6. THE BUCKLED RAILROAD TRACK
Railroad designers are always looking for ways to
improve the safety and comfort of train travel.
Suppose technology made it possible to make and
transport straight rails one mile long. If one winter
two pairs of these rails were installed along a two
mile portion of track in the desert, then cach rail
would expand approximately one foot in length in the summer heat. Suppose that
instead of buckling, these rails keep their (straight) shape. In this case, the ends
where they meet could jut upward to form a triangle. How high above the ground
would the ends of the rails be?
Let H be the height (in feet) of the tracks above the ground where the two rails come
together.
a) How large do you think H is? Is it big enough for you to stick your arm
between the ground and the tracks? Is it big enough walk through? Could
you drive a car under the buckled tracks? Make a guess.
b) Draw a picture and calculate H. (Note: a mile is 5280 feet long.)
c) How does your calculated value for H compare with your guess in part (a)?