Answer:
a
The velocity is ![v =17.98 \ m/s](https://tex.z-dn.net/?f=v%20%3D17.98%20%5C%20m%2Fs)
b
The diameter is ![d = 0.00184m](https://tex.z-dn.net/?f=d%20%3D%200.00184m)
Explanation:
The diagram of the set up is shown on the first uploaded image
From the question we are told that
The height of the water tank is ![h = 20.0 \ m](https://tex.z-dn.net/?f=h%20%3D%2020.0%20%5C%20m)
The position of the hole
below water level
The rate of water flow ![\r V = 2.90 *10^{-3} m^3 /min = \frac{2.90 *10^{-3}}{60} = 0.048*10^{-3} m^3/s](https://tex.z-dn.net/?f=%5Cr%20V%20%3D%20%202.90%20%2A10%5E%7B-3%7D%20m%5E3%20%2Fmin%20%3D%20%5Cfrac%7B2.90%20%2A10%5E%7B-3%7D%7D%7B60%7D%20%3D%200.048%2A10%5E%7B-3%7D%20m%5E3%2Fs)
According to Bernoulli's theorem position of the hole
Where u is the initial speed the water through the hole = 0 m/s
is the atmospheric pressure
![v = \sqrt{2gh}](https://tex.z-dn.net/?f=v%20%3D%20%5Csqrt%7B2gh%7D)
Substituting value
![v = \sqrt{2 * 9.8 * 16.5 }](https://tex.z-dn.net/?f=v%20%3D%20%5Csqrt%7B2%20%2A%209.8%20%2A%20%2016.5%20%7D)
![v =17.98 \ m/s](https://tex.z-dn.net/?f=v%20%3D17.98%20%5C%20m%2Fs)
The Volumetric flow rate is mathematically represented as
![\r V = A * v](https://tex.z-dn.net/?f=%5Cr%20V%20%3D%20A%20%2A%20v)
Making A the subject
![A = \frac{\r V}{v}](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7B%5Cr%20V%7D%7Bv%7D)
substituting value
![A = \frac{0.048 *10^{-3}}{17.98}](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7B0.048%20%2A10%5E%7B-3%7D%7D%7B17.98%7D)
![= 2.66*10^{-6}m^2](https://tex.z-dn.net/?f=%3D%202.66%2A10%5E%7B-6%7Dm%5E2)
Area is mathematically represented as
![A = \frac{\pi d^2}{4}](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7B%5Cpi%20d%5E2%7D%7B4%7D)
making d the subject
![d = \sqrt{\frac{4*A}{\pi} }](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%5Cfrac%7B4%2AA%7D%7B%5Cpi%7D%20%7D)
Substituting values
![d = \sqrt{\frac{4 * 2.67 *10^{-6}}{3.142} }](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%5Cfrac%7B4%20%2A%20%202.67%20%2A10%5E%7B-6%7D%7D%7B3.142%7D%20%7D)
![d = 0.00184m](https://tex.z-dn.net/?f=d%20%3D%200.00184m)
What happens is that if u put gas in a ball and placed in a hot climate it will start burning Bc u have gas inside the ball
To solve this problem we will use the concepts related to Magnification. Magnification is the process of enlarging the apparent size, not physical size, of something. This enlargement is quantified by a calculated number also called "magnification".
The overall magnification of microscope is
![M = \frac{Nl}{f_ef_0}](https://tex.z-dn.net/?f=M%20%3D%20%5Cfrac%7BNl%7D%7Bf_ef_0%7D)
Where
N = Near point
l = distance between the object lens and eye lens
= Focal length
= Focal of eyepiece
Given that the minimum distance at which the eye is able to focus is about 25cm we have that N = 25cm
Replacing,
![M = \frac{25*10}{3*5}](https://tex.z-dn.net/?f=M%20%3D%20%5Cfrac%7B25%2A10%7D%7B3%2A5%7D)
![M = 16.67\approx 17\\](https://tex.z-dn.net/?f=M%20%3D%2016.67%5Capprox%2017%5C%5C)
Therefore the correct answer is C.
Answer:
Let's define t = 0 as the moment when the ball hits the wall.
in this moment, we have a given acceleration, but if we only want to calculate the average acceleration, then let's consider the acceleration constant.
a(t) = A.
To find the velocity equation we should integrate, and the constant of integration will be the initial velocity, in this case, is 14.3m/s.
v(t) = A*t + 14.3m/s
Now we know that at t = 0.011s, the velocity is -13.5m/s (the sign is negative because the ball is moving in the opposite direction as before).
Then we can solve the equation:
v(0.011s) = -13.5m/s = A*0.011s + 14.3m/s
Now we can solve it for A, the average acceleration:
-13.5m/s - 14.3m/s = A*0.011s
(-27.8m/s)/0.011s = A = -1313.5 m/s^2
If u mean black hole*
It’s a space where gravity pulls so much that even light can not get out. The gravity is so strong because matter has been squeezed into a tiny space. This can happen when a star is dying because no light can get out, people can’t see black holes. They are invisible.
Black holes of stellar mass form when very massive starts collapse at the end of their life cycle.
- info from NASA