Three disks are spinning independently on the same axle without friction. Their respective rotational inertias and angular speeds are I,ω (clockwise); 2I,3ω (counterclockwise); and 4I,ω/2 (clockwise). The disks then slide together and stick together, forming one piece with a single angular velocity. What will be the direction and the rate of rotation ωnet of the single piece? Express your answer in terms of one or both of the variables I and ω and appropriate constants. Use a minus sign for clockwise rotation.

Answer:

13 m/s^2

Explanation:

The acceleration of gravity near the surface of a planet is:

g = MG / R^2

For planet 1, g = 26 m/s^2.

The gravity on planet 2 in terms of the mass and radius of planet 1 is:

g = (2M)G / (2R^2)

g = 1/2 MG / R^2

Since MG/R^2 = 26 m/s^2, then:

g = 13 m/s^2

The free-fall acceleration on planet 2 is "13 m/s²".

According to the question,

→ [tex]g_1 = \frac{GM_1}{R_1^2}[/tex]

       [tex]= 26 \ m/s^2[/tex]

→ [tex]g_2 = \frac{GM_2}{R_2^2}[/tex]

Now,

→ [tex]g_2 = \frac{G(2M_1)}{(2R_1)^2}[/tex]

       [tex]= \frac{2GM_1}{4R_1^2}[/tex]

       [tex]= \frac{1}{2} (\frac{GM_1}{R^2} )[/tex]

       [tex]= \frac{1}{2} g_1[/tex]

       [tex]= \frac{1}{2}\times 26[/tex]

       [tex]= 13 \ m/s^2[/tex]

Thus the above answer is right.

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In circuits, the average power is defined as the average of the instantaneous power  over one period. The instantaneous power can be found as:

[tex]p(t)=v(t)i(t)[/tex]

So the average power is:

[tex]P=\frac{1}{T}\intop_{0}^{T}p(t)dt[/tex]

But:

[tex]v(t)=v_{m}cos(\omega t) \\ \\ i(t)=i_{m}cos(\omega t)[/tex]

So:

[tex]P=\frac{1}{T}\intop_{0}^{T}v_{m}cos(\omega t)i_{m}cos(\omega t)dt \\ \\ P=\frac{v_{m}i_{m}}{T}\intop_{0}^{T}cos^{2}(\omega t)dt \\ \\ But: cos^{2}(\omega t)=\frac{1+cos(2\omega t)}{2}[/tex]

[tex]P=\frac{v_{m}i_{m}}{T}\intop_{0}^{T}(\frac{1+cos(2\omega t)}{2} )dt \\\\P=\frac{v_{m}i_{m}}{T}\intop_{0}^{T}[\frac{1}{2}+\frac{cos(2\omega t)}{2}]dt \\\\P=\frac{v_{m}i_{m}}{T}[\frac{1}{2}(t)\right|_0^T +\frac{sin(2\omega t)}{4\omega} \right|_0^T] \\ \\ P=\frac{v_{m}i_{m}}{2T}[(t)\right|_0^T +\frac{sin(2\omega t)}{2\omega} \right|_0^T] \\ \\ P=\frac{v_{m}i_{m}}{2}[/tex]

In terms of RMS values:

[tex]V_{RMS}=V=\frac{v_{m}}{\sqrt{2}} \\ \\ I_{RMS}=I=\frac{i_{m}}{\sqrt{2}} \\ \\ Then: \\ \\ P=VI[/tex]

Answer:

True

Explanation:

Answer: True

Explanation:

Climate is an average condition of weather for 30 years in a particular region. It can be measured on the basis of humidity, temperature, precipitation, wind speed and others.

The climates are generally define by the temperature and precipitation. The temperature may vary from cold to hot. The precipitation may also decide the climatic condition of a region such as the area which receives very low rainfall is expected to have dry and hot climatic condition.

Answer:

Blue light

Explanation:

y=Lwm/d  

where:  

y is the distance between the finges  

w is the wavelength is light (I dont have a symbol for lambda)  

m is the fringe order (the central bright fringe is the zeroth- order, the next on either side is the + or - first order, et cet)  

d is the distace between the slits  

So to reduce y, the spacing between the fringes, you could move your screen closer to the slits, use slits that are spaced farther apart, or use a shorter wavelength of light (shift toward the blue)

To produce narrower-spaced fringes in a double-slit arrangement, blue light, which has a shorter wavelength than red light, should be used. This results in more closely spaced diffraction fringes.

To produce narrower-spaced fringes in a double-slit arrangement, blue light should be used instead of red light. This is because blue light has a shorter wavelength compared to red light. Given the same double-slit spacing (d), the smaller value of λ/d for blue light leads to smaller values of sin θ, resulting in a more closely spaced set of diffraction fringes. The concept of wavelength influencing the fringe spacing is crucial for understanding how light behaves in interference patterns. Thus, utilizing blue light, with its shorter wavelength, directly correlates to achieving narrower-spaced interference fringes in comparison to using red light.

Answer: [tex]2.13(10)^{-19} J[/tex]

Explanation:

The photoelectric effect consists of the emission of electrons (electric current) that occurs when light falls on a metal surface under certain conditions.  

If the light is a stream of photons and each of them has energy, this energy is able to pull an electron out of the crystalline lattice of the metal and communicate, in addition, a kinetic energy.  

This is what Einstein proposed:  

Light behaves like a stream of particles called photons with an energy  [tex]E[/tex]

[tex]E=h.f[/tex] (1)

Where:

[tex]h=6.63(10)^{-34}J.s[/tex] is the Planck constant  

[tex]f[/tex] is the frequency

Now, the frequency has an inverse relation with the wavelength [tex]\lambda[/tex]:  

[tex]f=\frac{c}{\lambda}[/tex] (2)  

Where [tex]c=3(10)^{8}m/s[/tex] is the speed of light in vacuum  and [tex]\lambda=400nm=400(10)^{-9}m[/tex] is the wavelength of the absorbed photons in the photoelectric effect.

Substituting (2) in (1):

[tex]E=\frac{h.c}{\lambda}[/tex] (3)

So, the energy [tex]E[/tex] of the incident photon must be equal to the sum of the Work function [tex]\Phi[/tex] of the metal and the maximum kinetic energy [tex]K_{max}[/tex] of the photoelectron:  

[tex]E=\Phi+K_{max}[/tex] (4)  

Rewriting to find [tex]K_{max}[/tex]:

[tex]K_{max}=E-\Phi[/tex] (5)

Where [tex]\Phi[/tex] is the minimum amount of energy required to induce the photoemission of electrons from the surface of a metal, and its value depends on the metal:

[tex]\Phi=h.f_{o}=\frac{h.c}{\lambda_{o}}[/tex] (6)

Being [tex]\lambda_{o}=700nm=700(10)^{-9}m[/tex] the threshold wavelength (the minimum wavelength needed to initiate the photoelectric effect)

Substituting (3) and (6) in (5):  

[tex]K_{max}=\frac{h.c}{\lambda}-\frac{h.c}{\lambda_{o}}[/tex]

[tex]K_{max}=h.c(\frac{1}{\lambda}-\frac{1}{\lambda_{o}})[/tex] (7)

Substituting the known values:

[tex]K_{max}=(6.63(10)^{-34}J.s)(3(10)^{8}m/s)(\frac{1}{400(10)^{-9}m}-\frac{1}{700(10)^{-9}m})[/tex]

[tex]K_{max}=2.13(10)^{-19} J[/tex] >>>>>This is the maximum kinetic energy that ejected electrons must have when violet light illuminates the material

As the photoelectric effect takes place, the maximum kinetic energy of ejected electrons is obtained to be [tex]2.13\times 10^{-19}\,J[/tex].

Einstein's photoelectric effect equation is given as;

[tex]KE_{max}=h\nu - \Phi[/tex]

But the work function can be written as;

[tex]\Phi = h \nu_0=\frac{hc}{\lambda _0}[/tex]

Therefore, the photoelectric equation can be rewritten as

[tex]KE_{max}=\frac{hc}{\lambda} - \frac{hc}{\lambda _0}= hc\,(\frac{1}{\lambda}+ \frac{1}{\lambda_0} )[/tex]

Now, substituting the known values, we get;

[tex]KE_{max}= (6.6\times 10^{-34}\,Js)\times (3\times 10^8\,m/s)\times(\frac{1}{400\times 10^{-9}\,m}- \frac{1}{700\times 10^{-9}\,m} )\\\\\implies KE_{max}=2.13\times 10^{-19}\,J[/tex]

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Answer:

42.6 N/m

Explanation:

The spring constant can be found by using Hooke's law:

F = kx

where

F is the force applied

k is the spring constant

x is the stretching/compression of the spring

In this problem, the mass applied is

m = 0.10 kg

so the force applied is the weight of the mass:

[tex]F=mg=(0.10 kg)(9.8 m/s^2)=0.98 N[/tex]

The stretching of the spring is

x = 2.3 cm = 0.023 m

So the spring constant is

[tex]k=\frac{F}{x}=\frac{0.98 N}{0.023 m}=42.6 N/m[/tex]

Answer: The value of spring constant is 42.6 N/m

Explanation:

Force is defined as the mass multiplied by the acceleration of the object.

[tex]F=m\times g[/tex]

where,

F = force exerted on the spring

m = mass = 0.10 kg

g = acceleration due to gravity = [tex]9.8m/s^2[/tex]

Putting values in above equation, we get:

[tex]F=0.10kg\times 9.8m/s^2\\\\F=0.98N[/tex]

To calculate the spring constant, we use the equation:

[tex]F=k\times x[/tex]

where,

F = force exerted on the spring = 0.98 N

k = spring constant = ?

x = length of the spring = 2.3 cm = 0.023 m   (Conversion factor:  1 m = 100 cm)

Putting values in equation 1, we get:

[tex]0.98N=k\times 0.023m\\\\k=\frac{0.98N}{0.023m}=42.6N/m[/tex]

Hence, the value of spring constant is 42.6 N/m

Answer: If the balloon acquires charge, Sam's hair loses charge.

Explanation:

I JUST GOT THIS QUESTION RIGHT ON THE IA4 <3

Answer: C. If the balloon acquires charge, Sam's hair loses charge.

B. Ben has more power than Jerry.

Explanation: I took the test and these answers are correct. Have a nice day! :)

Answer:

By a magnetic field: no

By an electric field: yes

Explanation:

The force exerted by a magnetic field on an electron is

[tex]F=qvB sin \theta[/tex]

where

q is the electron charge

v is the speed of the electron

B is the strength of the magnetic field

[tex]\theta[/tex] is the angle between the direction of v and B

As we see from the formula, if the electron is at rest, then v = 0, and therefore the force is also zero: F = 0. Therefore, the magnetic field cannot set the electron into motion.

On the other hand, the force exerted on an electron by an electric field does not depend on the speed:

[tex]F=qE[/tex]

where E is the intensity of the electric field

Therefore, the electric force acts also when the electron is at rest, so it is able to set the electron into motion.

Final answer:

An electron at rest cannot be moved by a stationary magnetic field but can be set into motion by an electric field. The force exerted by electric fields acts on stationary charged particles, while magnetic fields only affect moving charges.

Explanation:

An electron at rest cannot be set into motion by a stationary magnetic field because a magnetic field only exerts a force on a moving charged particle. However, if an electron is at rest in an electric field, it will experience a force that can set it into motion. This is because electric fields exert forces on charged particles regardless of their state of motion. For instance, electrons starting from rest and accelerated through a potential difference will move in circular paths when entering a uniform magnetic field, due to the force that acts perpendicular to their velocity and the magnetic field

Moreover, the relationship between electric and magnetic fields demonstrates that a pure electric field in one reference frame can be perceived as a combination of electric and magnetic fields in another frame if the particle is moving. This interplay is fundamental to many devices that rely on electromagnetic forces to function.

Answer:

[tex]9.45\cdot 10^{15} m[/tex]

Explanation:

The speed of light in a vacuum is:

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

The distance that light travels in a time t is given by

[tex]d=ct[/tex]

where t is the time.

One year corresponds to a time of

[tex]t=3.156\cdot 10^7 s[/tex]

So, the distance travelled by the light in one year is

[tex]d=(3.0 \cdot 10^8 m/s)(3.156\cdot 10^7 s)=9.45\cdot 10^{15} m[/tex]

The size of a stable nucleus is limited due to the short range of the strong nuclear force. Heavy stable nuclei tend to have roughly the same number of protons as neutrons or fewer protons than neutrons.

The correct statements concerning stable nuclei are:

The strong nuclear force is an attractive force between nucleons, but it has a short range. This means that for larger nuclei, the repulsive force between protons is stronger than the attractive force, so more neutrons are needed to overcome the repulsion and stabilize the nucleus.

P=IV, where P is power, I is resistance, and V is voltage.  Plug in and solve:

P=400(20)

P=8000W

Hope this helps!!

To calculate the power dissipated by a 400.0 ohm resistor with a 20.0 volt potential difference, use the formula [tex]P = V^{2}/R[/tex], yielding a result of 1.0 watt.

The magnitude of the power dissipated by a resistor can be calculated using the formula [tex]P = I^{2}R or P = V^{2}/R[/tex], where P is the power in watts, I is the current in amperes, V is the potential difference in volts, and R is the resistance in ohms.

Given a 400.0 ohm resistor with a potential difference of 20.0 volts, we can use the formula [tex]P = V^{2}/R[/tex] to find the power dissipated. Thus, P = (20.02)/400.0 = 400/400 = 1.0 watt.

1. Domain, kingdom, phylum, class, order, family, genus, species, and subspecies.

2. If a variety of the species with a certain gene is vulnerable to a specific disease, predator, or environmental development, other members of the species with variants of the gene may be better equipped to handle the problem, and the species won't die out, just a portion of the disadvantaged.

The taxonomic groups are ordered from largest to smallest as: domain, kingdom, phylum, class, order, family, genus, species, and subspecies. Genetic diversity promotes survival of a population by offering variability that could be beneficial in changing environments.

The taxonomic groups from largest to smallest are: domain, kingdom, phylum, class, order, family, genus, species, and subspecies. Genetic diversity significantly determines a population's chances of survival. A wide genetic diversity allows a population to be more resilient to changes in the environment as it reduces the chance of the entire population being wiped out by a single threat. For instance, in a disease outbreak, a genetically varied population is more likely to contain individuals with resistance, ensuring survival of the population.

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At the beginning of the 20th century (especifically 1924) the French physicist Louis De Broglie proposed in its doctoral thesis the existence of matter waves, that is to say that all matter has a wave associated with it.

De Broglie, in addition, deduced an equation by which the electron had a wavelength that depended on its momentum (hence its velocity).

These postulations were tested with the double slit experiment (formerly applied to photons) applied to electrons, and the result was: electrons (as well as the other particles different from the photons) are able to behave as waves.

It is important to note, this experimente was done in 1927 by Clinton J. Davisson and Lester Halbert Germer and was called the electron diffraction experiment. It consisted of bombarding with an electron beam a sample (nickel) and observing the resulting interference pattern.

In this way they demonstrated what de Broglie deduced mathematically.

Answer:F = qv * Bsin( θ)

F : Magnetic force

q : charge of the particle

v : velocity of the particle

B: magnetic field

θ: angle between v and B

Explanation:

Answer:

F = qv * Bsin( θ)

F : Magnetic force

q : charge of the particle

v : velocity of the particle

B: magnetic field

θ: angle between v and B

Explanation:

Answer and Explanation:

[tex]Greetings![/tex]

[tex]Let's~answer~your~question![/tex]

[tex]The~scientist~said~``Are~you~positive?"[/tex]

[tex]and~that's~the~answer![/tex]

[tex]Hope~this~helps!~have~a~blessed~day~ahead![/tex]

Scientist say to the hydrogen atom that claimed it lost an electron is  "Are you positive ?"

A hydrogen atom is an atom of both the chlorine atom hydrogen. The Coulomb this while a single partial positive proton and a single negative charge electron to the electrically neutral atom's nucleus. Atomic hydrogen accounts for approximately 75% of both the universe's entire baryonic mass.

A hydrogen atom, on the other hand, frequently joins forces with some other atoms to form compounds and collaborates with another hydrogen atom to produce common (scientists are still trying) hydrogen gas, H2. Scientist say to the hydrogen atom that claimed it lost an electron is "Are you positive ?"

Therefore, scientist say to the hydrogen atom that claimed it lost an electron is  "Are you positive ?"

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Answer:

C) 6272 J

Explanation:

The work done by the student is equal to the increase in gravitational potential energy; therefore, it is given by

[tex]W=Fd[/tex]

where

F = 784 N is the force, which in this case is equal to the weight of the student

d = 8.0 m is the vertical distance covered

Substituting numbers into the formula, we find:

[tex]W=(784 N)(8.0 m)=6272 J[/tex]

Answer:

The forces (magnitude) would be the same; the electron would have a larger acceleration, and they will travel in opposite directions

Explanation:

- The magnitude of the force exerted on a charged particle by an electric field is

[tex]F=qE[/tex]

where q is the magnitude of the charge and E is the electric field strength. Since the proton and the electron have same electric charge magnitude (e, elementary charge), they will experience the same force under the same electric field.

- The acceleration of a particle is given by

[tex]a=\frac{F}{m}[/tex]

where F is the force exerted on the particle and m is the mass. Here, we said that the electron and the proton experience the same force F, however the mass of the proton is much larger (approx. 1800 times larger) than the mass of the electron, so the electron will experience a larger acceleration (because acceleration is inversely proportional to the mass)

- The direction of travel corresponds to the direction of the force. Since the proton is positively charged, the force exerted on it has same direction as the electric field; while since the electron is negatively charged, the force exerted on it has opposite direction to the electric field. Therefore, the two particles will travel into opposite directions.

Climate Change's Impact onEnvironment. Greenhouse gases, such as carbon dioxide, absorb heat fromsunlight, preventing it from escaping back into space. ... Though the Earth's climate has changed in the past, therapid severity of this change willdirectly affect ecosystems andbiodiversity.

Forests are impacted by seasonal and long-term changes in temperature, precipitation, and sunlight, affecting biodiversity. Adaptations are key for species survival in different biomes.

Forests are affected by seasonal and long-term changes in temperature, precipitation, and sunlight. For example, changes in temperature can alter the timing of plant growth and affect animal behavior. Changes in precipitation can impact soil moisture levels and plant distribution, while sunlight availability affects photosynthesis rates and overall ecosystem productivity.

These changes can significantly impact biodiversity in forests. Shifts in temperature and precipitation patterns can lead to changes in plant composition and distribution, which in turn affect the animals dependent on those plants for food and habitat. Changes in sunlight availability can also influence the types of plants that thrive in a particular forest, further shaping the biodiversity within the ecosystem.

Adaptations, such as those to extreme cold and dryness, play a crucial role in how plants and organisms survive in different biomes. These adaptations are essential for species to cope with the varying environmental conditions within forests and other ecosystems.

Answer:

Let's start by defining what is mass, gravity and weight:

The mass is the amount of matter that exists in a body, which only depends on the quantity and type of particles within it. This means mass is an intrinsic property of each body and remains the same regardless of where the body is located.

Gravity is an attraction force, which depends on the mass of the bodies and their distance.

Weight is the force that gravity exerts on matter and changes depending on where the body is located. Therefore, the weight of an object on Earth will not be the same as the weight of the same object on the Moon or on Mars.

Now, according to Newton's law of Gravitation, the force [tex]F[/tex] exerted between two bodies of masses [tex]m1[/tex] and [tex]m2[/tex]  and separated by a distance [tex]r[/tex]  is equal to the product of their masses and inversely proportional to the square of the distance:

[tex]F=G\frac{(m1)(m2)}{r^2}[/tex]    (1)

Where [tex]G[/tex]is the gravitational constant

In the case of our Earth, its mass  [tex]m1[/tex] and radius (distance [tex]r[/tex] from its center to its surface where an object is) are constant. So, we can write all these constant in one, in the following way:

[tex]g=G\frac{m1}{r^2}[/tex]   (2)

Where [tex]g[/tex]  is the gravity force on Earth and its value is [tex]9.8\frac{m}{{s}^2}[/tex]

.

Rewriting equation (1) with this consideration:

[tex]F=g.m_{2}[/tex]   (3)

Where [tex]F=W[/tex] is known as the weight:

[tex]W=g.m[/tex]    (4)

Here we can see the relationship among  mass [tex]m[/tex]  , weight [tex]W[/tex]  and gravity [tex]g[/tex]

Mass is a measure of the amount of matter in an object and is constant regardless of location. Weight, however, is a measure of the gravitational force acting on an object, varying with the force of gravity. Although often used interchangeably in everyday language, these concepts are distinct in physics.

Mass, weight, and gravity are closely related but distinct concepts in physics.

Mass is the quantity of matter in an object and does not change regardless of the object's location. It refers to how much 'stuff' an object is made of, measured typically in kilograms.

Weight, on the other hand, refers to the force that gravity exerts on an object. It is directly proportional to the object's mass and the acceleration due to gravity and is measured in newtons. Therefore, an object's weight can change depending on the gravitational force it experiences.

For example, an astronaut's mass remains the same whether she is on Earth or the moon. However, her weight changes, being only one-sixth on the moon of what it is on Earth because the moon's gravity is only one-sixth that of Earth's.

In conclusion, though often used interchangeably in everyday language, weight and mass are very different with weight being dependant on the force of gravity.

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Answer:

Explanation:

Assuming that h is much smaller than R, then we can say the acceleration of gravity is approximately constant.

Potential energy = Kinetic energy

mgh = 1/2 mv²

v = √(2gh)

v = √(2 (MG/R²) h)

v = √(2 MGh) / R

An expression for the object's speed as it hits the ground is:

v = √ [ ( 2GMh ) / ( R ( R + h ) ) ]

[tex]\texttt{ }[/tex]

Let's recall the Gravitational Force formula:

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

where:

F = Gravitational Force ( N )

G = Gravitational Constant ( = 6.67 × 10⁻¹¹ Nm²/kg² )

m = mass of object ( kg )

R = distance between object ( m )

Let us now tackle the problem!

[tex]\texttt{ }[/tex]

Given:

mass of object = m

height position of object = h

mass of planet = M

radius of planet = R

initial speed of object = u = 0 m/s

Asked:

final speed of object = v = ?

Solution:

We will calculate the object's speed by using Conservation of Energy formula as follows:

[tex]Ep_1 + Ek_1 = Ep_2 + Ek_2[/tex]

[tex]-G \frac{Mm}{R + h} + \frac{1}{2}m u^2 = -G \frac{Mm}{R} + \frac{1}{2}m v^2[/tex]

[tex]-G \frac{Mm}{R + h} + \frac{1}{2}m (0)^2 = -G \frac{Mm}{R} + \frac{1}{2}m v^2[/tex]

[tex]-G \frac{Mm}{R + h} = -G \frac{Mm}{R} + \frac{1}{2}m v^2[/tex]

[tex]G \frac{Mm}{R} -G \frac{Mm}{R + h} = \frac{1}{2}m v^2[/tex]

[tex]G \frac{M}{R} -G \frac{M}{R + h} = \frac{1}{2} v^2[/tex]

[tex]v^2 = 2GM ( \frac{1}{R} -\frac{1}{R + h} )[/tex]

[tex]v^2 = 2GM\frac{h}{R(R +h) }[/tex]

[tex]\boxed {v = \sqrt { \frac{ 2GMh } { R(R +h) } } }[/tex]

[tex]\texttt{ }[/tex]

[tex]\texttt{ }[/tex]

Grade: High School

Subject: Mathematics

Chapter: Gravitational Force

The loss of kinetic energy in a bouncing ball is due to the transformation of energy into other forms like heat and sound, and the inelastic nature of collisions, which prevent the ball from reaching its original dropped height.

The loss of kinetic energy during a collision when a ball bounces can be explained by several factors. When a ball is dropped from a certain height, it converts potential energy into kinetic energy. Upon hitting the floor, some kinetic energy is transformed into other forms of energy such as sound, heat, and internal energy due to the deformation of the ball. Therefore, not all the kinetic energy is available to convert back into potential energy, resulting in a lower rebound height. This conservation of energy principle dictates that the ball will only bounce up to a certain percentage of the original height, in this case, 80%. This energy transformation is due to the inelastic nature of real-world collisions.

Answer:

4 times taller

Explanation:

The horizontal distance travelled by a projectile is

[tex]d=v_x t[/tex] (1)

where [tex]v_x[/tex] is the horizontal velocity (which is constant) and t is the total time of the fall.

The total time of the fall can be found by analyzing the vertical motion of the projectile: the vertical position at time t is given by

[tex]y= h - \frac{1}{2}gt^2[/tex]

where h is the initial height, g = 9.8 m/s^2 is the acceleration due to gravity, t is the time.

The total time of the fall is the time t at which y=0 (the projectile reaches the ground), so

[tex]0=h-\frac{1}{2}gt^2\\t=\sqrt{\frac{2h}{g}}[/tex]

Substituting into (1),

[tex]d= v_x \sqrt{\frac{2h}{g}}[/tex]

This can be re-arranged as

[tex]d^2 = v_x ^2 \frac{h}{2g}\\h = \frac{2gd^2}{v_x^2}[/tex]

so we see that the initial height depends on the square of the horizontal distance travelled, d.

In this problem, one stands lands twice as far as the other stone does, so

d' = 2d

this means that the height of the taller builing is

[tex]h' = \frac{2g(2d)^2}{v_x^2}=4(\frac{2gd^2}{v_x^2})=4 h[/tex]

so the taller building is 4 times taller than the smaller one.

Answer:

142.2 m

Explanation:

The x-component of a certain vector can be found by using

[tex]v_x = v cos \theta[/tex]

where

v is the magnitude of the vector

[tex]\theta[/tex] is the angle between the direction of the vector and the positive x-direction

In this problem, we have

v = 253 m is the length (magnitude) of the vector

[tex]\theta=55.8^{\circ}[/tex] is the angle

Substituting into the formula, we find

[tex]v_x = (253 m) cos 55.8^{\circ}=142.2 m[/tex]

To find the X-component of a vector, use the formula Ax = A * cos(θ), where A is the magnitude and θ is the angle with the X-axis. For the given vector of 253 m at 55.8 degrees, calculate Ax = 253 * cos(55.8°).

The student is asking how to find the X-component of a vector with a given magnitude and direction. To find the X-component (Ax) of a vector, you can use the formula Ax = A * cos(θ), where A is the magnitude of the vector and θ is the angle it makes with the X-axis. In this case, the magnitude (A) is 253 m, and the angle (θ) is 55.8 degrees. Thus, applying the formula we get Ax = 253 m * cos(55.8°). You would need to use a calculator to find the cosine of 55.8 degrees and then multiply by 253 to find the X-component.

Answer:

Explanation:ruhfu

Final answer:

When the bottom microscope slide is rotated to make the wedge angle smaller while illuminated with monochromatic light, the interference fringes observed due to thin film interference become more closely spaced due to the more uniform air layer thickness.

Explanation:

When considering two identical microscope slides in air illuminated with monochromatic light, if the bottom slide is rotated counterclockwise about the point of contact in the side view so that the wedge angle gets a bit smaller, the fringes observed would change. These fringes are a result of thin film interference, a phenomenon where light waves that reflect off the different layers of a thin film interfere with each other, creating a pattern of bright (constructive interference) and dark (destructive interference) bands.

As the wedge angle decreases, the thickness of the air layer between the two slides changes more uniformly across the length of the slides. This uniformity in thickness leads to a more regular pattern of interference fringes. The fringes would become more closely spaced as the wedge angle decreases because the path difference between the light reflecting off the top and bottom surfaces of the air wedge changes more gradually. If the slides eventually become parallel, the fringes would theoretically form an infinitely fine pattern, but practically, the fringes would disappear as the condition for constructive or destructive interference would no longer be met in a discernible pattern.

Answer:

17 h

Explanation:

The command sent to the Voyager I is a radio wave signal, which travels at the speed of light:

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

The distance between the Voyager I and the Earth is

[tex]d=1.8\cdot 10^{13} m[/tex]

So, the time taken for the signal to reach the probe is

[tex]t=\frac{d}{c}=\frac{1.8\cdot 10^{13} m}{3\cdot 10^8 m/s}=60,000 s[/tex]

Consindering that the number of seconds in 1 hour is

[tex]60\cdot 60 = 3600 s[/tex]

Then the time elapsed converted into seconds is

[tex]t=\frac{60000 s}{3600 s}=16.7 h \sim 17 h[/tex]

Final answer:

To determine the transmission time for a command sent to Voyager 1 when it entered interstellar space, we calculate the time for light to travel the distance of 1.8 x 10¹³ meters, which comes to approximately 16.67 hours.

Explanation:

The Voyager 1 spacecraft is known for being the farthest human-made object from Earth. When it entered interstellar space in August 2012, it was 1.8 x 10¹³ meters away from our planet. To calculate the time taken for a command to travel this distance, we use the speed of light, which is approximately 299,792,458 meters per second. The formula to calculate the time (t) taken for light to travel a certain distance (d) is t = d / c, where c represents the speed of light.

For Voyager 1:

Therefore, about 16.67 hours elapse between the time a command is sent from Earth and the time it is received by Voyager 1 when it entered interstellar space.

Let [tex]x[/tex] be the distance between the base of the ladder and the bottom of the wall, and [tex]y[/tex] the distance between the top of the ladder and the bottom of the wall, so that

[tex]x^2+y^2=(25\,\mathrm{ft})^2[/tex]

Differentiate both sides with respect to time [tex]t[/tex]:

[tex]2x\dfrac{\mathrm dx}{\mathrm dt}+2y\dfrac{\mathrm dy}{\mathrm dt}=0[/tex]

When [tex]x=20\,\rm ft[/tex], the top of the ladder is

[tex]y=\sqrt{(25\,\mathrm{ft})^2-(20\,\mathrm{ft})^2}=15\,\mathrm{ft}[/tex]

above the ground. Then, given that the bottom of the ladder slides away from the wall at a rate of [tex]\dfrac{\mathrm dx}{\mathrm dt}=0.18\dfrac{\rm ft}{\rm s}[/tex], we have

[tex]2(20\,\mathrm{ft})\left(0.18\dfrac{\rm ft}{\rm s}\right)+2(15\,\mathrm{ft})\dfrac{\mathrm dy}{\mathrm dt}=0\implies\dfrac{\mathrm dy}{\mathrm dt}=-0.24\dfrac{\rm ft}{\rm s}[/tex]

That is, the top of the ladder is sliding downward at a rate of 0.24 ft/s.

The top of the ladder is sliding down the wall at a rate of approximately 0.576 ft/sec.

To determine how fast the top of the ladder is sliding down the wall, we can use related rates. Let's denote the distance from the bottom of the ladder to the wall as x and the distance from the top of the ladder to the ground as y. From the given information, we have dx/dt = -0.18 ft/sec (negative because the bottom of the ladder is sliding away from the wall) and we want to find dy/dt when x = 20 ft. Using the Pythagorean theorem, we have x^2 + y^2 = 25^2. Differentiating both sides with respect to time, we have 2x(dx/dt) + 2y(dy/dt) = 0. Substituting the known values, we can solve for dy/dt when x = 20 ft.

So, when the bottom of the ladder is 20 ft from the wall, the top of the ladder is sliding down the wall at a rate of approximately 0.576 ft/sec.

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Answer:

hand/thumb/finger

Explanation:

Final answer:

The term 'pollex' refers to the thumb, which is an essential digit of the hand for grasping and manipulating objects. It has two phalanx bones and a special structure that allows for a significant range of movement.

Explanation:

The medical term pollex refers to digit 1 of the hand, which is more commonly known as the thumb. The thumb is an essential part of the hand that allows for a wide range of movements and functions, such as grasping, holding, and manipulating objects. The pollex, or thumb, has two types of phalanx bones: the proximal and distal phalanges.

In the context of the human skeleton, the pollex is part of the upper limb anatomy which contains various bones including the bones of the arm, forearm, wrist, and hand. Its unique structure, having only two phalanx bones compared to three in the other digits, allows for the thumb's increased range of motion and the ability to oppose the fingers.