Question

Suppose a Railroad rail is 3 kilometers and it expands on a hot day by 20 centimeters in length. Approximately how many meters would the center of the rail rise above the ground

Answer 1

Center of the rail rise above the ground in 17 m.

Solution:

The railroad rail is 3 km = 3000 meter

It expands 20 cm = 0.2 meter on hot day in length

So it will form a triangle with base 3000 m and the equal sides will be
`(3000+0.2)/(2) meter = 1500.1 meter`

Let us assume that the center of the rail will raise x meter.

So using Pythagoras theorem,

`x^(2)+1500^(2)=1500.1^(2)`

`x^(2)=1500.1^(2)-1500^(2)`

`x^(2)=(1500.1+1500)(1500.1-1500)`

`x=3000.1*0.1`

`x^(2)=300.01`

Taking square roots on both sides we get,

`x=17(\text {approx})`

So, the rail raise 17 meter from the ground .