For a banked road of radius r and banking angle θ with coefficient of friction μ, the maximum possible speed is:
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For a banked road of radius r and banking angle θ with coefficient of friction μ, the maximum possible speed is:

G1 Physics · Accepted Answer

At maximum speed the vehicle tends to slide outward, so friction acts down the slope. Resolving forces vertically and horizontally gives v m a x 2 = g r ( s i n θ + μ c o s θ ) / ( c o s θ − μ s i n θ ) = g r ( μ + t a n θ ) / ( 1 − μ t a n θ ) . v_max²=gr(sinθ+μcosθ)/(cosθ-μsinθ)=gr(μ+tanθ)/(1-μtanθ). v m ​ a x 2 = g r ( s in θ + μ cos θ ) / ( cos θ − μ s in θ ) = g r ( μ + t an θ ) / ( 1 − μ t an θ ) .