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Question
The radius of a circular track is 200 m. Find the angle of banking of the track, if the maximum speed at which a car can be driven safely along it is 25 m/sec.
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Solution
Given:
v = 25 m/s,
r = 200 m,
g = 9.8 m/s2
To find:
Angle of banking (θ) = ?
Formula:
`tan theta = (v_max^2)/(rg)`
∴ `tan theta = ((25^2))/(200 xx 9.8)`
∴ `tan theta = 625/1960`
∴ `tan theta = 0.3189`
∴ θ = tan−1 (0.3189)
∴ θ = 17°41'
Therefore, the angle of banking of the track should be approximately 17°41' to allow a car to be driven safely along it at a maximum speed of 25 m/s.
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