A car rounds a banked curve of radius 50 m at the design speed (no friction needed). The bank angle is 20°. The design speed is closest to (g = 10 m/s²)

13.5 m/s (v = \sqrt{gR\tan\theta}) For frictionless banking: \tan\theta = v^2/(gR), so v = \sqrt{gR\tan\theta} = \sqrt{(10)(50)(0.364)} = 13.5 m/s.

13.5 m/s (v = \sqrt{gR\tan\theta})

Circular Motion

AP Physics 1· difficulty 4/5

20°

Explanation

\tan\theta = v^2/(gR)

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