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A car of mass 1000 kg negotiates a banked curve of radius 90 m on a frictionless road. If the banking angle is 45°, the speed of the car is:

1. 20 m/s
2. 30 m/s
3. 5 m/s
4. 10 m/s

Correct answer: 30 m/s

Solution

On a frictionless banked curve, the speed is given by v = √(r * g * tanθ). Substituting r = 90 m, g = 9.8 m/s², and θ = 45°, we get v = √(90 * 9.8 * 1) = √882 ≈ 30 m/s.

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