Answer:
15.49 metres
Explanation:
Given in the question that,
the railroad rail is 4 km before expansion.
To find,
the meters the centre of the rail rise above the ground on hot day.
When the railroad expands, it would approximate the forming of an isosceles triangle at the centre of the rail,
with base 4km
and
each isosceles side leg of the triangle is given by
(4 + 12x10^-5) / 2 = 4.00012 / 2 = 2.00006 kilometers
1cm = 10^-2 m = 10^-(2+3) = 10^-5 km
Taking one half of the isosceles triangle, we have a right triangle with base
base = 4 / 2 = 2 km
and
hypothenuse = 2.00006 kilometers.
By using the Pythagoras theorem, find the height of the right triangle as formed above.
hypo² = base² + height²
2.00006² - 2² = height²
height = √(2.00006² - 2²)
= 0.01549km
= 0.01549 x 10^3 m
= 15.49m
Thus, the centre of the rail will rise 15.49 metres above the ground.