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

Answer:

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 $\frac{3000+0.2}{2} meter = 1500.1 meter$

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

So using Pythagoras theorem,  

$x^{2}+1500^{2}=1500.1^{2}$

$x^{2}=1500.1^{2}-1500^{2}$

$x^{2}=(1500.1+1500)(1500.1-1500)$

$x=3000.1\times0.1$

$x^{2}=300.01$

Taking square roots on both sides we get,

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

So, the rail raise 17 meter from the ground .