Edexcel Mathematics January 2023 · Paper 1 · Question 13 · ExamRizz

ExamRizzEdexcel MathematicsMathematics

January 2023 · Paper 1 · Question 13 · 7 marks

13. On a roller coaster ride, passengers travel in carriages around a track. On the ride, carriages complete multiple circuits of the track such that • the maximum vertical height of a carriage above the ground is 60 m • a carriage starts a circuit at a vertical height of 2 m above the ground • the ground is horizontal The vertical height, H m, of a carriage above the ground, t seconds after the carriage starts the first circuit, is modelled by the equation H = a – b (t – 20)2 where a and b are positive constants. (a) Find a complete equation for the model. (3) (b) Use the model to determine the height of the carriage above the ground when t = 40 (1) In an alternative model, the vertical height, H m, of a carriage above the ground, t seconds after the carriage starts the first circuit, is given by H = 29 cos(9 t + α)° + β 0  α < 360° where α and β are constants. (c) Find a complete equation for the alternative model. (2) Given that the carriage moves continuously for 2 minutes, (d) give a reason why the alternative model would be more appropriate. (1) 35

Lesson: Laws of Indices