What's mostly missing is the common sense step of verifying what the high school homework problem actually is, determining what elements should be included, and if there's any variables that are missing or need clarification.
Thanks for posting the original exactly.
Making it a straight line means it is a lot less than 12 miles. Shouting doesn't change that.If we removed all the curves, making a straight line from top to bottom, how quickly could the car make it to the top?
Without knowing the distance, how? You seem to be arguing it surely wouid reach top speed before hill top, but then we have insufficient data to answer the question.you use the formulas to figure all of that out.
I offer an alternative assumption, that the curves are large enough radius that full speed can be maintained around them. (Since there was no map included, that still fits the description.)12.42 miles are the total real course mileage including 156 turns...the mileage to be ran its assumed to be shorter
I do not see the relevance of that observation. The curvy course of 12.42 miles is mere background and of no significance in the question being asked.I offer an alternative assumption, that the curves are large enough radius that full speed can be maintained around them. (Since there was no map included, that still fits the description.)
An "average" acceleration is of little use. The distance covered in a given time with a front-loaded acceleration will be greater than that covered in a given time with a more constant acceleration, even though the "average" is the same in both cases.so assume the given acceleration is "average" as stated
For what it's worth, the actual, real-world track length is 12.42 miles. That's one detail that matches the problem description given here.I am thinking that at a 6.4% slope the straight road would be longer than the curved road.
Possibly 73916.5 feet or 13.999 miles long.
I used a right triangle with a height of 4721 feet and calculated a base of 73765.625 feet based on the height and slope. Then Pythagoras did the rest.
I interpreted the slope given in the problem (6.4%) as a constant. A constant which would have to be ignored in order to use straight line displacement. This is not homework, it is a qualifying question for a contest.The problem statement, as written, has a few ambi
For what it's worth, the actual, real-world track length is 12.42 miles. That's one detail that matches the problem description given here.
But that's not the displacement between the two points, it's the total distance, which includes curves, hills, and all. The real-world displacement will is significantly shorter than 12.42 miles, not longer.
If your approach is to find the straight-line displacement of the real-world start and finish locations, you will need to look up their GPS coordinates on the Internet (presumably), and use geometry to calculate their 3-dimensinal displacement (and effective slope, if that's even relevant.) Keep in mind that these necessary details were not given in the problem statement, as it was described. This leads me to believe that this is probably not the approach the author of the problem intended. (Then again, this problem statement is so full of ambiguities, it's anybody's guess.)
So quite easy once it is explained that the straightening of the road was supposed to preserve the length, not the slope - despite that in the question statement the slope is given prominence, while the distance seems to be just background on the actual course.this is the answer to the previous problem
Although the 6.4% slope is re-iterated on the solution slide, it is never actually used in the calculation. Despite the prescription of the 0.91 g acceleration being average, the proffered calculation treats it as constant instead.So quite easy once it is explained that the straightening of the road was supposed to preserve the length, not the slope - despite that in the question statement the slope is given prominence, while the distance seems to be just background on the actual course.