Suppose a railroad rail is 7 kilometers and it expands on a hot day 17 centimeters in length. Approximately how many meters would the center of the rail rise above the ground?

We assume the deformed rails follow a circular curver wherer=radius in metres

Step 1: Express H in terms of rUsing the intersection chord relation, we defineH=maximum height of rail above horizontalthenH (2r-H) = 3500^2 = > H^2 - 2rH + 3500^2 = 0solve for H H=r-sqrt (r^2-3500^2) = >H = r - sqrt (r^2-12250000) ... (1)

Let x=half of the angle subtended by the chord at the centre. then by the difference of arc and chord:2r (x-sin (x)) = 0.017 = >2rx-2r (sin (x)) = 0.017 = >2rx-7000=0.017 = >2rx=7000.017 ... (2) together with the simple relation of chord and radius, r*sin (x) = 3500 ... (3) Solve (2) and (3) for r and x to getr=910451.67, x=0.003844256Substitute r in (1) to getH = r - sqrt (r^2-12250000) = 910451.67-sqrt (910451.67^2-12250000) = 6.7275m