10   4. The velocity v ms–1, of a raindrop, t seconds after it falls from a cloud, is modelled by the differential equation d d v t = –0.1 v 2 + 10    t  0 Initially the raindrop is at rest. (a) Use two iterations of the approximation formula d d y x y y h n n n 1 to estimate the velocity of the raindrop 1 second after it falls from the cloud. (5) Given that the initial acceleration of the raindrop is found to be smaller than is suggested by the current model, (b) refine the model by changing the value of one constant. 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_____________________________________________________________________________________ _____________________________________________________________________________________ Turn over 11   Question 4 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 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_____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 4 is 6 marks)