On a fun park ride the position of the carriage at time t > 0 (in minutes) is given by the parametric function t I = a(t

[answerhappygod]

On A Fun Park Ride The Position Of The Carriage At Time T 0 In Minutes Is Given By The Parametric Function T I A T 1 (42.53 KiB) Viewed 34 times

On a fun park ride the position of the carriage at time t > 0 (in minutes) is given by the parametric function t I = a(t) cos -b(t) sin 이 이 #66 이 이 y=a(tsin + b(t)cos where aft) and (t) are functions of time. Both r and y are measured in from the axis of rotation and are given in metres (a) Show the squared distance from the axis of rotation, i.e. d2 = +v. can be rewritten as f = (a(0)2 + (6(0)2 + 2a(t) b(t) sin () (10 marks) 3 (b) If the functions a(t) and (t) are given by a(t) = 1 - 2 sin at 3 b(t) = 2 + 2 sin 3 now show the squared distance from the axis of rotation, ie d = x2 + y can be rewritten as 4 = -8 sin* (T) + 4 sin? (T) + 8 sin +5 (9 marks) (c) Using (b) find algebraically all times. 10. (in exact form i.e. in terms of fractions) when the distance d is 3 mi.e. d = 3 or d = 9. Hint: periodic solutions can be represented in the form t = a + nT where a is one solution. T is the period, and n is an integer n = 0,1,... (33 marks) (a) What are the first four times that the distance d of the carringe is 3 m? Give your answers exactly (as a fraction) and approximately as a decimal (8 marks)