A curve in a road forms an arc of radius 800m If the road is 39.2m wide, calculate the safe speed for turning, if the outer edge of the road is 0.5m higher than the inner edge. Take g=9.8m/s2.
A
5m/s
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B
10m/s
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C
15m/s
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D
20m/s
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Solution
The correct option is B10m/s Here, radius of circular arc r=800m, Distance between the edges of the road i.e AB=39.2m Height of the outer edge with respect to the inner edge h=0.5m.
Applying the condition of banking, for maximum safe speed (v) : tanθ=v2rg.....(i)
From triangle ABC, sinθ=0.539.2=0.012tanθ=BCAC=0.5√39.22−0.52=0.012 We can see that values of sinθ and tanθ are very small.
For very small angle: tanθ≃θ≃sinθ=BCAB...(ii)
From Eq.(i) and Eq. (ii) ⇒v2rg=BCAB=hAB ∴v=√h×r×gAB=√0.5×800×9.839.2 or, v=10m/s