A car traveling at 90 km/h is moving around a curve that has a radius of 450 m. Assuming that the acceleration of gravity is 10 m/s², the angle at which the road should be banked if the driver wishes not to rely on lateral friction is A) 0.50°. B) 7.9°. C) 14°. D) unknown; the answer cannot be determined without knowing the mass of the object.

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Quizplus · Accepted Answer

The angle for a banked curve without relying on friction can be found using the formula $\tan(\theta) = \frac{v^2}{rg}$, where $v$ is the velocity in meters per second, $r$ is the radius of the curve in meters, and $g$ is the acceleration due to gravity in meters per second squared. Converting 90 km/h to meters per second gives $v = 90 \times \frac{1000}{3600} = 25$ m/s. Plugging in the values, $\tan(\theta) = \frac{25^2}{450 \times 10}$, solving for $\theta$ gives an angle close to 7.9°.

A Car Traveling at 90 Km/h Is Moving Around a Curve