Question 682077: Vehicle Car A is now passing a truck that is 90 feet long. Vehicle A is traveling 40 mph( or 60 feet per seconds) and truck B is traveling 30mph (or 45 feet per seconds. Vehicle A will being passing maneuver $ seconds behind the trucj to allow the truck to see him.Vehivle A will return to his lane when he is 60 feet ahead of truck B.
What is the distance between truc B & vehicle A after A passses the truck and return to his lane? And what us the Total amount Vehicle A must travel to complete this maneuver?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! MY INTERPRETATION OF THE PROBLEM:
Car A is now passing a truck (truck B) that is 90 feet long.
Car A is traveling at 60 feet per second all the time,even when changing lanes, and
truck B is traveling at 45 feet per second all the time.
Car A will begin the passing maneuver 4 seconds behind the truck,
meaning 4 seconds before it would hit the truck if it stayed on the same lane.
Car A will return to his lane when it is 60 feet ahead of truck B,
meaning when the car's front bumper is 60 feet ahead of the truck's front bumper.
MY INTERPRETATION OF THE PROBLEM'S QUESTIONS:
What is the distance (empty space) between truck B & vehicle A after A passes the truck and returns to its original lane?
What is the total distance vehicle A must travel to complete this maneuver?
THE PROBLEM WITH THIS PROBLEM is that there is too much open to interpretation, so my answers may not be the expected answers.
It is quite possible that a less realistic approach was expected.
We would use the speeds in feet per second (ft/s) rather than in mph.
Since the difference between the speed of the car and the speed of the truck is  ft/s, before passing the truck, the car would be reducing its distance from the truck at a rate of ft/s.
At that rate, in  seconds, the car would reduce its distance to the truck by
 feet, so the car would start the passing maneuver when  ft from the truck.
If I were driving car A, I would drive in the middle of each lane when not changing lanes.
To change lanes, I would turn at a  angle towards the other lane.
That way, my ft/s speed would have a forward component of  ft/s, matching the speed of the truck.
 .
The sideways component of my ft/s speed would be  ft/s.
The lane width in my highway would be  ft, and
at a lateral speed of ft/s, I would move ft laterally in
 seconds.
While doing the lane changes at that angle (before and after passing the truck), I would spend
 seconds moving at the same forward ft/s speed as the truck.
In between lane changes, on the passing lane, I would be gaining on the truck,
advancing forward from being seconds behind the truck
(feet),
to having my front bumper ft ahead of the front bumper of the truck.
Since my car is  feet long, that would mean my rear bumper would be
 feet in front of the front bumper of the truck after passing.
That would be my answer to the first question, but I do not think that is the expected answer, because it depends on the length of car A, the driver's lane change strategy and the width of the lane.
From the point of view of the truck driver, the truck is not moving, and the car is advancing at  ft/s while on the passing lane.
Also from the point of view of the truck driver, the car covers a distance of
 feet while moving forward on the passing lane.
At ft/s, those  feet would be covered in
 seconds.
The whole passing maneuver would take
 seconds,  for the two lane changes, and  seconds on the fast lane.
During that time, the truck would have advanced at ft/s, covering
 feet.
The car would have advanced  relative to the truck, advancing
 feet forward during the whole passing maneuver,
while on a lane shifting trajectory of total length
 feet, and that would be my answer to the second question.
The two slanted lane change portions of that trajectory would have accounted for
 feet.
During the seconds moving straight forward on the passing lane, the car would have covered
 feet.
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