Answer:
L = 5.68 10¹⁷ m
Explanation:
The resolution of the telescope is given by diffraction
a sin θ = m λ
Where a is the separation of the linear slits, λ the wavelength, m an integer that determines the order of diffraction
In this case, suppose that the premieres meet Rayleigh's criteria, which establishes that the central maximum of the diffraction of an object coincides with the first minimum of diffraction of the second object. In this case m = 1
sin θ = λ / a
In the case of circular openings, polar coordinates must be used, so the equation is
sin θ = 1.22 λ / D
Where D is the diameter of the lens or tightness. Since the distances are very large and the small angles we can approximate the sine to the radian angle value
θ = 1.22 λ / D
Let's use trigonometry to find the angle. We have the separation of the premieres y = 3.7 10¹¹ m and
tan θ = y / L
θ = y / L
Let's replace
y / L = 1.22 λ / D
L = y D / 1.22 λ
calculate
L = 3.7 10¹¹ 1.03 / (1.22 550 10⁻⁹)
L = 5.68 10¹⁷ m
Hey :)
The water potential of pure water<span> in an open container is zero because there is no solute and the pressure in the container is zero</span>
The Average velocity for the bacterium is 0.75 unit/sec.
<u>Explanation:</u>
The given values are in the vector form
Where,
dS = distance covered
dT = time interval
Now, to calculate distance covered, we have

&

d S=(4.6 i+1.9 k)-(2.2 i+3.7 j - 1.2 k)
d S=(4.6-2.2) i+(0-3.7) j+(1.9+1.2) k
d S=2.4 i-3.7 j+3.1 k
Now, putting these values in the standard formula to evaluate the average velocity, we get;


As dT=7.2 sec
Now,
Solving the equation, we get;


Hence, the average velocity for the bacterium is 0.75 unit/sec.
Answer:
The time elapsed at the spacecraft’s frame is less that the time elapsed at earth's frame
Explanation:
From the question we are told that
The distance between earth and Retah is 
Here c is the peed of light with value 
The time taken to reach Retah from earth is 
The velocity of the spacecraft is mathematically evaluated as

substituting values


The time elapsed in the spacecraft’s frame is mathematically evaluated as

substituting value
![T = 90000 * \sqrt{ 1 - \frac{[2.4*10^{8}]^2}{[3.0*10^{8}]^2} }](https://tex.z-dn.net/?f=T%20%20%3D%20%2090000%20%2A%20%20%5Csqrt%7B%201%20-%20%20%5Cfrac%7B%5B2.4%2A10%5E%7B8%7D%5D%5E2%7D%7B%5B3.0%2A10%5E%7B8%7D%5D%5E2%7D%20%7D)

=> 
So The time elapsed at the spacecraft’s frame is less that the time elapsed at earth's frame
To solve this problem with the given elements we will apply the linear motion kinematic equations. We will start by calculating the time taken, with the vertical displacement data. Subsequently, with the components of the acceleration, we will obtain the magnitude of the total acceleration, to finally obtain the horizontal displacement with the data already found.
PART A) From vertical movement we know that the acceleration is equivalent to gravity and the displacement is 8m so the time taken to carry out the route would be

Here,


Replacing,


PART B) Now, Magnitude of acceleration



Thus, magnitude of net acceleration

PART C) Finally the displacement along horizontal direction is:



Therefore the distance traveled along the horizontal direction before it hits the ground is 3.098m