Question

Suppose a railroad rail is 6 kilometers and it expands on a hot day by 18 centimeters in length. Approximately how many meters would the center of the rail rise above the​ ground?

The center of the rail would rise approximately __ meters above the ground.
​(Type an integer or decimal rounded to the nearest tenth as​ needed.)

Answer 1

Answer 1

Center of the rail rise above ground would be 0.01732058 or 17.32 meters

Explanation:

The railroad is 6 km before expansion so when the railroad expands it makes an isosceles triangle at the centre of the rail. The base will be 6 km while each side of triangle will be 3.00005 km

(6+10/10,000)/2 as 100,000 cm gives 1km.

Taking half of the isosceles triangle we will make a right triangle as

6/2 = 3 km and

hypotenuse = 6 km.

Using Pythagoras Theorem we will find the height of the triangle.

h^2 = 3.00005^2 - 3^2

h= square root 0.0003000025

h= 0.01732058

Answer 2

17.32 meters

Explanation:

The centre of the railroad will rise 0.01732058 km. We have found this figure from the calculation in part 1 of this answer. After this we will be converting this figure of decimal numbers into metres by multiplying by 1000. From 1000 meters, because are 1000 metres in 1 km. Therefore as a conclusion, we got the answer that is 17.32 metres above the ground.