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- Numerical Method Need Answer Fast I Appreciated It Tq My Id Is De190075 1 (18.62 KiB) Viewed 71 times
Q3 (a) The velocity of an upward rocket is given by, v(t) = u In mo mo-91 81, where me is the initial mass of a rocket at 1 = 0s, q is the rate at which fuel is expelled (kg/s) and u is the velocity at which is being expelled (m/s). Given the initial mass of the rocket is 90,000 kg, the rocket expels fuel at a velocity of 1300 m/s, at consumption rate of 2000 kg/s and g =9.8067 (m/s). (i) Identify a suitable time interval between 6.8 seconds to 7.1 seconds that has 16-al = 0.1 using intermediate value theorem, so that the rocket able to reach a velocity of 150 m/s. (3 marks) (ii) Examine the time needed for the rocket to reach a velocity about 150 m/s by using bisection method with the suitable interval found in Q3(a)(i) and iterate until |$(1)<E=0.0005 or 4h iteration.
(b) A system which is represented by the given equation below, is able to work effectively even when the time is zero. f(t) = 7t3 - 0.31t+ lat -cost However, there will be a time where the system is put on resting mode for several seconds. (i) Find the derivative of f(t). (2 mark) (ii) By using Newton-Raphson Method, select the approximate resting time in between the interval [1 2] seconds with the absolute system function tolerance is less than 0.0005 or until 4th iteration. Choose to 1 second. (6 marks) =