Answer:
I can help but I need to know what it looking for
Answer:
t = 2244.3 sec
Explanation:
calculate the thermal diffusivity
![\alpha = \frac{k}{\rho c}](https://tex.z-dn.net/?f=%5Calpha%20%3D%20%5Cfrac%7Bk%7D%7B%5Crho%20c%7D)
![= \frac{50}{7800\times 480} = 1.34 \times 10^{-5} m^2/s](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B50%7D%7B7800%5Ctimes%20480%7D%20%3D%201.34%20%5Ctimes%2010%5E%7B-5%7D%20m%5E2%2Fs)
Temperature at 28 mm distance after t time = = 50 degree C
we know that
![\frac[ T_{28} - T_s}{T_i -T_s} = erf(\frac{x}{2\sqrt{at}})](https://tex.z-dn.net/?f=%5Cfrac%5B%20T_%7B28%7D%20-%20T_s%7D%7BT_i%20-T_s%7D%20%3D%20erf%28%5Cfrac%7Bx%7D%7B2%5Csqrt%7Bat%7D%7D%29)
![\frac{ 50 -25}{300-25} = erf [\frac{28\times 10^{-3}}{2\sqrt{1.34\times 10^{-5}\times t}}]](https://tex.z-dn.net/?f=%5Cfrac%7B%2050%20-25%7D%7B300-25%7D%20%3D%20erf%20%5B%5Cfrac%7B28%5Ctimes%2010%5E%7B-3%7D%7D%7B2%5Csqrt%7B1.34%5Ctimes%2010%5E%7B-5%7D%5Ctimes%20t%7D%7D%5D)
![0.909 = erf{\frac{3.8245}{\sqrt{t}}}](https://tex.z-dn.net/?f=0.909%20%3D%20erf%7B%5Cfrac%7B3.8245%7D%7B%5Csqrt%7Bt%7D%7D%7D)
from gaussian error function table , similarity variable w calculated as
erf w = 0.909
it is lie between erf w = 0.9008 and erf w = 0.11246 so by interpolation we have
w = 0.08073
![erf 0.08073 = erf[\frac{3.8245}{\sqrt{t}}]](https://tex.z-dn.net/?f=erf%200.08073%20%3D%20erf%5B%5Cfrac%7B3.8245%7D%7B%5Csqrt%7Bt%7D%7D%5D)
![0.08073 = \frac{3.8245}{\sqrt{t}}](https://tex.z-dn.net/?f=0.08073%20%3D%20%5Cfrac%7B3.8245%7D%7B%5Csqrt%7Bt%7D%7D)
solving fot t we get
t = 2244.3 sec
Answer:
![\theta_1=15^o\\\theta_2=75^o](https://tex.z-dn.net/?f=%5Ctheta_1%3D15%5Eo%5C%5C%5Ctheta_2%3D75%5Eo)
Explanation:
<u>Projectile Motion</u>
In projectile motion, there are two separate components of the acceleration, velocity and displacement. The horizontal component has zero acceleration (assuming no friction), and the acceleration in the vertical direction is always the acceleration of gravity. The basic formulas are shown below:
![V_x=V_{ox}=V_ocos\theta](https://tex.z-dn.net/?f=V_x%3DV_%7Box%7D%3DV_ocos%5Ctheta)
Where
is the angle of launch respect to the positive horizontal direction and Vo is the initial speed.
![V_y=V_{oy}-gt=V_osin\theta-gt](https://tex.z-dn.net/?f=V_y%3DV_%7Boy%7D-gt%3DV_osin%5Ctheta-gt)
The horizontal and vertical distances are, respectively:
![x=V_{o}cos\theta t](https://tex.z-dn.net/?f=x%3DV_%7Bo%7Dcos%5Ctheta%20t)
![\displaystyle y=y_o+V_{o}sin\theta t-\frac{gt^2}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3Dy_o%2BV_%7Bo%7Dsin%5Ctheta%20t-%5Cfrac%7Bgt%5E2%7D%7B2%7D)
The total flight time can be found as that when y = 0, i.e. when the object comes back to ground (or launch) level. From the above equation we find
![\displaystyle t_f=\frac{2V_osin\theta}{g}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20t_f%3D%5Cfrac%7B2V_osin%5Ctheta%7D%7Bg%7D)
Using this time in the horizontal distance, we find the Range or maximum horizontal distance:
![\displaystyle R=\frac{V_o^2sin2\theta}{g}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20R%3D%5Cfrac%7BV_o%5E2sin2%5Ctheta%7D%7Bg%7D)
Let's solve for ![\theta](https://tex.z-dn.net/?f=%5Ctheta)
![\displaystyle sin2\theta=\frac{R.g}{V_o^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20sin2%5Ctheta%3D%5Cfrac%7BR.g%7D%7BV_o%5E2%7D)
This is the general expression to determine the angles at which the projectile can be launched to hit the target. Recall the angle can have to values for fixed positive values of its sine:
![\displaystyle \theta_1=\frac{asin\left(\frac{R.g}{V_o^2}\right)}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ctheta_1%3D%5Cfrac%7Basin%5Cleft%28%5Cfrac%7BR.g%7D%7BV_o%5E2%7D%5Cright%29%7D%7B2%7D)
![\displaystyle \theta_2=\frac{180^o-asin\left(\frac{R.g}{V_o^2}\right)}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ctheta_2%3D%5Cfrac%7B180%5Eo-asin%5Cleft%28%5Cfrac%7BR.g%7D%7BV_o%5E2%7D%5Cright%29%7D%7B2%7D)
Or equivalently:
![\theta_2=90^o-\theta_1](https://tex.z-dn.net/?f=%5Ctheta_2%3D90%5Eo-%5Ctheta_1)
Given Vo=37 m/s and R=70 m
![\displaystyle \theta_1=\frac{asin\left(\frac{70\times 9.8}{37^2}\right)}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ctheta_1%3D%5Cfrac%7Basin%5Cleft%28%5Cfrac%7B70%5Ctimes%209.8%7D%7B37%5E2%7D%5Cright%29%7D%7B2%7D)
![\theta_1=15^o](https://tex.z-dn.net/?f=%5Ctheta_1%3D15%5Eo)
And
![\theta_2=90^o-15^o=75^o](https://tex.z-dn.net/?f=%5Ctheta_2%3D90%5Eo-15%5Eo%3D75%5Eo)
Answer:
The time required to elute the two species is 53.3727 min
Explanation:
Given data:
tA = retention time of A=16.63 min
tB=retention time of B=17.63 min
WA=peak of A=1.11 min
WB=peak of B=1.21 min
The mathematical expression for the resolution is:
![Re_{s} =\frac{2(t_{B}-t_{A})}{W_{A}+W_{B} } =\frac{2*(17.63-16.63)}{1.11+1.21} =0.8621](https://tex.z-dn.net/?f=Re_%7Bs%7D%20%3D%5Cfrac%7B2%28t_%7BB%7D-t_%7BA%7D%29%7D%7BW_%7BA%7D%2BW_%7BB%7D%20%7D%20%3D%5Cfrac%7B2%2A%2817.63-16.63%29%7D%7B1.11%2B1.21%7D%20%3D0.8621)
The mathematical expression for the time to elute the two species is:
![\frac{t_{2}}{t_{1}} =(\frac{Re_{B} }{Re_{s} } )^{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bt_%7B2%7D%7D%7Bt_%7B1%7D%7D%20%3D%28%5Cfrac%7BRe_%7BB%7D%20%7D%7BRe_%7Bs%7D%20%7D%20%29%5E%7B2%7D)
Here
ReB = 1.5
![t_{2} =t_{1} *(\frac{Re_{B} }{Re_{s} } )^{2} =17.63*(\frac{1.5}{0.8621} )^{2} =53.3727min](https://tex.z-dn.net/?f=t_%7B2%7D%20%3Dt_%7B1%7D%20%2A%28%5Cfrac%7BRe_%7BB%7D%20%7D%7BRe_%7Bs%7D%20%7D%20%29%5E%7B2%7D%20%3D17.63%2A%28%5Cfrac%7B1.5%7D%7B0.8621%7D%20%29%5E%7B2%7D%20%3D53.3727min)