Enrico Fermi (1901–1954) was a famous physicist who liked to pose what are now known as Fermi problems, in which several assumptions are made in order to make a seemingly impossible estimate. Probably the most famous example is the estimate of the number of piano tuners in Chicago using the approximate population of the city and assumptions about how many households have pianos, how often pianos need tuning, and how many hours a given tuner works in a year. Another famous example of a Fermi problem is "Caesar's last breath," which estimates that you, right now, are breathing some of the molecules exhaled by Julius Caesar just before he died. The assumptions made are: The gas molecules from Caesar's last breath are now evenly dispersed in the atmosphere. The atmosphere is 50 km thick, has an average temperature of 15 °C , and an average pressure of 0.20 atm . The radius of the Earth is about 6400 km . The volume of a single human breath is roughly 500 mL . Perform the calculations, reporting all answers to two significant figures.

Explanation:

(a)

Since the earth is assumed to be a sphere.

Volume of atmosphere = volume of (earth +atm osphere) — volume of earth

Hence the volume of atmosphere is

(b)

Write the ideal gas equation as foll ows:

Hence the required molecules is

(c)

Write the ideal gas equation as follows:

Hence the required molecules in Caesar breath is

(d)

Volume fraction in Caesar last breath is as follows:  

(e)

Since the volume capacity of the human body is 500 mL.

since you're a real machine, your ama is always less than your ima, because you can never totally eliminate friction.

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.