The Phenomenon: Christine throws a ball straight up, letting go of the ball at a height of yi above the ground. When she lets go, the ball has an initial speed vi. The ball travels straight up to its maximum height ymax and falls back down. Assume the frictional effects from air resistance are insignificant. New Question: If the initial upward speed of the ball in the phenomenon described above is 10 m/s, and the ball is released at a height of 1.5 m above the floor, what is the maximum height above the floor that the ball reaches? How far above Christine’s hand is the ball when it reaches its maximum height? How is this value relate to ∆y = yf - yi? Does the sign of ∆y make sense for this scenario? How do you know?

nah.   i'm just sleepy.

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.