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 :

total distance/total time

(85 + 82)/(5+3)

167/8

20 just over