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**1. Homework Statement**

An engineer wishes to design a curved exit ramp for a toll road in such a way that a car will not have to rely on friction to round the curve without skidding. She does so by banking the road in such a way that the force causing the centripetal acceleration will be supplied by the circular path.

**a)**Show that for a given speed (v) and a radius (r), the curve must be banked at the angle (theta) such that [tex]tan \theta= \frac{v^2}{rg}[/tex]

**Find the angle at which the curve should be banked if a typical car rounds it at a 50m radius and a speed of 13.4 m/s.**

b)

b)

**2. Homework Equations**

[tex]tan \theta= \frac{v^2}{rg}[/tex]

**3. The Attempt at a Solution**

I have no idea what a) means or how to start it. I know that you have to show it by using the variables given. However, I don't know how you would show it. =P

b) [tex]tan \theta= \frac{v^2}{rg}[/tex]

[tex]tan \theta= \frac{13.4m/s^2}{(50m)(9.8m/s^2)}[/tex]

[tex] tan \theta= 0.366449 radians [/tex]

[tex] \theta= tan^{-1}{}0.366449 radians [/tex]

theta=20.125 radianstheta=20.125 radians

Thanks for your help!