Question

Determine the minimum angle at which a roadbed should be banked so that a car traveling at 20.0 m/s can safely negotiate the curve if the radius of the curve is 2.00 X 10^2 m

A) .200 degrees
B) .581 degrees
C) 11.5 degrees
D) 19.6 degrees
E) 78.2 degrees

Answer 1

The minimum angle at which the roadbed should be banked for a car traveling at 20.0 m/s on a 200 m radius curve is approximately 11.5 degrees, which is option C in the provided choices.

Step-by-step explanation:

To determine the minimum angle at which a roadbed should be banked so that a car traveling at 20.0 m/s can negotiate a curve with a radius of 200 m, we use the formula for an ideally banked curve. This angle can be calculated using the equation \( \tan(\theta) = \frac{v^2}{rg} \), with \( v \) being the velocity, \( r \) the curve's radius, and \( g \) the acceleration due to gravity (9.8 m/s2). Substituting the provided values, we get \( \tan(\theta) = \frac{(20.0 \text{ m/s})^2}{(200 \text{ m})(9.8 \text{ m/s}^2)} \), which simplifies to \( \tan(\theta) = \frac{400}{1960} \), and \( \tan(\theta) = 0.2041 \). The arc tangent of 0.2041 gives us \( \theta \approx 11.5 \) degrees, which corresponds to option C from the choices provided.