Meriam, Kraige & Bolton — Kinematics of Particles: Problem 2_81

2/81 An accelerometer \( C \) is mounted to the side of the roller-coaster car and records a total acceleration of \( 3.5g \) as the empty car passes the bottommost position of the track as shown. If the speed of the car at this position is \( 215 \text{ km/h} \) and is decreasing at the rate of \( 18 \text{ km/h} \) every second, determine the radius of curvature \( \rho \) of the track at the position shown.