A circular racetrack of radius 300 m is banked at an angle of 15°. If the coefficient of friction between the wheels of a race-car and the road is 0.2, what is the (a) optimum speed of the race-car to avoid wear and tear on its tyres, and (b) maximum permissible speed to avoid slipping?

1.  ${\mathrm{v}}_{\mathrm{o}} = 28.1 \mathrm{m}/\mathrm{s} \mathrm{and} {\mathrm{v}}_{\max } = 38.1 \mathrm{m}/\mathrm{s}$

2.  ${\mathrm{v}}_{\mathrm{o}} = 38.1 \mathrm{m}/\mathrm{s} \mathrm{and} {\mathrm{v}}_{\max } = 28.1 \mathrm{m}/\mathrm{s}$

3.  ${\mathrm{v}}_{\mathrm{o}} = 0 \mathrm{m}/\mathrm{s} \mathrm{and} {\mathrm{v}}_{\max } = 28.1 \mathrm{m}/\mathrm{s}$

4.  ${\mathrm{v}}_{\mathrm{o}} = 38.1 \mathrm{m}/\mathrm{s} \mathrm{and} {\mathrm{v}}_{\max } = 100 \mathrm{m}/\mathrm{s}$