has been proposed to use an array of infrared telescopes spread over thousands of kilometers of spaceto observe planets orbiting other stars. Consider such an array with an effective diameter of 6000 km, whichobserves infrared radiation at a wavelength of 10m. If it is used to observe a planet orbiting the star 70Virginis, which is 59 light years from our solar system, what is the size of the smallest details that the arraymight resolve on the planet

Answers

Answer 1

Answer:

[tex]\triangle x=1.135 *10^9km[/tex]

Explanation:

From the question we are told that:

Diameter of array[tex]d=6000km \approx 6000*10^3[/tex]

Infrared wavelength [tex]\lambda =10m[/tex]

Distance of planet [tex]d=59 light\ years \approx 55.82*10^{16}m[/tex]

 

Generally the equation for Diffraction is mathematically given by

 [tex]sin\theta =1.22\frac{\lambda}{D}[/tex]

Given that

 [tex]sin\theta=\frac{\triangle x}{R}[/tex]

Therefore

 [tex]\frac{\triangle x}{R}=1.22\frac{\lambda}{D}[/tex]

 [tex]\triangle x=1.22\frac{R \lambda}{D}[/tex]

 [tex]\triangle x=1.22\frac{10 *55.82*10^{16}}{6000*10^3}[/tex]

 [tex]\triangle x=1.135 *!0^1^2m[/tex]

 [tex]\triangle x=1.135 *10^9km[/tex]


Related Questions

1. A train is moving north at 5 m/s on a straight track. The engine is causing it to accelerate northward at 2 m/s^2.
How far will it go before it is moving at 20 m/s?
A) 83
B) 43
C) 39
D) 94
E) 20

Answers

Answer:

(D) x = 93.8 m

Explanation:

v^2 = v0^2 + 2ax

(20 m/s)^2 = (5 m/s)^2 + 2(2 m/s^2)x

Solving for x,

x = 93.8 m

2..Read the following statements carefully and choose the correct option
Statement 1: Angle of incidence is equal to angle of reflection
Statement 2: Angle between incident ray and reflected ray is double that of the
Angle of incidence.
A) Statement (1) is correct while statement (2) is incorrect
B) Statement (2) is correct while statement (1) is incorrect
C) Both statements are correct
D) Both statements are incorrect

Answers

Answer:

statement 1 is correct

2 not sure

Explanation:

A candle is placed 50 cm from a diverging lens with a focal length of 28. What is the image distance in cm.

Answers

Answer:

v = -17.94 cm

Explanation:

Given that,

The candle is placed at a distance of 50 cm, u = -50 cm

The focal length of the diverging lens, f = -28 cm (negative in case of a concave lens)

We need to find the image distance. We know that the lens formula is as follows:

[tex]\dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{f}\\\\\dfrac{1}{v}=\dfrac{1}{f}+\dfrac{1}{u}\\\\\dfrac{1}{v}=\dfrac{1}{(-28)}+\dfrac{1}{(-50)}\\\\v=-17.94\ cm[/tex]

So, the image distance is equal to 17.94 cm.

Which electromagnetic wave has the shortest wavelength?



Which electromagnetic wave would have a wavelength approximately the size of the tip of a pencil?



Which electromagnetic wave has the longest wavelength?

Answers

Answer:

shortest - gamma Ray's

size of a pencil tip : most likely microwaves

longest - radio waves

Gamma rays have the shortest wavelength whereas Radio waves have the longest wavelength. The wave whose wavelength is about the size of the tip of a pencil is infrared ray.

What is an Electromagnetic spectrum?

The whole electromagnetic waves are divided into several classes based on their frequencies or energies as follows, in the order of increasing frequency:

Radio waves

Microwaves

Infrared

Visible

Ultraviolet

X-rays

Gamma rays

The Gamma rays are the shortest wavelength group with frequencies greater than 3 × 10²⁰ Hz.

The Radio waves are the longest wavelength group. Their frequency is lower than 3 × 10⁷ Hz.

The tip of a pencil is about 0.5mm in width.

Calculate the frequency of the wave whose wavelength is about the size of the tip of a pencil i.e. λ = 0.5 mm,

ν = 3×10⁸/(0.5×10⁻³) = 6×10¹¹ Hz.

The infrared rays have frequencies in the range of 3×10¹¹ Hz to 3×10¹³ Hz. So, the wave is infrared.

Infrared waves have a wavelength about the tip of a pencil.

Learn more about the electromagnetic spectrum here

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Saved Which of the following is NOT an important function of facial display? Multinio Choic
A. emotion
B. attractiveness
c. Primacy
d. identity

Answers

Answer:

C

Explanation:

Primacy means being first or important so thats not an important facial display as the others.

A 2:2 kg toy train is con ned to roll along a straight, frictionless track parallel to the x-axis. The train starts at the origin moving at a speed of 1:6m=s in the +x direction, and continues until it reaches a position 7:5m down the track from where it started. During its journey, it experiences a force pointing in the same direction as the vector 0:6 +0:8 , with magnitude initially 2:8N and decreasing linearly with its x-position to 0N when the train has finished its journey.

Required:
a. Calculate the work done by this force over the entire journey of the train.
b. Find the speed of the train at the end of its journey.

Answers

Answer:

a) 10.51 J

b) 3.48 m/s

Explanation:

Given data :

mass of train ( M ) = 2.2 kg

Given initial velocity ( u ) = 1.6 m/s

a) calculating work done by the force over the journey of the train

F = mx + b  ------ ( 1 )

m = slope  = ( Δ f / Δ x ) = 2.8 / -7.5 = - 0.373 N/m

x = distance travelled on the x axis by the train = 7.5 m

F = force experienced by the train = 2.8 N

x = 0

∴ b = 2.8

hence equation 1 can be written as

F = ( -0.373) x + 2.8   ----- ( 2 )

hence to determine the work done by the force

W   = [tex]\int\limits^7_0 { ( -0.373) x + 2.8 )} \, dx[/tex]     Note:  the limits are actually 7.5 and 0

∴ W ( work done ) = -10.49 + 21 = 10.51 J

b) calculate the speed of the train at the end of its journey

we will apply the work energy theorem

W = 1/2 m*v^2  -  1/2 m*u^2

∴ V^2 = 2 / M ( W + 1/2 M*u^2 )  ( input values into equation )

 V^2 = 12.11

hence V = 3.48 m/s

5. A 6.0-kilogram mass is moving with a speed of 2.0 m/s. What is the kinetic energy of the mass?

Answers

Answer:

K.E. = ½ × mv²

= ½ × 6 × (2)²

= ½ × 6 × 4

= 3 × 4

= 12 J

The fictional rocket ship Adventure is measured to be 65 m long by the ship's captain inside the rocket.When the rocket moves past a space dock at 0.5c. As rocket ship Adventure passes by the space dock, the ship's captain flashes a flashlight at 1.20-s intervals as measured by space-dock personnel.

Required:
How often does the flashlight flash relative to the captain?

Answers

Answer:

1.04 s

Explanation:

The computation is shown below:

As we know that

t = t' × 1 ÷ (√(1 - (v/c)^2)

here

v = 0.5c

t = 1.20 -s

So,

1.20 = t' × 1 ÷ (√(1 - (0.5/c)^2)

1.20 = t' × 1 ÷ (√(1 - (0.5)^2)

1.20 = t' ÷ √0.75

1.20 = t' ÷ 0.866

t' = 0.866 × 1.20

= 1.04 s

The above formula should be applied

Why would the kinetic energy at the bottom of the track be less than the potential energy at the top of the track?

Answers

Answer:

This is because of friction and heat lost.

Explanation:

stored energy is _________ ___________
kinetic energy
energy in motion
potential energy

Answers

Answer:

Potential energy

Explanation:

Potential energy is stored energy

potential energy is the answer

A running Marites launched the egg she
stole as she was about to be caught with
a velocity of 25 m/s in a direction making
an angle of 20° upward with the
horizontal
a) What is the maximum height reached by
the egg?
b) What is the total flight time (between
launch and touching the ground) of the
egg?
c) What is the horizontal range (maximum
* above ground) of the egg?
d) What is the magnitude of the velocity
of the egg just before it hits the ground?

Answers

Answer:

a)   y = 3.73 m,  b)  t = 1.74 s,  c)  R = 40.99 m,

d) vₓ  = 23.49  m/s,   v_y = -8.5 m / s

Explanation:

This is a projectile launching exercise, we start by breaking down the initial velocity

          sin θ = v_{oy} / v₀

          cos θ = v₀ₓ / v₀

          v_{oy} = v₀ sin θ

          v₀ₓ = v₀ cos θ

          v_{oy} = 25 sin 20 = 8.55 m / s

          v₀ₓ = 25 cos 20 = 23.49 m / s

a) when the egg reaches the maximum height its vertical speed is zero

          v_y² = v_{oy}² - 2 g y

          0 = v_[oy}² - 2g y

           y = v_{oy}² / 2g

          y = [tex]\frac{8.55^2}{2 \ 9.8 }[/tex]

          y = 3.73 m

b) flight time

          y = v_{oy} t - ½ g t²

the time of flight occurs when the body reaches the ground y = 0

          0 = (v_{oy} - ½ g t) t

         

The results are

          t₁ = 0s        this time is for using the body star

          v_{oy} - ½ g t = 0

           t = [tex]\frac{2v_{oy}^2}{g}[/tex]

           t = 2 8.55 / 9.8

           t = 1.74 s

c) the range

           R = v₀² sin 2θ / g

           R = 25² sin (2 20) / 9.8

           R = 40.99 m

d) speed at the point of arrival

horizontal speed is constant

           vₓ = v₀ₓ = 23.49  m/s

vertical speed is

           v_y = Iv_{oy} - g t

           v_y = 8.55 - 9.8  1.74

           v_y = -8.5 m / s

Carbon-14 is the typical radioisotope used to date materials; however, it has a limitation to 40,000 years. A scientist who wants to date materials older than 40,000 years would most likely use which radioisotope?

Answers

Answer:

the decay of uranium ending in lead,  of potassium (40K) that becomes argon,  the decay of rubidium

Explanation:

For the radioactive dating process, a material is needed that has a known average life time and that we can know the amount of material at a given moment,

In the case of carbon 14 (14C), living beings stop capturing it from the air and plants when they die, so knowing the amount they currently have, it is possible to calculate the time in which they stopped absorbing, but the life time average is 5730 years, the maximum time that can be used is up to about 10 average visa times

To analyze extra samples have high half-life times

* the decay of uranium ending in lead

* the decay of potassium (40K) that becomes argon T1 / 2 = 1,251 10⁹ years

* the decay of rubidium (87Ru) which becomes strontium T1 / 2 = 4.92 10¹⁰ years

What makes a 10 year old girl perfect?

Answers

Answer:

kindness

Explanation:

A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s. During a 5.0-s interval the angular velocity increases to 40 rad/s. Assume that the angular acceleration was constant during the 5.0-s interval. How many revolutions does the wheel turn through during the 5.0-s interval ( in revelations)? Hint: You need to use one of the equations of constant angular acceleration that independent of angular acceleration.

Answers

Answer:

The appropriate solution is "23.87 rev".

Explanation:

The given values are:

Initial angular velocity,

[tex]\omega_i=20 \ rad/s[/tex]

Final angular velocity,

[tex]\omega_f=40 \ rad/s[/tex]

Time taken,

[tex]t = 5.0 \ s[/tex]

If, α be the angular acceleration, then

⇒  [tex]\omega_f=\omega_i+\alpha t[/tex]

or,

⇒  [tex]\alpha t=\omega_f-\omega_i[/tex]

⇒  [tex]\alpha=\frac{\omega_f-\omega_i}{t}[/tex]

On substituting the values, we get

⇒     [tex]=\frac{40-20}{5.0}[/tex]

⇒     [tex]=\frac{20}{5.0}[/tex]

⇒     [tex]=4 \ rad/s^2[/tex]

If, ΔФ be the angular displacement, then

⇒  [tex]\Delta \theta=\omega_i t+\frac{1}{2} \alpha t^2[/tex]

On substituting the values, we get

⇒        [tex]=[(20\times 5.0)+(\frac{1}{2})\times 4\times (5.0)^2][/tex]

⇒        [tex]=100+50[/tex]

⇒        [tex]=150[/tex]

On converting it into "rev", we get

⇒  [tex]\Delta \theta=(\frac{150}{2 \pi} )[/tex]

⇒        [tex]=23.87 \ rev[/tex]

A long time ago on top of a mountain, the rocks were jagged and pointy. Over thousands of years, the rocks have become smooth.

What process explains this change?


pulling

weathering

depositing

eroding

Answers

Answer:

Eroding

Explanation:

A long time ago on top of a mountain, the rocks were jagged and pointy. Over thousands of years, the rocks have become smooth. The process explains this change is Eroding. Hence, Option D is the correct answer.

What is Erosion?

Erosion is  a  process  of  eroding some solids by wind, water and other  natural  agent  while  weathering  is  breaking  down  of  rocks, soil  and  minerals.

 

The  different types of Erosion includes,

Gully erosionsheet  erosionRill  erosionsheet  erosion

These factors that will contribute to the rate of water erosion includes the climatic factor (rainfall amount, intensity and frequency).

TopographySoil coverSoil properties

Mass wasting erosion if it is a type of erosion but not by water. It is a type of erosion that is generated mainly by the effect of gravity. It is also called mass movement, in which the material detaches from an inclined surface and falls as a result of gravity.

Here, A long time ago on top of a mountain, the rocks were jagged and pointy. Over thousands of years, the rocks have become smooth. The process explains this change is Eroding. Hence, Option D is the correct answer.

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A level of
class one
has a length of
4m
and is
able
to lift
a load of 40kg with a force of 40N. Find
the position Of
fulcrum.

Answers

Answer:

x = 2 meters.

Explanation:

Let the position (distance) of fulcrum to the load be x.

Given the following data;

Load = 40 kg

Effort (force) = 40 Newton

Effort arm = 4 - x

To find the position of the fulcrum, we would use the expression;

Effort * effort arm = load * load arm

40 * (4 - x) = 40 * x

160 - 40x = 40x

160 = 40x + 40x

160 = 80x

x = 160/80

x = 2 meters

Therefore, the position (distance) of fulcrum to the load is 2 meters.

please help, no links please! I dont understand stand this question and im going to cry

Which part of this system is in the gas phase?

Answers

Answer:

I'm pretty sure its helium

The air Inside the balloon is in the gas phase

Why don’t the northern and Southern Hemisphere experience summer at the same time?

Answers

Answer:

It is because of the tilt of the earth.

Explanation:

the earth is tilted at 23.5 degrees. this makes it so that either the northern or southern hemisphere will be exposed to more rays from the sun. In the areas that are getting more rays from the sun, it gets warmer.  Think about it like this, because the earth is tilted, part of it is more in the shade and part of it is more in the light. And its colder in the shade, so thats why seasons happen and why they dont happen at the same time.


People, animals, and all matter on Earth are

A. drawn toward the center of Earth by the planet's gravity

B. drawn toward other matter on Earth like the trees and the buildings, since all matter has gravity

C. not affected by Earth's gravity because people are so small in
comparison to the planet

D. held to Earth's surface by their own gravity

Answers

Answer:

A

Explanation:

To answer this, we can use process of elimination.

B: This question states that all matter has gravity. This is not correct. All matter is *effected* by gravity, but we do not have gravity inside of us.

C: If this were the case, we would all be floating off into space.

D: Same issue as question B.

Careful measurements reveal that a star maintains a steady apparent brightness at most times except that at precise intervals of 127 hours the star becomes dimmer for about 4 hours. The most likely explanation is that Careful measurements reveal that a star maintains a steady apparent brightness at most times except that at precise intervals of 127 hours the star becomes dimmer for about 4 hours. The most likely explanation is that:________

a. the star is a white dwarf.
b. the star is periodically ejecting gas into space, every 127 hours.
c. the star is a Cepheid variable.
d. the star is a member of an eclipsing binary star system.

Answers

Answer:

d. the star is a member and also a part of an eclipsing binary star system.

Explanation:

If any star happens to be brighter for an extended period of time, however, at some times, it becomes dimmer, is due to the fact that the star is being overshadowed (hiding behind another star that is known as eclipse).

The above-mentioned eclipsing binary star system is essentially what has been defined. It occurs when two stars' orbit planes are so similar that one star will obscure (the light) of the other.

Thus, option D is correct.

A 0.5kg ball of clay originally moving at 6 m/s strikes a wall and comes to rest in 0.25s, what is the magnitude of the impulse given to the ball of clay?
A) 0.75 kg m/s
B) 1.5 kg m/s
C) 3.0 kg m/s
D) 12 kg m/s

Answers

Answer:

C I did USA testprep

Explanation:

8. What is the mass and charge of a proton?
A. 1 amu, no charge
B. 1 amu, charge of +1
C. Mass of O, charge of -1
D. None of the above

Answers


B.

Step By Step Explanation:

Can someone take there time and answer this :)

Answers

Answer: I think B.)

Explanation:

the answer is D, because if there are the exact same organisms that are extinct in these two places, that means that they must have started at a similar place that no longer is connected.

15 points!

a. Calculate the electric potential energy stored in a 1.4 x 10-7 F capacitor
that stores 3.40 x 10-6 C of charge at 24.0 V.

Answers

Answer:

[tex]4.12\times 10^{-5}\ J[/tex].

Explanation:

Given that,

Capacitance, [tex]C=1.4\times 10^{-7}\ F[/tex]

Charge stored in the capacitor, [tex]Q=3.4\times 10^{-6}\ C[/tex]

We need to find the electric potential energy stored in the capacitor. The formula for the electric potential energy stored in the capacitor is given by :

[tex]E=\dfrac{Q^2}{2C}[/tex]

Put all the values,

[tex]E=\dfrac{(3.4\times 10^{-6})^2}{2\times 1.4\times 10^{-7}}\\\\=4.12\times 10^{-5}\ J[/tex]

So, the required electric potential eenergy is equal to [tex]4.12\times 10^{-5}\ J[/tex].

Earth's neighboring galaxy, the Andromeda Galaxy, is a distance of 2.54×107 light-years from Earth. If the lifetime of a human is taken to be 90.0 years, a spaceship would need to achieve some minimum speed vmin to deliver a living human being to this galaxy. How close to the speed of light would this minimum speed be? Express your answer as the difference between vmin and the speed of light c.

Answers

Answer:

[tex]0.0018833\ \text{m/s}[/tex]

Explanation:

[tex]d[/tex] = Distance of Andromeda Galaxy from Earth = [tex]2.54\times 10^7\ \text{ly}[/tex]

[tex]t[/tex] = Time taken = [tex]90\ \text{years}[/tex]

[tex]c[/tex] = Speed of light = [tex]3\times 10^8\ \text{m/s}[/tex]

We have the relation

[tex]t=t_o\sqrt{1-\dfrac{v^2}{c^2}}\\\Rightarrow 90=2.54\times 10^7\sqrt{1-\dfrac{v^2}{c^2}}\\\Rightarrow \dfrac{90^2}{(2.54\times 10^7)^2}=1-\dfrac{v^2}{c^2}\\\Rightarrow 1-\dfrac{90^2}{(2.54\times 10^7)^2}=\dfrac{v^2}{c^2}\\\Rightarrow v=c\sqrt{1-\dfrac{90^2}{(2.54\times 10^7)^2}}[/tex]

[tex]c-v=c(1-\sqrt{1-\dfrac{90^2}{(2.54\times 10^7)^2}})\\\Rightarrow c-v=3\times 10^8(1-\sqrt{1-\dfrac{90^2}{(2.54\times 10^7)^2}})\\\Rightarrow c-v=0.0018833\ \text{m/s}[/tex]

The required answer is [tex]0.0018833\ \text{m/s}[/tex].

A fisherman notices that his boat is moving up and down periodically without any horizontal motion, owing to waves on the surface of the water. It takes a time of 2.00 s for the boat to travel from its highest point to its lowest, a total distance of 0.600 m . The fisherman sees that the wave crests are spaced a horizontal distance of 6.40 m apart.

Required:
a. How fast are the waves traveling?
b. What is the amplitude of each wave?
c. If the total vertical distance traveled by the boat were 0.30 m but the other data remained the same, how would the answers to parts (a) and (b) be affected?

Answers

Answer:

a. Speed = 1.6 m/s

b. Amplitude = 0.3 m

c. Speed = 1.6 m/s

Amplitude = 0.15 m

Explanation:

a.

The frequency of the wave must be equal to the reciprocal of the time taken by the boat to move from the highest point to the highest point again. This time will be twice the value of the time taken to travel from the highest point to the lowest point:

frequency = [tex]\frac{1}{2(2\ s)}[/tex] = 0.25 Hz

The wavelength of the wave is the distance between consecutive crests of wave. Therefore,

Wavelength = 6.4 m

Now, the speed of the wave is given as:

Speed = (Frequency)(Wavelength)

Speed = (0.25 Hz)(6.4 m)

Speed = 1.6 m/s

b.

Amplitude is the distance between the mean position of the wave and the extreme position. Hence, it will be half the distance between the highest and lowest point:

Amplitude = (0.5)(0.6 m)

Amplitude = 0.3 m

c.

frequency = [tex]\frac{1}{2(2\ s)}[/tex] = 0.25 Hz

Speed = (Frequency)(Wavelength)

Speed = (0.25 Hz)(6.4 m)

Speed = 1.6 m/s

Amplitude = (0.5)(0.3 m)

Amplitude = 0.15 m

A geologist notices that a river is eroding its valley at a constant rate. Knowing the height of the valley walls, how could the geologist figure out when the river started carving the valley?
A.
Count growth rings of trees growing on the valley floor.
B.
Divide the height of the valley walls by the rate of erosion.
C.
Fill up the river valley with rocks, and time how long it takes the rocks to wash out.
D.
Sit and observe the river for a few hours until the valley walls double in height.

Answers

Answer:

B.

Divide the height of the valley walls by the rate of erosion.

Explanation:

There is a relationship between the rate of erosion and the hieght at which it is eroded according to Newton's law of motion. In the case of the scenario above, the best way to determine the time the river started carving the valley would be the division of the height of the valley walls by the rate of erosion.

19. Using the formula V - IX R, find the voltage in an electrical component with a current of 2 A, and a resistance of 5 omega

O A 20 v
O 8.5v
O C. 2.5 V
O D. 10 v

Answers

Answer:

B

Explanation:

Answer:

B

Explanation:

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What is a negative effect of increased carbon dioxide within the carbon cycle?

Answers

Answer:

Explanation:

Carbon dioxide controls the amount of water vapor in the atmosphere and thus the size of the greenhouse effect. Rising carbon dioxide concentrations are already causing the planet to heat up.

What is surface tension ​

Answers

Answer:

Surface tension is,  the surface where the water meets the air, water molecules cling even more tightly to each other.

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