We know that the banked curve formula is given by:
[tex]\begin{gathered} \tan\theta=\frac{v^2}{rg} \\ \text{ where} \\ \theta\text{ is the angle} \\ v\text{ is the velocity } \\ r\text{ is the radius } \\ g\text{ is the gravitational acceleration} \end{gathered}[/tex]
Plugging the values given and solving for v:
[tex]\begin{gathered} \tan30=\frac{v^2}{(105)(9.81)} \\ v^2=(105)(9.81)\tan30 \\ v=\sqrt{(105)(9.81)\tan30} \\ v=24.4 \end{gathered}[/tex]
Therefore, the ideal speed is 24.4 m/s
