Answer:
2.When they reach the bottom of the fall
Explanation:
The potential energy of the waterfall is maximum at the maximum height and decreases with decrease in height. Based on the law of conservation of mechanical energy, as the potential energy of the water fall is decreasing with decrease in height of the fall, its kinetic energy will be increasing and the kinetic energy will be maximum at zero height (bottom of the fall).
Thus, the correct option is "2" When they reach the bottom of the fall
Answer:
162500000.
Explanation:
Given that
Diameter of the wire , d= 1.8 mm
The length of the wire ,L = 15 cm
Current ,I = 260 m A
The charge on the electron ,e= 1.6 x 10⁻¹⁹ C
We know that Current I is given as
![I=\dfrac{q}{t}](https://tex.z-dn.net/?f=I%3D%5Cdfrac%7Bq%7D%7Bt%7D)
I=Current
q=Charge
t=time
q= I t
q= 260 m t
The total number of electron = n
q= n e
![n=\dfrac{260\times 10^{-3}\ t}{1.6\times 10^{-9}}](https://tex.z-dn.net/?f=n%3D%5Cdfrac%7B260%5Ctimes%2010%5E%7B-3%7D%5C%20t%7D%7B1.6%5Ctimes%2010%5E%7B-9%7D%7D)
n=162500000 t
![\dfrac{n}{t}=16250000](https://tex.z-dn.net/?f=%5Cdfrac%7Bn%7D%7Bt%7D%3D16250000)
The number of electron passe per second will be 162500000.
Integrating the velocity equation, we will see that the position equation is:
![$f(t)=\frac{\cos ^3(\omega t)-1}{3}](https://tex.z-dn.net/?f=%24f%28t%29%3D%5Cfrac%7B%5Ccos%20%5E3%28%5Comega%20t%29-1%7D%7B3%7D)
<h3>How to get the position equation of the particle?</h3>
Let the velocity of the particle is:
![$v(t)=\sin (\omega t) * \cos ^2(\omega t)](https://tex.z-dn.net/?f=%24v%28t%29%3D%5Csin%20%28%5Comega%20t%29%20%2A%20%5Ccos%20%5E2%28%5Comega%20t%29)
To get the position equation we just need to integrate the above equation:
![$f(t)=\int \sin (\omega t) * \cos ^2(\omega t) d t](https://tex.z-dn.net/?f=%24f%28t%29%3D%5Cint%20%5Csin%20%28%5Comega%20t%29%20%2A%20%5Ccos%20%5E2%28%5Comega%20t%29%20d%20t)
![$\mathrm{u}=\cos (\omega \mathrm{t})](https://tex.z-dn.net/?f=%24%5Cmathrm%7Bu%7D%3D%5Ccos%20%28%5Comega%20%5Cmathrm%7Bt%7D%29)
Then:
![$d u=-\sin (\omega t) d t](https://tex.z-dn.net/?f=%24d%20u%3D-%5Csin%20%28%5Comega%20t%29%20d%20t)
![\Rightarrow d t=-d u / \sin (\omega t)](https://tex.z-dn.net/?f=%5CRightarrow%20d%20t%3D-d%20u%20%2F%20%5Csin%20%28%5Comega%20t%29)
Replacing that in our integral we get:
![$\int \sin (\omega t) * \cos ^2(\omega t) d t$](https://tex.z-dn.net/?f=%24%5Cint%20%5Csin%20%28%5Comega%20t%29%20%2A%20%5Ccos%20%5E2%28%5Comega%20t%29%20d%20t%24)
![$-\int \frac{\sin (\omega t) * u^2 d u}{\sin (\omega t)}-\int u^2 d t=-\frac{u^3}{3}+c$](https://tex.z-dn.net/?f=%24-%5Cint%20%5Cfrac%7B%5Csin%20%28%5Comega%20t%29%20%2A%20u%5E2%20d%20u%7D%7B%5Csin%20%28%5Comega%20t%29%7D-%5Cint%20u%5E2%20d%20t%3D-%5Cfrac%7Bu%5E3%7D%7B3%7D%2Bc%24)
Where C is a constant of integration.
Now we remember that ![$u=\cos (\omega t)$](https://tex.z-dn.net/?f=%24u%3D%5Ccos%20%28%5Comega%20t%29%24)
Then we have:
![$f(t)=\frac{\cos ^3(\omega t)}{3}+C](https://tex.z-dn.net/?f=%24f%28t%29%3D%5Cfrac%7B%5Ccos%20%5E3%28%5Comega%20t%29%7D%7B3%7D%2BC)
To find the value of C, we use the fact that f(0) = 0.
![$f(t)=\frac{\cos ^3(\omega * 0)}{3}+C=\frac{1}{3}+C=0](https://tex.z-dn.net/?f=%24f%28t%29%3D%5Cfrac%7B%5Ccos%20%5E3%28%5Comega%20%2A%200%29%7D%7B3%7D%2BC%3D%5Cfrac%7B1%7D%7B3%7D%2BC%3D0)
C = -1 / 3
Then the position function is:
![$f(t)=\frac{\cos ^3(\omega t)-1}{3}](https://tex.z-dn.net/?f=%24f%28t%29%3D%5Cfrac%7B%5Ccos%20%5E3%28%5Comega%20t%29-1%7D%7B3%7D)
Integrating the velocity equation, we will see that the position equation is:
![$f(t)=\frac{\cos ^3(\omega t)-1}{3}](https://tex.z-dn.net/?f=%24f%28t%29%3D%5Cfrac%7B%5Ccos%20%5E3%28%5Comega%20t%29-1%7D%7B3%7D)
To learn more about motion equations, refer to:
brainly.com/question/19365526
#SPJ4
Answer:
A. False, frequency can increase or decrease wavelength.
For example: a high frequency would mean there are shorter wavelengths that occur in a period. Meanwhile, a low frequency would indicate that the wavelengths are longer and in longer periods.
Ventilation is very important because it helps remove the gas form people’s homes and schools and it redirects the random gas outside so it is less likely to hurt people