A roller coaster cart with a mass of 116 kg is originally moving at 22 m/s at a height of 24 meters above the ground on a frictionless hill (approximated by an incline which is fricitonless). At the bottom of the hill is a horizontal surface which has friction. The length of this surface is unknown, but its coefficient of kinetic friction is 0.59. After this surface, is a frictionless circular loop with a radius of 5.4 meters. At the top of the of loop, the cart is moving at a speed such that the normal force's magnitude on the cart is 3.3 times the weight of the cart. What is the length of the horizontal surface which had friction at the bottom of the hill in meters?