Astandard four-drawer filing cabinet is 52 inches high and 15 inches wide. if it is evenly loaded, the center of gravity is at the center of the cabinet. a worker is tilting a filing cabinet to the side to clean under it.
part a
to what angle can he tilt the cabinet before it tips over?
express your answer using two significant figures.

x=16.10°

Explanation:

You can go through a bunch of equations, but basically the cabinet can be moved until the CG is past the vertical line of the rotation point. After the CG crosses the line the weight of the cabinet will keep the rotation going in the direction.

to Find the angle from one corner to the CG

angle =atan(52/15) = 73.90

So, to make that angle vertical...

90° = x + 73.90°

x=16.10°

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.