Ahunter aims horizontally at a target on the same level as his rifle. if the bullet leaves his rifle at a velocity of 154.6 m/s and hits 0.64 meters below the target, how far away is the target? (hint: you are looking for dx)round your answer to the nearest 0.01. do not add units.

The bullet's position vector has components

where we're given the initial velocity and the initial height of the bullet , and is the acceleration due to gravity. Note that we take the bullet's starting position to be the origin.

We're also told that after some time , the time it takes for the bullet to hit the target, the bullet's vertical position is 0.64 m below where it was aimed, which translates to at this time . Then we can solve for this time:

Finally, the target's distance from the origin is at this time :

the answer would be a

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.