Centripetal Force at an Angle

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[SOLVED] Centripetal Force at an Angle

Homework Statement



The design of a new road includes a straight stretch that is horizontal and flat but that suddenly dips down a steep hill at 22 degrees. The transition should be rounded with what minimum radius so that cars traveling 90 km/h will not leave the road?

Homework Equations



v=(2*pi*R)/T
F=ma
a=(v^2)/R

The Attempt at a Solution



90 km/hr=25 m/s. I tried setting up an equation where the centripetal force equaled the force of gravity:(25^2)/r=9.8 sin 22 , but that gives me a radius of approximately 170.25m, when the correct answer is 63.8m.

EDIT: Solved. (25^2)/r=9.8
 
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