Question

calculate the angle of banking of a smooth curved road of radius $100$ m if vehicles can safely travel along it with a speed of $108km/h$.

Answer 1

$v=180\frac{km}{hr}=50\frac{m}{s}$

$r=600m$

$g=9.81\frac{m}{s^2}$

$\theta ={tan}^{-1}\left(\frac{v^2}{rg}\right)={tan}^{-1}\left(\frac{50\times 50}{600\times 9.8}\right)={tan}^{-1}\left(0.4252\right)={23}^o{18}^{{}^{\prime }}$