Answer:
v =
m/s
Explanation:
The position vector r of the bug with linear velocity v and angular velocity ω in the laboratory frame is given by:
![\overrightarrow{r}=vtcos(\omega t)\hat{x}+vtsin(\omega t)\hat{y}](https://tex.z-dn.net/?f=%5Coverrightarrow%7Br%7D%3Dvtcos%28%5Comega%20t%29%5Chat%7Bx%7D%2Bvtsin%28%5Comega%20t%29%5Chat%7By%7D)
The velocity vector v is the first derivative of the position vector r with respect to time:
![\overrightarrow{v}=[vcos(\omega t)-\omega vtsin(\omega t)]\hat{x}+[vsin(\omega t)+\omega vtcos(\omega t)]\hat{y}](https://tex.z-dn.net/?f=%5Coverrightarrow%7Bv%7D%3D%5Bvcos%28%5Comega%20t%29-%5Comega%20vtsin%28%5Comega%20t%29%5D%5Chat%7Bx%7D%2B%5Bvsin%28%5Comega%20t%29%2B%5Comega%20vtcos%28%5Comega%20t%29%5D%5Chat%7By%7D)
The given values are:
![t=\frac{x}{v}=\frac{14}{3.8}=3.7 s](https://tex.z-dn.net/?f=t%3D%5Cfrac%7Bx%7D%7Bv%7D%3D%5Cfrac%7B14%7D%7B3.8%7D%3D3.7%20s)
![\omega=\frac{45\times2\pi}{60s}=4.7\frac{1}{s}](https://tex.z-dn.net/?f=%5Comega%3D%5Cfrac%7B45%5Ctimes2%5Cpi%7D%7B60s%7D%3D4.7%5Cfrac%7B1%7D%7Bs%7D)
This question involves the concepts of dynamic pressure, volume flow rate, and flow speed.
It will take "5.1 hours" to fill the pool.
First, we will use the formula for the dynamic pressure to find out the flow speed of water:
![P=\frac{1}{2}\rho v^2\\\\v=\sqrt{\frac{2P}{\rho}}](https://tex.z-dn.net/?f=P%3D%5Cfrac%7B1%7D%7B2%7D%5Crho%20v%5E2%5C%5C%5C%5Cv%3D%5Csqrt%7B%5Cfrac%7B2P%7D%7B%5Crho%7D%7D)
where,
v = flow speed = ?
P = Dynamic Pressure = 55 psi
= 379212 Pa
= density of water = 1000 kg/m³
Therefore,
![v=\sqrt{\frac{2(379212\ Pa)}{1000\ kg/m^3}}](https://tex.z-dn.net/?f=v%3D%5Csqrt%7B%5Cfrac%7B2%28379212%5C%20Pa%29%7D%7B1000%5C%20kg%2Fm%5E3%7D%7D)
v = 27.54 m/s
Now, we will use the formula for volume flow rate of water coming from the hose to find out the time taken by the pool to be filled:
![\frac{V}{t} = Av\\\\t =\frac{V}{Av}](https://tex.z-dn.net/?f=%5Cfrac%7BV%7D%7Bt%7D%20%3D%20Av%5C%5C%5C%5Ct%20%3D%5Cfrac%7BV%7D%7BAv%7D)
where,
t = time to fill the pool = ?
A = Area of the mouth of hose =
= 1.98 x 10⁻⁴ m²
V = Volume of the pool = (Area of pool)(depth of pool) = A(1.524 m)
V =
= 100.1 m³
Therefore,
![t = \frac{(100.1\ m^3)}{(1.98\ x\ 10^{-4}\ m^2)(27.54\ m/s)}\\\\](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B%28100.1%5C%20m%5E3%29%7D%7B%281.98%5C%20x%5C%2010%5E%7B-4%7D%5C%20m%5E2%29%2827.54%5C%20m%2Fs%29%7D%5C%5C%5C%5C)
<u>t = 18353.5 s = 305.9 min = 5.1 hours</u>
Learn more about dynamic pressure here:
brainly.com/question/13155610?referrer=searchResults
Answer:
![a=\frac{mBg-mAgSin\theta}{mA+mB}](https://tex.z-dn.net/?f=a%3D%5Cfrac%7BmBg-mAgSin%5Ctheta%7D%7BmA%2BmB%7D)
Explanation:
Given two mass on an incline code
and
and an angle of inclination
.
. Assume that
is the weight being pulled up and
the hanging weight.
-The equations of motion from Newton's Second Law are:
where a is the acceleration.
#Substituting for
(tension) gives:
![mBg-mAsin\theta-mAa=mBa](https://tex.z-dn.net/?f=mBg-mAsin%5Ctheta-mAa%3DmBa)
#and solving for ![a:](https://tex.z-dn.net/?f=a%3A)
which is the system's acceleration.
Answer:
Part a)
%
Part b)
%
Explanation:
As we know that total power used in the room is given as
![P = P_1 + P_2 + P_3 + P_4](https://tex.z-dn.net/?f=P%20%3D%20P_1%20%2B%20P_2%20%2B%20P_3%20%2B%20P_4)
here we have
![P_1 = (110)(3) = 330 W](https://tex.z-dn.net/?f=P_1%20%3D%20%28110%29%283%29%20%3D%20330%20W)
![P_2 = 100 W](https://tex.z-dn.net/?f=P_2%20%3D%20100%20W)
![P_3 = 60 W](https://tex.z-dn.net/?f=P_3%20%3D%2060%20W)
![P_4 = 3 W](https://tex.z-dn.net/?f=P_4%20%3D%203%20W)
![P = 330 + 100 + 60 + 3](https://tex.z-dn.net/?f=P%20%3D%20330%20%2B%20100%20%2B%2060%20%2B%203)
![P = 493 W](https://tex.z-dn.net/?f=P%20%3D%20493%20W)
Part a)
Since power supply is at 110 Volt so the current obtained from this supply is given as
![110\times i = 493](https://tex.z-dn.net/?f=110%5Ctimes%20i%20%3D%20493%20)
![i = 4.48 A](https://tex.z-dn.net/?f=i%20%3D%204.48%20A)
now resistance of transmission line
![R = \frac{\rho L}{A}](https://tex.z-dn.net/?f=R%20%3D%20%5Cfrac%7B%5Crho%20L%7D%7BA%7D)
![R = \frac{(2.8 \times 10^{-8})(10\times 10^3)}{\pi(4.126\times 10^{-3})^2}](https://tex.z-dn.net/?f=R%20%3D%20%5Cfrac%7B%282.8%20%5Ctimes%2010%5E%7B-8%7D%29%2810%5Ctimes%2010%5E3%29%7D%7B%5Cpi%284.126%5Ctimes%2010%5E%7B-3%7D%29%5E2%7D)
![R = 5.23 \ohm](https://tex.z-dn.net/?f=R%20%3D%205.23%20%5Cohm)
now power loss in line is given as
![P = i^2 R](https://tex.z-dn.net/?f=P%20%3D%20i%5E2%20R)
![P = (4.48)^2(5.23)](https://tex.z-dn.net/?f=P%20%3D%20%284.48%29%5E2%285.23%29)
![P = 105 W](https://tex.z-dn.net/?f=P%20%3D%20105%20W)
Now percentage loss is given as
![percentage = \frac{loss}{supply} \times 100](https://tex.z-dn.net/?f=percentage%20%3D%20%5Cfrac%7Bloss%7D%7Bsupply%7D%20%5Ctimes%20100)
![percentage = \frac{105}{493} \times 100](https://tex.z-dn.net/?f=percentage%20%3D%20%5Cfrac%7B105%7D%7B493%7D%20%5Ctimes%20100)
%
Part b)
now same power must have been supplied from the supply station at 110 kV, so we have
![110 \times 10^3 (i ) = 493](https://tex.z-dn.net/?f=110%20%5Ctimes%2010%5E3%20%28i%20%29%20%3D%20493)
![i = 4.48\times 10^{-3} A](https://tex.z-dn.net/?f=i%20%3D%204.48%5Ctimes%2010%5E%7B-3%7D%20A)
now power loss in line is given as
![P = i^2 R](https://tex.z-dn.net/?f=P%20%3D%20i%5E2%20R)
![P = (4.48 \times 10^{-3})^2(5.23)](https://tex.z-dn.net/?f=P%20%3D%20%284.48%20%5Ctimes%2010%5E%7B-3%7D%29%5E2%285.23%29)
![P = 1.05 \times 10^{-4} W](https://tex.z-dn.net/?f=P%20%3D%201.05%20%5Ctimes%2010%5E%7B-4%7D%20W)
Now percentage loss is given as
![percentage = \frac{loss}{supply} \times 100](https://tex.z-dn.net/?f=percentage%20%3D%20%5Cfrac%7Bloss%7D%7Bsupply%7D%20%5Ctimes%20100)
![percentage = \frac{1.05 \times 10^{-4}}{493} \times 100](https://tex.z-dn.net/?f=percentage%20%3D%20%5Cfrac%7B1.05%20%5Ctimes%2010%5E%7B-4%7D%7D%7B493%7D%20%5Ctimes%20100)
%