Question

Suppose a railroad rail is 3km and it expands on a hot day by 13 cm in length. Approximately how many meters would the center of the rail rise above the ground

Answer 1

the rise of the center of the rail will be given by =
`\sqrt{hypotenuse^(2)\hspace{0.15cm} -\hspace{0.15cm} base^(2) }`

=
`\sqrt{1500.065^(2) \hspace{0.15cm} -\hspace{0.15cm}1500^(2) }` m = 13.964 m

Explanation:

i) the normal length of the railroad is 3 km = 3000 m.

ii) on a hot day day the railroad rail expands by 13cm = 0.13m

iii) the center of the railroad is at 1500 m which is half of the total length.

iv) the expansion of the railroad in either half of the road is 0.065m which is half of the total expansion.

v) each half of the railroad can be represented by a right angled triangle whose base will be = 1500 m and hypotenuse will be = 1500.065 m .

vi) the rise of the center of the rail will be given by =
`\sqrt{hypotenuse^(2)\hspace{0.15cm} -\hspace{0.15cm} base^(2) }`

=
`\sqrt{1500.065^(2) \hspace{0.15cm} -\hspace{0.15cm}1500^(2) }` m = 13.964 m