Calculating Averages - Physics Q&A for Help

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The discussion revolves around a user seeking assistance with calculating averages in a physics context, emphasizing the relevance of physics to their question. They have attached data and calculations, highlighting a specific inquiry at the end. The user expresses gratitude for any help received and notes that the same question has been successfully addressed in a math thread. A link to the resolved math discussion is provided for those interested. Overall, the focus is on obtaining clarity on average calculations within a physics framework.
Astro
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The attachment contains the data, calculations, and my question at the end in italics.

I have posted my question in the physics category because it is my only point of reference for a question of this type. In other words, I believe physics are best suited to answering my question.

I would be grateful for any help.

Thanks.
 

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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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Thread 'Struggle to understand the concept of the question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
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