Josiah has a mass of 75kgand wants to know how many helium-filled balloons it would take to fly. The density of helium is about 1kg/m^3 less than regular air, which means a cubic meter of helium can lift about 1kg. Fully inflated, a balloon has a diameter of 0.3m and can be modeled as a sphere. He neglects the mass of the balloon in his calculations. nHow mnay balloons would it take to lift a person of 75 kg mass?

Explanation:

According to the Archimedes' Principle, the buoyant force exerted on the helium ballons is equal to the weight of displaced air. A simplified scheme for the system person-ballons is presented below. The correspondent equation of equilibrium is:

The minimum net volume is:

The volume of each ballon is:

The minimum quantity of ballons needed to lift Josiah is:

hypothesising or postulating

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.