which technique of extrasolar planet detection can tell us about the orbital period of a planet?

Assuming both billiard balls have the same mass, conservation of momentum says

[tex]m\vec v_1 + m\vec v_2 = m{\vec v_1}\,' + m{\vec v_2}\,'[/tex]

where m = mass of both billiard balls, and v₁ and v₂ = their initial velocities, and v₁' and v₂' = their final velocities. The masses are the same so the exact value of m is irrelevant. The first ball has initial speed 5 m/s and the second is at rest, so

[tex]\left(5 \dfrac{\rm m}{\rm s}\right) \, \vec\imath = {\vec v_1}\,' + {\vec v_2}\,'[/tex]

After the collision, the first ball has speed 4.35 m/s and is moving at angle of 30° below the original path, so

[tex]{\vec v_1}\,' = \left(4.35\dfrac{\rm m}{\rm s}\right)\left(\cos(30^\circ) \, \vec\imath + \sin(30^\circ) \, \vec\jmath\right) \approx \left(3.77 \dfrac{\rm m}{\rm s}\right) \vec\imath + \left(-2.18 \dfrac{\rm m}{\rm s}\right) \vec\jmath[/tex]

Then the second ball has final velocity vector

[tex]{\vec v_2}\,' \approx \left(1.23 \dfrac{\rm m}{\rm s}\right) \vec\imath + \left(2.18 \dfrac{\rm m}{\rm s}\right) \vec\jmath[/tex]

so it moves with speed

[tex]\left\|{\vec v_2}\,'\right\| \approx \sqrt{\left(1.23\dfrac{\rm m}{\rm s}\right)^2 + \left(2.18\dfrac{\rm m}{\rm s}\right)^2} \approx \boxed{2.50 \dfrac{\rm m}{\rm s}}[/tex]

at an angle of

[tex]\theta \approx \tan^{-1}\left(\dfrac{2.18}{1.23}\right) \approx \boxed{60.5^\circ}[/tex]

or about 60.5° above the original line of motion.

the independent variable and the dependent variable.

Evaporation is a type of vaporization which usually occurs in liquid when molecules of that liquid transform into the gaseous phase.

 Evaporation causes cooling. This is because, when a molecule wants to evaporate, it requires heat to do so.

    This heat is derived from the surface from which the molecule is about to evaporate. The emission of heat from this surface results in the cooling of the surface left behind.

Liquid molecules are in constant random motion while possessing different velocities.

  Molecules which are near the surface possess higher velocities and kinetic energy escape from the surface.

  Since the average kinetic energy is a measure of temperature, it implies that the  temperature is lowered and hence a person who is soaking wet feels cold when evaporation  occurs.

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Answer:

The tilt of the Earth causes some places to be hit more by the sun's rays, while the topography affects wind travel.

Explanation:

Because of the way the Earth is tilted on its axis, some parts receive more heat due to being hit more directly by the sun's rays. This is the reason why the North pole is very cold since it doesn't get directly hit by the sun's rays. As for the topography, the way the wind travels is affected by mountains, and the temperature of winds are affected by the places the wind originated from. Also, high altitude places such as mountain summits are colder, while low altitude places are warmer. So, when an area is under direct sunlight, it causes warm climate, and when an area receives warm air because of its topography, it causes further heat.

The final speed of the combined masses is 0.21 m/s

Applying the law of conservation of momentum:

Total momentum before collision = Total momentum after collision.

⇒ Formula:

MU+mu = V(M+m).................. Equation 1

⇒ Where:

From the question,

⇒ Given:

⇒ Substitute these values into equation 1

⇒ Solve for V

Hence the final speed of the combined masses is 0.21 m/s

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Answer:

500 J.

Explanation:

Work done = force * distance

= 25 * 20

= 500 Joules.

Answer:

try 2.4136 as an answer/ good luck

Applying Charles law

[tex]\\ \sf\Rrightarrow \dfrac{V_1}{T_1}=\dfrac{V_2}{T_2}[/tex]

[tex]\\ \sf\Rrightarrow \dfrac{100}{313}=\dfrac{V_2}{263}[/tex]

[tex]\\ \sf\Rrightarrow V_2=\dfrac{26300}{313}[/tex]

[tex]\\ \sf\Rrightarrow V_2=84.02ml[/tex]

Answer:

a 5 kilogram mass, at a height of 3 meters, while acted on by Earth's gravity would have 147.15 Joules of potential energy, PE = 3kg * 9.81 m/s2 * 5m = 147.15 J.

Explanation:

The final velocity of an object that starts from rest and travels for 5 seconds at an acceleration of 4.3 m/s² is 21.5m/s.

EQUATION OF MOTION:

The final velocity of a moving object can be calculated by using one of the equations of motion as follows:

V = u + at

Where;

According to this question,

v = 0 + 4.3(5)

v = 21.5m/s.

Therefore, the final velocity of an object that starts from rest and travels for 5 seconds at an acceleration of 4.3 m/s² is 21.5m/s.

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Answer:

TRUE !!

Explanation:

An atom is the smallest particle of an element

Start from the top and go 7 down then go to the right 9 times and there you should fine the letter "one"

Answer:

Explanation:

The kinetic energy of an object can be found by using the formula

[tex]k = \frac{1}{2} m {v}^{2} \\ [/tex]

m is the mass in kg

v is the velocity in m/s

From the question

m = 1500 kg

v = 35 m/s

We have

[tex]k = \frac{1}{2} \times 1500 \times {35}^{2} \\ = 750 \times 1225 \\ = 918750[/tex]

We have the final answer as

Hope this helps you

Answer:

When an object is balanced, about a pivot, the total clockwise moment must be equal to the total anticlockwise moment about that pivot.

Hope that helps.

When an object is balanced about a pivot, the total clockwise moment must be equal to the total anticlockwise moment.

Clockwise involves turning to the right while going in the direction of a clock's hands. The moment is referred to as a clockwise moment if the force acting on a body rotates the body clockwise with regard to the axis of rotation.

On the other hand, the moment is referred to as an anti-clockwise moment if the force rotates the body in the opposite direction. The clock face rule can be used to determine this magnet's polarity.

The face of the loop will display the North Pole if the current is flowing counterclockwise. On the other hand, if the current is moving counterclockwise, the South Pole is visible on the loop's face.

Therefore, the total clockwise and total counterclockwise moments must match when an object is balanced about a pivot.

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Ek = 1/2 mv^2

9 × 10^4 = 1/2 × 800 × v^2

9 × 10^4/400 = 400 v^2 / 400

9 × 10^4/400 = v^2

√225 = v

15 ms⁻¹ = v

That's the only way I know how to work it out

I think in this case velocity and speed would be considered the same because me

s = d/t and v=d/t

one is distance travelled and the other is displacement of a body

The momentum of the water balloon at the given speed is 7.2 kgm/s.

The given parameters:

The momentum of the water balloon is calculated as follows;

P = mv

Substitute the given values of mass and velocity as follows;

P = 0.4 x 18

P = 7.2 kg m/s.

Thus, the momentum of the water balloon at the given speed is 7.2 kgm/s.

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f(3) represents the number of additional square feet the construction crew has paved after 3 hours, not including the initial paved amount.

Mathematical models are representations of real situations. Models often serve the purpose of prediction and can help to explain and simplify certain mathematical problems.

The model; f(x) = 300x + 1,000 represents the number of additional square feet that can be paved in an hour after 1,000 square feet has already been paved.

From the above we can see that the correct answer is; "900 square feet; f(3) represents the number of additional square feet the construction crew has paved after 3 hours, not including the initial paved amount."

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The final temperature of water is equal to 50.9999°C

Given the following data:

To determine the final temperature of water:

Mathematically, quantity of heat is given by the formula;

[tex]Q=mc\theta[/tex]

Where:

Substituting the given parameters into the formula, we have;

[tex]5000=2.38892 \times 10^{-2}\times 4186 \times \theta\\\\5000=100.0001912 \theta\\\\ \theta=\frac{5000}{100.0001912} \\\\ \theta=49.9999^{\circ}C[/tex]

For the final temperature:

[tex]\theta = T_2 - T_1\\\\T_2 = \theta+T_1\\\\T_2 = 49.9999 + 50[/tex]

Final temperature = 50.9999°C

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Answer:

Flow is proportional to change in pressure and inversely proportional to resistance.

Answer:

Slinky is the correct answer.

The relationship of the photoelectric effect and the de Broglie expression allows us to find the result for the wavelength of the ejected electrons is:

The photoelectric effect was explained by Einstein assuming that the light rays behave like particles called photons, therefore the

                 [tex]E_{photon} = K + \Phi[/tex]  

where [tex]E_{photon}[/tex] is the energy of the photon given by the Planck relation, K is the kinetic energy of the ejected electrons and Ф the work function of the material.

The Planck relationship states that the energy of the photons is proportional to the frequency.

            [tex]E_{photon} = h f[/tex]

Where h is Planck's constant and f is the frequency of the photons.

They indicate The work function is Ф= 2.25 10⁻¹⁹ J, the energy of the photon [tex]E_{photon}[/tex] = 4.52 10⁻¹⁹ J, let's find the kinetic energy of the ejected electrons.

            [tex]K = E_{photon} - \Phi[/tex]  

Let's calculate.

           K = (4.52-2.25) 10⁻¹⁹

           K = 2.27 10⁻¹⁹ J

Kinetic energy is the energy of motion and is given by the relationship.

          [tex]K = \frac{p^2}{2m}[/tex]  

The wave-particle duality was established by de Broglie with the relation.

         [tex]p = \frac{h}{\lambda }[/tex]  

Let's replace.

         [tex]K = \frac{1}{2m} (\frac{h}{\lambda} )^2 \\\lambda^2 = \frac{h^2}{2m K}[/tex]

let's calculate.

        [tex]\lambda^2 = \frac{(6.63 \ 10^{-34})^2 }{2 \ 9.1 \ 10^{-31 } \ 2.27 \ 10^{-19}}[/tex]

        [tex]\lambda = \sqrt{1.06397 \ 10^{-18}}[/tex]

        λ  = 1.03 10⁻⁹m

In conclusion with the relationship of the photoelectric effect and the de Broglie expression we can find the result for the wavelength of the ejected electrons is:

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Answer:

Density of the mixture = 855.56kgm-3

Explanation:

Density = Mass / Volume

Volume of Liquid X = 0.5m³

Density of Liquid X = 900kgm-3

Mass of Liquid X = Density × Volume

= 900kgm-3 × 0.5m³ = 450kg

Volume of Liquid Y = 0.4m³

Density of Liquid Y = 800kgm-3

Mass of Liquid Y = Density × Volume

= 800kgm-3 × 0.4m³= 320kg

As X and Y are mixed, we add their masses and volumes together:

Mass = 770kg

Volume = 0.9m³

Now we can find the density of the mixture:

Density = 770kg / 0.9m³ = 855.56kgm-3 (rounded to the 2nd decimal)

The type of bond found in pure gold is metallic bonding, indicated by metallic bonds. Therefore option A is correct.

Metallic bonding occurs between metal atoms, such as gold, and is characterized by the sharing of electrons among a sea of delocalized electrons.

In metallic bonds, the valence electrons of metal atoms are not strongly bound to any particular atom but are free to move throughout the metal lattice.

This sharing of electrons gives rise to properties such as high electrical and thermal conductivity, malleability, and ductility, which are characteristic of metals like gold.

Unlike ionic or covalent bonds, metallic bonds do not involve the transfer or sharing of electrons between different elements.

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Using Joules law

[tex]\\ \sf\Rrightarrow H=VIt[/tex]

[tex]\\ \sf\Rrightarrow H=5(2)(1)[/tex]

[tex]\\ \sf\Rrightarrow H=10Kwh[/tex]

Answer: 25N to the right

Explanation: 35N - 10N = 25N

[tex] = \frac{1}{2} \times 0.008 \times 420J \\ = 1.68J[/tex]

[tex]1.68J = \frac{1}{2} \times 75 \: kg \times v2 \\ = > v2 = \frac{1.68 \times 2}{75} m {s}^{ - 1} \\ = 0.0448 \: m \: {s}^{ - 1} [/tex]

Answer:

0.0448 m/s

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

1. 60 kg m/s

2. 2.4 kg

3. none they both have same momentum

Answer:

  4/3 m/s

Explanation:

Assuming momentum is conserved, the sum of products of mass and speed before the collision is the same as after:

  (2000 kg)(4 m/s) +(4000 kg)(0 m/s) = (2000 +4000 kg)(Vt)

  Vt = (8000 kg·m/s)/(6000 kg) = 4/3 m/s

The speed of the combined objects after the collision is 4/3 m/s.