A railroad curve is to be laid out on a circle. What radius should be

1.	A railroad curve is to be laid out on a circle. What radius should be used if the track is to change direction by 25° at a distance of 40 meters?
Answer» Given length of arc = 40 m And θ = 25° We know that 180° = π rad ⇒ 1° = π/ 180 rad ⇒ 25° = \((25\times\frac{π}{180})\) = \(\frac{5π}{36}\) radius We know that θ = \(\frac{arc}{radius}\) ⇒ \(\frac{5π}{36}\) = \(\frac{40}{radius}\) ⇒ Radius = \(\frac{40}{\frac{5π}{36}}\) = \(\frac{40\times36\times7}{5\times22}\) = 91.64 m So, the radius of the track should be 91.64 m.

A railroad curve is to be laid out on a circle. What radius should be used if the track is to change direction by 25° at a distance of 40 meters?

Answer»

Given length of arc = 40 m

And θ = 25°

We know that 180° = π rad ⇒ 1° = π/ 180 rad

⇒ 25° = \((25\times\frac{π}{180})\) = \(\frac{5π}{36}\) radius

We know that θ = \(\frac{arc}{radius}\)

⇒ \(\frac{5π}{36}\) = \(\frac{40}{radius}\)

⇒ Radius = \(\frac{40}{\frac{5π}{36}}\)

= \(\frac{40\times36\times7}{5\times22}\)

= 91.64 m

So,

the radius of the track should be 91.64 m.