At what angle should the roadway on a curve with a 50m radius be banked to allow cars to negotiate the curve at 12 m/s even if the roadway is icy (and the frictional force is zero)?
A)0°
B)16°
C)17°
D)35°
E)73°

Question

Quizplus · Accepted Answer

The angle for a banked curve that allows a car to negotiate the curve without relying on friction (ideal for icy conditions) can be found using the formula $\tan(\theta) = \frac{v^2}{rg}$, where $v$ is the velocity, $r$ is the radius of the curve, and $g$ is the acceleration due to gravity (approximately $9.8 m/s^2$). Plugging in the given values ($v = 12 m/s$, $r = 50m$), we get $\tan(\theta) = \frac{(12)^2}{50 \times 9.8}$. Solving for $\theta$ gives an angle close to 16 degrees.

At What Angle Should the Roadway on a Curve with a 50m