Following a lecture on transverse and longitudinal waves, four students make venn diagrams to characterize these waves. which venn diagram is correct? a venn diagram with two intersecting circles. the circle on the left is labeled transverse waves with entries light, can travel through a vacuum, vibrating string, created by a disturbance and medium motion is perpendicular. the circle on the right is labeled longitudinal waves with entries medium motion is parallel, has regions of high and low density, sound and travel faster in a denser medium. the overlapping region has entries has speed and travels through solids. a venn diagram with two intersecting circles. the circle on the left is labeled transverse waves with entries light, can travel through a vacuum, vibrating string and medium motion is perpendicular. the circle on the right is labeled longitudinal waves with entries medium motion is parallel, has regions of high and low density, sound and travel faster in a denser medium. the overlapping region has entries, created by a disturbance, has speed and travels through solids. a venn diagram with two intersecting circles. the circle on the left is labeled transverse waves with entries light, all parts of the electromagnetic spectrum, vibrating string, medium motion is perpendicular. the circle on the right is labeled longitudinal waves with entries medium motion is parallel, has regions of high and low density, sound and can travel through a vacuum. the overlapping region has entries, created by a disturbance, has speed and travels through solids. a venn diagram with two intersecting circles. the circle on the left is labeled transverse waves with entries light, can travel through a vacuum, vibrating string and medium motion is perpendicular. the circle on the right is labeled longitudinal waves with entries medium motion is parallel, has regions of high and low density, all parts of the electromagnetic spectrum and travel faster in a denser medium. the overlapping region has entries, created by a disturban

Answers

Answer 1

Venn diagram B is correct. A Venn diagram is a type of graph that uses circles to depict connections between objects or fixed groups of entities.

What Is a Venn Diagram and how does It Work?

A Venn diagram is a diagram that uses circles to depict relationships between objects or finite groups of objects. Circles that overlap share characteristics, whereas circles that do not overlap do not.

A Venn diagram with two intersecting circles. the circle on the left is labeled transverse waves with entries light, can travel through a vacuum, vibrating string and medium motion is perpendicular.

The circle on the right is labeled longitudinal waves with entries medium motion is parallel, has regions of high and low density, sound and travel faster in a denser medium.

The overlapping region has entries, created by a disturbance, has speed, and travels through solids.

Hence Venn diagram B is correct

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Related Questions

What units are appropriate to express specific heat?.

Answers

Answer:

The units for specific heat can either be joules per gram per degree (J/goC) or calories per gram per degree

Explanation:

Pls answer this questions

Answers

For 23 i believe it’s C

Does the buoyant force on a submerged object depend on the volume of the object or on the weight of the object?.

Answers

Answer:

The buoyant force on a submerged object depends upon the volume of the object.

Explanation:

A car is traveling in a race. The car went from the initial velocity of 35 m/s to the final velocity of 65 m/s in 5 seconds
What is the acceleration?
- 13 m/s
om/
6 m/s
13 m/s

Answers

Answer:

6m/s

Explanation:

a = (v-u)/t

acceleration, a

initial velocity, u

final velocity, v

time, t

substitute values and you'll get the answer

Answer:

6 m/s

Explanation:

A room with translucent windows that include some colored parts. use the drop-down menus the complete the statements about the image. the windowpanes are . the colors of the panes are due to the wavelengths of light that the glass .

Answers

(a)The window panes are transparent  

(b)The colors of the panes are due to the wavelengths of light that the glass allows to pass through.

What are trasparent glasses?

The glasses which allows the light rays to pass through them are called as the transparent glasses.

or visible light is electromagnetic radiation within the portion of the electromagnetic spectrum that is perceived by the human eye.[1] Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm),

corresponding to frequencies of 750-420 terahertz, between the infrared (with longer wavelengths) and the ultraviolet (with shorter wavelengths

Hence  the  window panes are transparent the colors of the panes are due to the wavelengths of light that the glass allows to pass through.

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Answer:

The windowpanes are- transparent.

The color of the panes are due to the wavelengths of light that the glass- allows to pass through

Explanation:

What do tripped circuit breakers and blown fuses indicate.

Answers

Answer:

When a circuit breaker regularly trips or a fuse repeatedly blows, it is a sign that you are making excessive demands on the circuit and need to move some appliances and devices to other circuits. Or, it may indicate that your house has too few circuits and is in need of a service upgrade.

A 23. 6 g ball of clay is thrown horizontally to the right at 40. 4 m/s toward a 1. 70 kg block sitting at rest on a frictionless surface. The clay hits and sticks to the block.


What is the speed of the block and clay right after the collision?


Answer in m/s to three significant figures

Answers

Answer:

0.142 m/s

Explanation:

You solve it by conservation of momentum.

Before the impact the total momentum is, considering right the positive direction,

[tex]m_1v_1+m_2v_2 =6\cdot10^-^3\times 40.4\ kg\cdot m/s + 1.7\times 0 \ kg\cdot m/s =242.4\cdot 10^-^3\ kg\cdot m/s[/tex]

After the impact, we have a single body of mass [tex]m_1+m_2[/tex] and thus a single value of speed, V.

[tex](m_1+m_2)V =1.703 kg \cdot V[/tex]

Since no external forces are applied, the two quantities are equal after the impact. That allows us to solve for V

[tex]V= (242.4\cdot10^-^3 \ kg\cdot m/s )\div (1.703\ kg)=142.337\cdot10^-^3 m/s = 0.142 m/s[/tex]

A car’s tire rotates 5.25 times in 3 seconds. What is the tangential velocity of the tire?

Answers

The tangential velocity of the car's tire is the product of the angular velocity and radius of the car's tire which is 11(r) m/s.

Angular velocity of the tire

The angular velocity of the tire is the rate of change of angular displacement of the tire with time.

The magnitude of the angular velocity of the tire is calculated as follows;

ω = 2πN

where;

N is the number of revolutions per second

ω = 2π x (5.25 / 3)

ω =  11 rad/s

Tangential velocity of the tire

The tangential velocity of the car's tire is the product of the angular velocity and radius of the car's tire.

The magnitude of the tangential velocity is caculated as follows;

v = ωr

where;

r is the radius of the car's tire

v = 11r m/s

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1. What is one way that light waves differ from sound waves?

A. Light waves all have the same frequency..

B. Light waves travel by oscillation.

C. Light waves do not require a medium to propagate.

D. Light waves transfer energy.

2. Which best explains why high frequency electromagnetic waves are more likely to cause harm to living things?(1 point)

A. As a wave's frequency increases, more energy is carried by the wave in a given time period.

B. As a wave's frequency increases, less energy is carried by the wave in a given time period.

C. As a wave's frequency increases, a constant energy is carried by the wave in a given time period.

D. As a wave's frequency increases, the energy carried by the wave in a given time period is equal to zero.

3. How do the frequencies and the speeds of yellow light and blue light compare?

Answers

One way Light waves differ from sound waves it that it does not require a medium to propagate.

High frequency electromagnetic waves are more likely to cause harm because as a wave's frequency increases, more energy is carried by the wave in a given time period.

The frequency of yellow light is greater than that of blue light.

What is a Wave?

This is defined as a propagation of disturbances from place to place in a regular and organized way.

The answers provided above are therefore the most appropriate choices in this scenario.

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Answer: Light waves do not require a medium to propagate and As a wave's frequency increases, more energy is carried by the wave in a given time period.

Explanation:

At what constant velocity must a spacecraft travel from earth if it is to reach the star in 3. 7 years, as measured by travelers on the spacecraft?

Answers

The constant velocity that the spacecraft must travel is : 3.49 * 10⁸ m/s

Given data :

Distance of star from earth = 4.3 light years

Observers time = 3.7 years

Determine the constant velocity the spacecraft must travel

Observers time = 3.7 * 365 * 24 * 60 * 60

Distance of star from earth = 4.3 * 9.46 * 10¹⁵

The velocity the spacecraft must travel will be calculated using the equation

V = distance / time

   = ( 4.3 * 9.46 * 10¹⁵ ) / ( 3.7 * 365 * 24 * 60 * 60 )

   = 3.49 * 10⁸ m/s

Hence we can conclude that The constant velocity that the spacecraft must travel is : 3.49 * 10⁸ m/s

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Attached below is the missing detail related to the question

The constant velocity must the spacecraft travels from the earth will be 3.49×10⁸ m/sec.

What is velocity?

The change of distance with respect to time is defined as speed. Speed is a scalar quantity. It is a time-based component. Its unit is m/sec.

The given data in the problem is

Distance of earth from stars = 4.3 light year

The given time = 3.7 year

One year converted into the second as;

[tex]\rm 1 \ year = 3.7 \times 365 \ days \ \times 24 \ hour \times 60 \ minute \times 60 \ sec \\\\ 1 year = 116 \times 10^6 \ sec[/tex]

1 light-year into a kilometer as;

[tex]\rm 4.3 \ light year = 4.3 \times 9.46 \times 10^{15 metre} \\\\[/tex]

At what constant velocity must a spacecraft travel from the earth if it is to reach the star in 3. 7 years,

The velocity of the spacecraft's travel from the earth will be;

[tex]\rm V = \frac{d}{t} \\\\ V= \frac{4.3 \times 9.46 \times 10^{15}}{3.7 \times 365 \times 24 \times 60 \times 60 } \\\\\ V= 3.49 \times 10^8 \ m/sec[/tex]

Hence the constant velocity must the spacecraft travels from the earth will be  3.49×10⁸ m/sec.

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a
13. Chemical energy is a form of___________
energy.

Answers

Answer:

Potential energy.

Explanation:

Batteries are a form of chemical energy which  is stored in the bonds of molecules contained within the battery acid, batteries are a form of potential energy making chemical potential energy too.

The wavelengths of visible light vary from about 300 nm to 700 nm. what is the range of frequencies of visible light in a vacuum?

a) 90 hz to 210 hz
b) 9*10^10 hz to 2.1*10 hz
c) 4.28*10^5 hz to 1*10^6 hz
d) 4.29*10^14 hz to 1*10^15 hz

Answers

The range of frequencies of visible light in a vacuum with wavelength between 300 nm to 700 nm is determined as 4.29 x 10¹⁴ Hz to 1 x 10¹⁵ Hz.

Frequency of the visible light

The frequency of the visible light is determined  by using the following formulas relating speed of light and frequency of light.

c = fλ

where;

c is speed of lightf is frequency of lightλ is the wavelength

Frequency of light at 300 nm wavelength

f = c/λ

f = (3 x 10⁸) / (300 x 10⁻⁹)

f = 1 x 10¹⁵ Hz

Frequency of light at 700 nm wavelength

f = c/λ

f = (3 x 10⁸) / (700 x 10⁻⁹)

f = 4.29 x 10¹⁴ Hz

Thus, the range of frequencies of visible light in a vacuum with wavelength between 300 nm to 700 nm is determined as 4.29 x 10¹⁴ Hz to 1 x 10¹⁵ Hz.

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Which of these circuits has a voltmeter?
O
(A)
(B)
(C)
(D)
(E)
ОА А
OBB
Ос. с
ODD
О Е Е

Answers

Answer:

I think is o or mavey it could be D

Uranus and neptune have methane clouds but jupiter and saturn do not. Which factor explains why?.

Answers

Answer:

Temperature on Jupiter and Saturn are too high for methane to condense.

Explanation:

However, methane can condense on Uranus and Neptune because they are farther from the sun and hence colder.

If a star is 720 , 000 , 000 , 000 , 000 meters from Earth, how many seconds does it take light to travel from the Earth to the star

Answers

Answer:

anywhere between 100000 to about 400000 human years .

Explanation:

The reflection of a 10. 0 cm object appears to be 18 cm tall and 9 cm behind the mirror. What distance is the object from the mirror? cm.

Answers

The distance is the object from the mirror will be 5cm.

What is a mirror equation?

A mirror equation is an equation that relates object distance and image distance to focal length. It is often referred to as a mirror formula.

The object distance in a spherical mirror is the distance between the object and the pole of the mirror (u).

The given data in the problem is;

Image height = 18cm

Object height = 10cm

u is the object distance

v is the image distance = 9 cm

From the symmetry of the triangle;

[tex]\frac{image \ height }{object \ height} = \frac{v}{u} \\\\ \frac{18 }{10} = \frac{9}{u}\\\\ \rm u=\frac{90}{8} \\\\ u = 5\ cm[/tex],

Hence the distance is the object from the mirror will be 5cm.

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In your own words describe the physiological significance of the fev1/fvc ratio

Answers

Answer:

if you doctor suspect that you have COPD , they will calculate your fev1/fvc ratio . this represent the percentage of your lung capacity that you can explain in one second. the higher your percentage , the larger your lung capacity and the healthier your lungs

The ratio  [tex]\frac{FEV1}{FVC}[/tex]  indicates the diameter of an airway. The greater the value, the more quickly air can pass through the airway.

What is lung volume?

The volume of air in the lungs at different stages of the respiratory cycle is referred to as lung volumes and lung capacities. An adult human male's entire lung capacity is around 6 liters of air.

The ratio  [tex]\frac{FEV1}{FVC}[/tex]  indicates the diameter of an airway. The greater the value, the more quickly air can pass through the airway. As a result, the lower the resistance, the broader the airway becomes.

Hence the lower the resistance, the broader the airway becomes.

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12. Tom has two pendulums with him. Pendulum 1 has a ball of mass 0.1 kg attached to it and has a length of 5 m. Pendulum 2 has a ball of mass 0.5 kg attached to a string of length 1 m. How does mass of the ball affect the frequency of the pendulum? Which pendulum will have a higher frequency and why?

Show all of your work.

Answers

According to Hooke 's law

[tex]\\ \rm\rightarrowtail \nu=k\sqrt{\dfrac{\ell}{m}}[/tex]

[tex]\\ \rm\rightarrowtail \nu\propto \dfrac{1}{\sqrt{m}}[/tex]

Hence lower the mass higher the frequency

First ball will have a higher frequency

A piston in an automobile engine is in simple harmonic motion. Its amplitude of oscillation from the equilibrium (centered) position is ±6.83 cm and its mass is 2.708 kg.
Find the maximum velocity of the piston when the auto engine is running at the rate of 3590 rev/min.
Answer in units of m/s.

Answers

The maximum velocity of the piston when the auto engine is running at the given speed is 25.68 m/s.

Angular speed of the automobile

The angular speed of the automobile in radian per second is calculated as follows;

ω = 2πN

ω = 2π x (3590 /60 s)

ω = 375.94 rad/s

Maximum velocity

The maximum velocity of the piston is calculated using the following formula;

v(max) = Aω

v(max) = 0.0683 x 375.94

v(max) = 25.68 m/s

Thus, the maximum velocity of the piston when the auto engine is running at the given speed is 25.68 m/s.

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A magnifier allows one to look at a very near object by forming an image of it farther away. The object appears larger. To create a magnifier, one would use a.

Answers

In order to create a magnifier in convex lens, you should choose a short focal length that is lesser than 1 meter.

What is a convex lens?

A convex lens is also referred to as converging lens and it can be defined as a type of lens that typically causes parallel rays of light with respect to its principal axis to come to a focus (converge) and form a real image.

In Science, a magnifier refer to an optical instrument that allow us to look at a very near object because its image is generally formed farther away. Thus, the image of the object appears to be much larger.

In this context, you should choose a short focal length that is lesser than 1 meter when you want to create a magnifier in convex lens because the nearer the object is to the lens, the larger would be the image formed.

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Identify the aspects of the pictured graph that are missing or contain errors.

Answers

Answer:

ooops ignore this it wont let me leave this screen it does this weirdly s

Explanation:

A 100-cm long dipole is excited by a sinusoidally varying current with an amplitude i0=2 a. Determine the time average power radiated by the dipole if the oscillating frequency is 150 mhz

Answers

For A 100-cm long dipole is excited by a sinusoidally varying current with an amplitude i0=2 , the time average power radiated  is mathematically given as

P=0.1577w

What is the time average power radiated by the dipole if the oscillating frequency is 150 mhz?

Generally, the equation for the   is mathematically given as

[tex]\lambda =\frac{c}{f}[/tex]

Therefore

[tex]\lambda=\frac{3\times 10^{8}}{10^{6}}[/tex]

lambda=300m

In conclusion, for the power

[tex]P=40\pi^{2}(I_{0})^{2}(\frac{l}{\lambda})^{2}\\\\P=40* (3.14)^{2}\times6^{2} (\frac{1}{300})^{2}[/tex]

P=0.1577w

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The time-averaged power radiated by the dipole if the oscillating frequency is 150 MHz is 0.1577 w.

What is wavelength?

The distance between identical points (adjacent crests) in adjacent cycles of a waveform signal carried in space or down a wire is defined as the wavelength.

Given that the current is 2 amp, while the frequency is 150 MHz. Therefore, the wavelength can be written as,

[tex]\lambda = \dfrac cf = \dfrac{3 \times 10^8}{10^6} = 300\rm\ m[/tex]

Now, the power can be written as,

[tex]P=40 \pi^2 \times (I_o)^2 \times (\dfrac{l}{\lambda})^2\\\\P = 40 \times \pi ^2 \times 6^2 \times (\dfrac{1}{300})^2\\\\P = 0.1577\rm\ w[/tex]

Hence,  the time-average power radiated by the dipole if the oscillating frequency is 150 MHz is 0.1577 w.

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what is the result of ocean acidification

Answers

Answer:

Ocean acidification reduces the amount of carbonate, a key building block in seawater. This makes it more difficult for marine organisms, such as coral and some plankton, to form their shells and skeletons, and existing shells may begin to dissolve.

Answer:

The intake of carbon dioxide (CO2) from the atmosphere causes ocean acidification, which is the continual decline in the pH value of the Earth's oceans. The burning of fossil fuels by humans is the primary cause of ocean acidification. The amount of carbon dioxide absorbed by the ocean grows in lockstep with the amount of carbon dioxide in the atmosphere. This causes a sequence of chemical reactions in the seawater, which has a negative impact on the, however, their rine life that lives beneath the surface. Carbonic acid is formed when carbon dioxide dissolves in seawater (H2CO3). The pH value of the ocean surface is estimated to have decreased from approximately 8.25 to 8.14 between 1751 and 1996, representing a nearly 30% increase in H+ ion concentration in the world's oceans (note that the pH scale is logarithmic, so a change of one pH unit equals a tenfold change in H+ ion concentration). The pH of the ocean in 2020 will be 8.1, according to the National Oceanic and Atmospheric Administration.

Explanation:

does a five pound ball weigh more or less 40000 miles above sea level​

Answers

It would weigh less bc the higher you are the less gravity there is.

Consider a system consisting of three particles: m1 = 4 kg, vector v1 = < 10, -5, 15 > m/s, m2 = 9 kg, vector v2 = < -15, 5, -3 > m/s, m3 = 3 kg, vector v3 = < -24, 36, 18 > m/s.
a) what is the total momentum of this system?
b) what is the velocity of the center of mass of this system?
c) what is the total kinetic energy of this system?
d) what is the translational kinetic energy of this system?
e) what is the kinetic energy of this system relative to the center of mass?
one way to calculate krel is to calculate the velocity of each particle relative to the center of mass, by subtracting the center-of-mass velocity from the particle's actual velocity to get the particle's velocity relative to the center of mass, then calculating the corresponding kinetic energy, then adding up the three relative kinetic energies. however, there is a much simpler way to determine the specified quantity, without having to do all those calculations; think about what you know about the relationships among the various kinds of kinetic energy in a multiparticle system.

Answers

The answers to your questions are as listed below

A) The total momentum of the system is :  < - 167, 133, 87 >   kg m/s

B) Velocity of the center of mass of this system : < - 10.44 , 8.31, 5.44 > m/s

C) Total kinetic energy of the system : 5159.5 J  

D) Translational kinetic energy of the system :  1660.84 J

E) kinetic energy relative to the center of mass : 3498.66 J

Given data :

m₁ = 4 kg ,   V₁ = < 10, -5, 15 > m/s

m₂ = 9 kg,   V₂ = < -15, 5, -3 > m/s

m₃ = 3 kg    V₃ = < -24, 36, 18 > m/s.

A) Determine the total momentum of the system

Total momentum = Σ mv

= < 4*10 + 9*(-15) + 3*(-24), 4*(-5) + 9*5 + 3*36, 4*15 + 9 (-3) + 3*18 >

= < - 167, 133, 87 >   kg m/s

B) Velocity at the center of mass of this system

Velocity = < - 167 / 16 , 133/ 16, 87/ 16 >

              =  < - 10.44 , 8.31, 5.44 > m/s

C) Determine the total kinetic energy of the system

Total Kinetic energy = 1/2 m₁v₁² + 1/2 m₂v₂²  + 1/2 m₃v₃²  --- ( 1 )

where : v² = v₁² + v₂² + v₃²

therefore

Total kinetic energy = 700 + 1165.5 + 3294

                                  = 5159.5 J  

D) Determine the translational kinetic energy of the system

Translational kinetic energy ( Kcm ) = 1/2 ( m₁ + m₂ + m₃ ) * Velocity²

                                                           = 1/2 ( 16 ) * (  - 10.44² + 8.31² + 5.44² )

Hence translational kinetic energy = 1660.84 J

E) The Kinetic energy of the system relative to the center of mass

Krel = Ktotal - Kcm

       = 5159.5 - 1660.84

       = 3498.66 J

Hence we can conclude that the answers to your questions are as listed above.

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An empty corn silo in the shape of a cylinder is being filled with corn

Answers

The percent of the silo filled with corn at 10 hours is 90.98%.

What is silo?

Silos are used in order to maximize the grain storage life and preserve them. They are round and tall towers with high capacity for commercial or industrial purposes.  

As the silo is in shape of cylinder, volume of the cylinder is

V = πr²h

where r = d/2 = 19/2 =9.5 ft

and h = 32 ft

Substitute the values, we get the volume of silo,

V = 3.14 x (9.5)² x 32 = 9068.32 ft³

The silo is filled with the constant rate. After 10 hours, in silo, the amount of corn will be gone doubled as compared to that of in 5 hours.

Amount of corn after 10 hours = 4125 x 2 = 8250 ft³

Percentage of silo filled in 10 hours = (amount after 10 hrs / total amount) x 100

Substitute the values, we get

=(8250 /9068.32 ) x 100 %

=90.98 %

Thus, the percent of the silo filled with corn at 10 hours is 90.98%.

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What is the new period if the pendulum is taken to a planet that has 4 times the mass and 4 times the radius of earth

Answers

The new period of the pendulum when it is taken to the new planet is  double of its period on Earth.

Period of a pendulum

The period of a pendulum is given by the following formula;

[tex]T = 2\pi \sqrt{\frac{l}{g} }[/tex]

where;

g is acceleration due to gravity of the pendulumL is length of the pendulumAcceleration due to gravity of the new planet

The acceleration due to gravity of the new planet is calculated as follows;

[tex]g_E = \frac{GM_E}{R_E^2} = 9.81 \ m/s^2 \\\\g(new \ planet) = \frac{G(4M_E)}{(4R_E)^2} = \frac{4GM_E}{16R_E^2} = \frac{GM_E}{4R_E^2} = \frac{9.81}{4} = 2.45 \ m/s^2[/tex]

New period of the pendulum

[tex]T = 2\pi \sqrt{\frac{l}{g} } \\\\T =\frac{2\pi \sqrt{l} }{\sqrt{g} } \\\\T_1\sqrt{g_1} = T_2\sqrt{g_2} \\\\T_E\sqrt{g_E} = T\sqrt{g} \\\\T = \frac{T_E\sqrt{g_E}}{\sqrt{g} } \\\\T = \frac{T_E \times \sqrt{9.81} }{\sqrt{2.45} } \\\\T = 2T_E[/tex]

Thus, the new period of the pendulum when it is taken to the new planet is double of its period on Earth.

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All things being equal,
in which of the
following locations
would you expect to
find the deepest and
richest topsoil?
B. on a mountain top
A. in the Arctic
C. in a valley
D. on the side of a mountain

Answers

Answer:

C. In a valley .

.............................

If you have 10 ounces of meat, what percentage of the calories comes from fat if the meat is 90% lean?

Answers

Answer:

There are 602 calories in 10 ounces of Ground Beef (85% Lean / 15% Fat).  serving sizes of Ground Beef

Explanation:

hope this helps if not please let me now

From the top of a tall cliff of height y, a soccer ball is kicked horizontally so that it leaves the cliff with a velocity v. Assuming air friction is negligible, the speed of the ball just before it hits the ground is:

Answers

Answer:

[tex]\sqrt{v^{2} + 2\, g\, y}[/tex].

Explanation:

Apply the SUVAT equation [tex]{v_{1}}^{2} - {v_{0}}^{2} = 2\, a\, x[/tex] to the vertical component of the soccer ball's motion to find the vertical velocity right before the ball lands. In this equation:

[tex]v_{1}[/tex] represents the vertical velocity of the ball right before it lands (needs to be found);[tex]v_{0}[/tex] represents the initial vertical velocity of the soccer ball ([tex]0[/tex] in this question since the ball was initially travelling horizontally); [tex]a[/tex] represents the acceleration (equal to [tex]g[/tex] since air friction is negligible);[tex]x[/tex] represents the vertical displacement of this ball (in this question, this vertical displacement is equal [tex]y[/tex], the height of the cliff.)

Rearrange this equation to find an expression for the vertical velocity [tex]v_{1}[/tex] in terms of [tex]y[/tex] and [tex]g[/tex]:

[tex]\begin{aligned}v_{1} &= \sqrt{{v_{0}}^{2} + 2\, a\, x} \\ &= \sqrt{2\, g\, y}\end{aligned}[/tex].

Since air friction is negligible, the horizontal velocity of the ball would stay unchanged. Thus, the horizontal velocity of the ball would still be [tex]v[/tex] right before the ball lands.

Notice that these two components of velocity are perpendicular to one another. Thus, find the combined velocity of the ball right before landing could be found using Pythagorean's Theorem:

[tex]\sqrt{v^{2} + {v_{1}}^{2}} = \sqrt{v^{2} + 2\, g\, y}[/tex].

Other Questions
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