In an amusement park water slide, people slide down an essentially frictionless tube. the top of the slide is 3.2 m above the bottom where they exit the slide, moving horizontally, 1.2 m above a swimming pool. does the mass of the person make any difference?

No

Explanation:

When the person slides down, the change in gravitational potential energy is converted into kinetic energy, according to

where

m is the mass of the person

g is the acceleration of gravity

v is the final speed

is the change in heigth of the person

Here we have assumed that the initial speed is zero.

Re-arranging the equation,

and we see that this quantity does not depend on the mass of the person, so every person will have the same speed at the bottom of the slide, equal to:

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.