.8 × 10⁻· m) ≈ 2.026 × 10⁻ J per photon.

Now, we find the number of photons by dividing the total energy by the energy per photon:

Number of photons = Total energy / Energy per photon = (2.5 × 10⁻ J) / (2.026 × 10⁻ J/photon) ≈ 1.23 × 10² photons.

IF you are skateboarding and push back with one leg, and, as a result the skateboard moves forward. Which law of motion is being described

Answers

Newton first law of motion 

Newton's First Law states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force
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