Question

Problem H I The Ferris Wheel pictured above, has a diameter of 30 meters. Passengers board this amazing wheel, at a cost of $10 each, from a platform 1.5 meters above the ground. On average the passengers get 3 full revolutions in 15 minutes. a) Determine a trigonometric function that models the height of a passenger above the ground t minutes after boarding. b) Graph this function for Osts 15

Answer 1

Solutions ( 30 ml 31.5 1.5m ak y = Standard form of the equation of the cosine and sine function is A cos {B(x-c)}+D y = A sin {B (4-0+1 Amplitude max.- min. А a A = 2 31.5 1.5 30 2 2 . А 15 Period zr 22 3 Revolutions in is min. 1 Revolutions in 15 = 5 min. 250 O 3 5 = B 5 5 C = 2.5 c 1.25 DE B: ar Phase Shift for cosine function : for sine function : 4 Vertical Shiff : max.t min Do 31.5 +1.5 0 = 31.52 10, 664)- y = 15 cos ( 24 (-2.5)) +33 hit)=y = 15 cos ( 25 %- 56) + h.lt) = Y = 15 sin ( 25k-$)+ 33 2 33 t 33 2

h(t) 35 31-5 30 25 20 IS M 10 5 1.5 t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15