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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 of40 metres?

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91.636 m

61.456 m

81.476 m

71.426 m

answer is A.

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Detailed Solution

Given,
Distance l= 40 meters
It is known that
Angle measured in radians,

θ = \frac{25 π}{180}

θ = \frac{5 π}{36}

Suppose, r is the circle's radius,
Then, using by

θ = \frac{l}{r}

, we get
Here,

r = \frac{l}{θ}

r = \frac{40}{\frac{5 π}{36}}

r = \frac{288}{π}

r = \frac{288 \times 7}{22}

r = 91.636 m

Correct option is 1.

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