Q.A racing track of radius of curvature 9.9 m is banked at $\tan^{-1} 0.5$. Coefficient of static friction between the track and the tyres of a vehicle is 0.2. Determine the speed limits with 10 % margin. (Take g = 10 m/s²)

On a banked rough road the friction-assisted speed window is $v_{min}=\sqrt{rg\,\frac{\tan\theta-\mu_s}{1+\mu_s\tan\theta}}$ to $v_{max}=\sqrt{rg\,\frac{\tan\theta+\mu_s}{1-\mu_s\tan\theta}}$; the 10 % margin tightens both ends. …

A racing track of radius of curvature 9.9 m is banked at $\tan\theta=0.5$, with coefficient of static friction $\mu_s=0.2$ between track and tyres (g = 10 m/s^2). Using the full lower/upper limit formulas $v_{min}=\sqrt{rg\frac{\tan\theta-\mu_s}{1+\mu_s\tan\theta}}$ and $v_{max}=\sqrt{rg\frac{\tan\theta+\mu_s}{1-\mu_s\tan\theta}}$, the example first computes the bare $v_{min}\approx5.2$ m/s and $v_{max}\approx8.78$ m/s, then applies the requested 10% safety margin -- the ALLOWED minimum is raised by 10% (to be safely above the bare minimum) and the allowed maxim …

Compute the no-friction most-safe speed first: $v_s=\sqrt{rg\tan\theta}=\sqrt{49.5}\approx7.04$ m/s — the friction window $[5.196,\,8.775]$ m/s must brac …

Applying the 10 % margin in the wrong direction (lowering $v_{min}$ or raising $v_{max}$) — the margin must make …