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Imagine dropping a steel ball bearing into a tall cylinder full of motor oil Viscous...

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Calculus

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Imagine dropping a steel ball bearing into a tall cylinder full of motor oil Viscous drag has a significant effect on the ball bearing s downward velocity v t One family of dynamic models for this takes the form g kv where g is the acceleration of gravity and k is a constant The size of k is related to the viscosity of the medium when k 0 equation is the familiar friction free approximation for a falling mass The exponent p is an interesting topic for dicussion for this problem we consider p 1 du dt In this problem we use SI units so t is in seconds v is in metres per second etc Use the international standard value g 9 807 and assume motor oil has viscosity parameter k 18 a Find v t Assume v 0 0 v t b Let y t denote the distance the ball bearing has dropped at time t This terminology entails y 0 0 and y t 0 for t 0 Find y t y t c Using computer assistance as appropriate find the time required for the ball bearing to drop 1 metre from its release point y t 1 when t B

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