$30.$ Integrated Concepts

If a car takes a banked curve at less than the ideal speed, friction is needed to keep it from sliding toward the inside of the curve $($a real problem on icy mountain roads$).($a$)$ Calculate the ideal speed to take a $100$ m radius curve banked at $\backslash (15\mathrm{.}0^\{\backslash$circ$\}\backslash ).($b$)$ What is the minimum coefficient of friction needed for a frightened driver to take the same curve at $\backslash (20\mathrm{.}0\backslash$mathrm$\{$~km$\}/\backslash$mathrm$\{$h$\}\backslash )?$