Question

A rail road curve is to be laid out on a circle. What radius should be used if the track is to change direction by ${25}^{\circ }$ in a distance of 40 metres?

Answer 1

Let AB be the rail road

$\angle AOB={25}^{\circ }=25\times \frac{\pi }{180}={\left(\frac{5\pi }{36}\right)}^c[\because 1^{\circ }={\left(\frac{\pi }{180}\right)}^c]$

We know that

$\theta =\frac{\text{arc}}{\text{radius}}\Rightarrow \angle AOB=\frac{AB}{OA}\Rightarrow \frac{5\pi }{36}=\frac{40}{r}\Rightarrow r=\frac{40\times 36}{5\pi }\Rightarrow r=\frac{288}{\pi }\text{meter}\Rightarrow r=91.64\text{meter}[\because \pi =\frac{22}{7}]$

$\Rightarrow$ r = 91.64 meter