The optimum (design) speed for a car on a frictionless road banked at 45° along a curve of radius 100 m is (g = 10 m s⁻²):
A31.6 m s⁻¹
B10.0 m s⁻¹
C45.0 m s⁻¹
D22.4 m s⁻¹
Answer & Solution
Correct answer: A. 31.6 m s⁻¹
On a frictionless banked curve the design speed satisfies tanθ = v²/(rg), so v = √(rg tanθ) = √(100×10×tan45°) = √1000 ≈ 31.6 m s⁻¹.
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