Mastering the Sunrise Equation: Understanding Daytime Variations with Latitude

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The discussion focuses on understanding the Sunrise equation and its application in calculating the total daylight duration based on latitude (gamma). A user seeks assistance in proving the delta of total daytime as outlined in the formula. Participants encourage the user to demonstrate their initial approach to the problem before receiving further help. Additionally, there is a suggestion to utilize LaTeX for better equation formatting. The conversation emphasizes the importance of engaging with the problem-solving process.
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Homework Statement
Sunrise equation help
Relevant Equations
Sunrise equation
Hi, I need help with the Sunrise equation.
I need to proof the delta of total day time in a day, as seen in the formula.
gama is latitude.
Thank you for helping :)
 

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CaptainAntiFunn said:
Homework Statement:: Sunrise equation help
Relevant Equations:: Sunrise equation

Hi, I need help with the Sunrise equation.
I need to proof the delta of total day time in a day, as seen in the formula.
gama is latitude.
Thank you for helping :)
Welcome to PF. :smile:

YOu are required to show your best efforts to start the problem before we can offer tutorial assistance. Please show us how you are thinking of approaching this problem. Be sure to look at the LaTeX Guide link below the Edit window to see how to post equations here. Thanks.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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