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Exam-Style Questions on Sinusoidal Modelling

Problems on Sinusoidal Modelling adapted from questions set in previous Mathematics exams.

1.

IB Standard

A Big Wheel at an amusement park has a diameter of length 70 metres which rotates at a constant speed. The bottom of the wheel is h metres above the ground. A seat starts at the bottom of the wheel.The wheel completes one revolution in 4 minutes. [The diagram is not to scale]

Big Wheel

(a) After 2 minutes, the seat is 76m above the ground. Find h.

(b) After t minutes, the height of the seat above ground is given by \(f(t) =41+ k \cos{ \frac{\pi t}{2}} \) for \(0 \le t \le 16 \).
Find the value of k.

(c) Find when the seat is 40 m above the ground for the third time.


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