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**1. Homework Statement**

What is the fastest possible velocity for a bicyclist travelling down a path with a width of 'w', can have while they go around a 90 degree corner, with a curvature with a radius of 'r

_{c}'? Friction = static friction [itex]\mu[/itex]

_{s}.

**2. Homework Equations**

F

_{ac}=(mV

^{2})/2

F

_{f}=[itex]\mu[/itex]F

_{N}

**3. The Attempt at a Solution**

So I've started off by making a diagram of the path and the potential bike path, I've made it such that the radius r

_{c}at 45 degrees is the x-axis. I've moved the axis back to account for the new radius of the bikers path, which we can call radius effective. From there I'm able to go 45 degree in either direction but I'm confused as to where to go from here.

This question was given as a 'challenge question' just now and it's got me stumped, any hints would be appreciated.