# Banked Curves (finding smallest & largest speed)

by helen3743
Tags: banked, curves, largest, smallest, speed
 P: 9 Hello, thank you for helping. My Question: On a banked race track, the smallest circular path on which cars can move has a radius r1 = 107 m, while the largest has a radius r2 = 163. The height of the outer wall is 18 m. Find the smallest speed and largest speed at which cars can move on this track without relying on friction. I already solved the problem but I was wondering if it was correct. r2-r1 = 163m-107m= 56m. tan(theta) = 18/56 tan(theta) = v^2 / (rg) v = sqrt(tan(theta)rg) for smallest speed: v = sqrt(tan(18/56)107*9.8) = 2.45 m/s for largest speed: v = sqrt (tan(18/56)163*9.8) = 2.99 m/s Thanks again!
 HW Helper P: 879 tan(@) = 18/56 = 0.34143 But you used tan(18/56)! which = 5.61x10^-3 That's why your answers are so low. If you use tan@ = 0.34143, you will get the correct answers.
 P: 9 oooo.. makes sense. Thank you!

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