Abug flying horizontally at 1.7 m/s collides and sticks to the end of a uniform stick hanging vertically from its other end. after the impact, the stick swings out to a maximum angle of 7.0â° from the vertical before rotating back. if the mass of the stick is 16 times that of the bug, calculate the length of the stick (in m).

12.11 m

Explanation:

Given

Bug speed =1.7 m/s

Let mass of bug is m

mass of rod 16m

maximum angle turned by rod is 7^{\circ}[/tex]

From Energy conservation

kinetic energy of bug =Gain in potential energy of rod

L=12.11 m

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.