Physics

Problem

Two adjacent lanes of a curved speedway are banked at the same angle of

35^{\circ}

. The inner lane has a radius of

50\,\text{m}

, while the outer lane has a radius of

70\,\text{m}

. Derive an expression for the design speed

v

of a frictionless banked curve in terms of the radius

r

, then compute the ratio

v_{\text{outer}}/v_{\text{inner}}

to two significant figures.