Arocket, initially at rest on the ground, accelerates straight upward from rest with constant acceleration 58.8 m/s^2. the acceleration period lasts for time 8.00 s until the fuel is exhausted. after that, the rocket is in free fall. find the maximum height ymax reached by the rocket. ignore air resistance and assume a constant acceleration due to gravity equal to 9.80 m/s^2 .

The maximum height will be 7408.8 meters

Explanation:

final velocity = initial velocity + acceleration × time  

final velocity = 0 m/s + 58.8 m/s^2 ×6 s  

Final velocity = 352.8 m/s  

final velocity ^2 = initial velocity ^2 + 2 × acceleration × displacement  

(352.8)^2 = (0)^2 + 2×58.8 ×displacement  

Solving for displacement,

height = 1058.4 meters.  

After this, the rocket is in free fall, we can use the same equation.  

final velocity ^2 = initial velocity ^2 + 2 ×acceleration×displacement  

final velocity = 0  

0^2 = 352.8^2 + 2×(-9.8)×displacement  

displacement = 6350.4 meters  

the maximum height will be 7408.8 meters

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.

t = 1/400 h   ⇔ 0.0025 h ⇔ 9s ⇔ 0.15 m

any of the answers are correct.