5) You are on a rollercoaster, and your path is modeled by a vector function r(t), where t is in seconds, the output units are in feet, and t = 0 represents the start of the ride. Assume the standard cardinal directions and elevation for x, y, and z. a. For each ofthese equations, explain what it means in context. i. r(0) = r(120) ii. N(t) = 0 on the interval 0 S t S 25 iii. |r'(20)| = 100 b. Each of these represents a common rollercoaster section. Describe the shape ofthe path, giving detailed dimensions when possible: i. r(20) = (a, b, 10), r(22) = ((1,!) + 8,100), r(24) 2 (61,!) + 16,10). T(20) and T(24) are equal and pointing in the positive X direction, T(22) is the opposite of those. ii. For 40 S t S 44-, Mt) = 215 and z is constant. iii. For 80 S t S 82, 3 begins by pointing toward positive 2, and does one full rotation in the normal (NB) plane, all while T remains constant. iv. For 100 g r g 104, r(t) = as sin (3:) , 20:, 15cos (gt) + 20)