Question

What is the ideal speed to take a $100\mathrm{m}$ radius curve banked at ${20.0}^{\circ }$ angle?

Short answer

The ideal speed is $18.9\mathrm{m}/\mathrm{s}$.

Step-by-step solution

Definition of Banking of road

To supply the centre gravity force required for a vehicle to perform a safe turn, the outside edge of curved roadways is raised above the inner edge. This is referred to as road banking.

Calculating Ideal speed 

The ideal speed for a banked road is,

$v=\sqrt{Rg\tan \theta }$

Here, $R$ is the radius of the turn, $g$ is the acceleration due to gravity, and $\theta$ is the ideal banking angle.

Substitute $100\mathrm{m}$ for $R$, $9.8\mathrm{m}/{\mathrm{s}}^2$ for $g$, and ${20.0}^{\circ }$ for $\theta$,

$\begin{array}{c}v=\sqrt{\left(100\mathrm{m}\right)\times \left(9.8\mathrm{m}/{\mathrm{s}}^2\right)\times \tan \left({20.0}^{\circ }\right)}\\ =18.9\mathrm{m}/\mathrm{s}\end{array}$

Hence, the ideal speed is $18.9\mathrm{m}/\mathrm{s}$.