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Date November 2009 Marks available 10 Reference code 09N.2.hl.TZ0.12
Level HL only Paper 2 Time zone TZ0
Command term Determine and Find Question number 12 Adapted from N/A

Question

Below is a sketch of a Ferris wheel, an amusement park device carrying passengers around the rim of the wheel.


(a)     The circular Ferris wheel has a radius of 10 metres and is revolving at a rate of 3 radians per minute. Determine how fast a passenger on the wheel is going vertically upwards when the passenger is at point A, 6 metres higher than the centre of the wheel, and is rising.

(b)     The operator of the Ferris wheel stands directly below the centre such that the bottom of the Ferris wheel is level with his eyeline. As he watches the passenger his line of sight makes an angle α with the horizontal. Find the rate of change of α at point A.

Markscheme

(a)

dθdt=3     (A1)

y=10sinθ     A1

dydθ=10cosθ     M1

dydt=dydθdθdt=30cosθ     M1

at y=6 , cosθ=810     (M1)(A1)

dydt=24 (metres per minute) (accept 24.0)     A1

[7 marks]

 

(b)     α=θ2+π4     M1A1

dαdt=12dθdt=1.5     A1

[3 marks]

 

Total [10 marks]

Examiners report

Many students were unable to get started with this question, and those that did were generally very poor at defining their variables at the start.

Syllabus sections

Topic 6 - Core: Calculus » 6.2 » Related rates of change.

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