Answer:
Maximum height reached by the rocket is
![y_{max} = 308 m](https://tex.z-dn.net/?f=y_%7Bmax%7D%20%3D%20308%20m)
total time of the motion of rocket is given as
![T = 16.44 s](https://tex.z-dn.net/?f=T%20%3D%2016.44%20s)
Explanation:
Initial speed of the rocket is given as
![v_i = 50 m/s](https://tex.z-dn.net/?f=v_i%20%3D%2050%20m%2Fs)
acceleration of the rocket is given as
![a = 2 m/s^2](https://tex.z-dn.net/?f=a%20%3D%202%20m%2Fs%5E2)
engine stops at height h = 150 m
so the final speed of the rocket at this height is given as
![v_f^2 - v_i^2 = 2 a d](https://tex.z-dn.net/?f=v_f%5E2%20-%20v_i%5E2%20%3D%202%20a%20d)
![v_f^2 - 50^2 = 2(2)(150)](https://tex.z-dn.net/?f=v_f%5E2%20-%2050%5E2%20%3D%202%282%29%28150%29)
![v_f = 55.68 m/s](https://tex.z-dn.net/?f=v_f%20%3D%2055.68%20m%2Fs)
so maximum height reached by the rocket is given as the height where its final speed becomes zero
so we will have
![v_f^2 - v_i^2 = 2 a d](https://tex.z-dn.net/?f=v_f%5E2%20-%20v_i%5E2%20%3D%202%20a%20d)
![0 - 55.68^2 = 2(-9.81)(y - 150)](https://tex.z-dn.net/?f=0%20-%2055.68%5E2%20%3D%202%28-9.81%29%28y%20-%20150%29)
![y_{max} = 308 m](https://tex.z-dn.net/?f=y_%7Bmax%7D%20%3D%20308%20m)
Now the total time of the motion of rocket is given as
1) time to reach the height of 150 m
![v_f - v_i = at](https://tex.z-dn.net/?f=v_f%20-%20v_i%20%3D%20at)
![55.68 - 50 = 2 t](https://tex.z-dn.net/?f=55.68%20-%2050%20%3D%202%20t)
![t_1 = 2.84 s](https://tex.z-dn.net/?f=t_1%20%3D%202.84%20s)
2) time to reach ground from this height
![\Delta y = v_y t + \frac{1}{2}gt^2](https://tex.z-dn.net/?f=%5CDelta%20y%20%3D%20v_y%20t%20%2B%20%5Cfrac%7B1%7D%7B2%7Dgt%5E2)
![-150 = 55.68 t - \frac{1}{2}(9.81) t^2](https://tex.z-dn.net/?f=-150%20%3D%2055.68%20t%20-%20%5Cfrac%7B1%7D%7B2%7D%289.81%29%20t%5E2)
![t_2 = 13.6 s](https://tex.z-dn.net/?f=t_2%20%3D%2013.6%20s)
so total time of the motion of rocket is given as
![T = 13.6 + 2.84 = 16.44 s](https://tex.z-dn.net/?f=T%20%3D%2013.6%20%2B%202.84%20%3D%2016.44%20s)
This is false. Atom in Greek means indivisible, or unable to be divided into smaller parts. We know now that it is not true, but they didn't.
Answer:
1) Measuring cylinder
2) Top Pan Balance
Explanation:
To find the density of the pebble Nabil should first accurately measure the mass of the pebble using the top pan balance
He should then fill the displacement can till the water reaches the outlet pipe at the to of the cylinder
He should then place the pebble into the cylinder carefully ans allow the water that would start coming out to stop
The volume of water in the displaced cylinder is then measured and the density is found by dividing the mass of the pebble by the volume of water in the measuring cylinder
![Density \ of \ pebble = \dfrac{Pebble \ mass}{Volume \ of \ water \ in\ the \ measuring \ cylinder} = \dfrac{Pebble \ mass}{Water \ volume \ displaced}](https://tex.z-dn.net/?f=Density%20%5C%20of%20%5C%20pebble%20%3D%20%20%5Cdfrac%7BPebble%20%5C%20mass%7D%7BVolume%20%5C%20of%20%5C%20water%20%5C%20in%5C%20the%20%5C%20measuring%20%5C%20cylinder%7D%20%3D%20%20%5Cdfrac%7BPebble%20%5C%20mass%7D%7BWater%20%5C%20volume%20%5C%20displaced%7D)
Answer:
Plate separation of each capacitor is 101.132 °A
Explanation:
The formula to calculate the capacitance in empty space as a function of distance (square parallel plates) is:
![C=\epsilon_{0}\frac{Area}{distance}](https://tex.z-dn.net/?f=C%3D%5Cepsilon_%7B0%7D%5Cfrac%7BArea%7D%7Bdistance%7D)
clearing for distance:
![distance=\epsilon_0 \frac{Area}{Capacitance} \\\\\epsilon_0=8.8542(10)^{-12}C^2/Nm\\\\Area=3.09(10)^{-11}m^2\\Capacitance=27(10)^{-15}F\\\\Replacing\\\\distance=\frac{8.8542(10)^{-12}*3.09(10)^{-11}}{27(10)^{-15}} =1.0133(10)^{-8}m\\\\In A\\distance= 101.132 A](https://tex.z-dn.net/?f=distance%3D%5Cepsilon_0%20%5Cfrac%7BArea%7D%7BCapacitance%7D%20%5C%5C%5C%5C%5Cepsilon_0%3D8.8542%2810%29%5E%7B-12%7DC%5E2%2FNm%5C%5C%5C%5CArea%3D3.09%2810%29%5E%7B-11%7Dm%5E2%5C%5CCapacitance%3D27%2810%29%5E%7B-15%7DF%5C%5C%5C%5CReplacing%5C%5C%5C%5Cdistance%3D%5Cfrac%7B8.8542%2810%29%5E%7B-12%7D%2A3.09%2810%29%5E%7B-11%7D%7D%7B27%2810%29%5E%7B-15%7D%7D%20%3D1.0133%2810%29%5E%7B-8%7Dm%5C%5C%5C%5CIn%20A%5C%5Cdistance%3D%20101.132%20A)