Assume that the two ends are fixed but that the track expands by one foot and buckles up in the shape of an arc of a Parabola. How far is the middle of that arc off of the ground?
Please provide a detailed explaination, I would be very grateful:)
A railroad track runs absolutely straight and level for exactly one mile?
5280 feet in a mile, so we can write the parabola as y=-a*(x+2640) *(x-2640), i.e., put the endpoints at x-intercepts (+/- 2640,0) and vertex of the upside down parabola at (0, 2640^2*a). Then integrate the arclength sqrt(1+y'^2) from x= -2640 to x=2640 to get a messy transcendental expression, then solve this equal to 5281 (one foot extra track) to get a=.6385012467 *10^-5 approximately. Then the y-intercept (ht of track) is 2640^2*a which is about 44.50098289 or 44.5 feet up.
Reply:It will be 50ft from the ground.
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