What Is the Correct Banking Angle for a Road Curve with No Friction?

[x86]

Homework Statement

you want to design a curve with a radius of curvature of 350 m, so a car can turn at a velocity of 15 m/s without relying on friction. Find the angle at which the road must be banked.

Homework Equations

I've derived this equation via free body diagram, x component is gravity pushing the car into the curvature

Fn sinx = mv^2/r
Fn cosx = mg

tanx = v^2 / (gr) where r = radius, g = gravity, v = velocity

I've used it before so I know its correct.

The Attempt at a Solution

tanx = 15^2 m^2/s^2 / (9.8 m/s^2 * 350 m)

x = 3.75 degrees.

The book says this answer is incorrect, and I'm not sure where I went wrong. (The book got around 30 degrees)

 

[ehild]

Youe solution is correct, but have you copied the data correctly?

350 m for the radius is a bit too great. Was not it 35 m instead?

ehild