Question

5. A highway curve is banked (inclined ) in such a way that a car travelling at speed of 13.5m/s can round the curve without skidding in the absence of friction. If the angle is 300, what is the radius of the curve?
A.10.5m B.21.0m C. 31.7m D.36.7m

Answer 1

For a frictionless banked curve: tan θ = v^2/(r g) ⇒ r = v^2/(g tan θ).

With v = 13.5 m/s, θ = 30°, tan30° = 1/√3 ≈ 0.57735, and g ≈ 9.8 m/s^2:

r = 13.5^2 / (9.8 × 0.57735) = 182.25 / 5.6598 ≈ 32.2 m.

Closest choice: C. 31.7 m.