What is the radius of the curve?

Question

i think my free diagram is wrong because for some reason, i cant derive the g*tan(theta) = v^2/r equation.

Answer 1

The banking of curves formula is

rg tan ø = v2

where

r = radius of curvature

g = acceleration due to gravity = 9.8 m/sec^2 (constant)

ø = angle of bank = 31.5 degrees

v = velocity = 22.7 m/sec (given)

Substituting appropriate values,

r(9.8)(tan 31.5) = 22.7^2

r = 22.7^2/(9.8 * tan 31.5)

r = 85.8 meters

Answer 2

7.13131m