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KKKQ 3013 PENGIRAAN BERANGKA

KKKQ 3013 PENGIRAAN BERANGKA. Assignment #5 – Ordinary Differential Equations 19 September 2007 8.00 pm – 10.00 pm. Assignment #5 (adapted courtesy of ref. [1]).

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KKKQ 3013 PENGIRAAN BERANGKA

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  1. KKKQ 3013PENGIRAAN BERANGKA Assignment #5 – Ordinary Differential Equations 19 September 2007 8.00 pm – 10.00 pm

  2. Assignment #5 (adapted courtesy of ref. [1]) Suppose that a projectile is launched upward from the earth’s surface. Assume that the only force acting on the object is the downward force of gravity. Under these conditions, a force balance can be used to derive, where t = time (s), x = altitude (m) measured upwards from the earth’s surface, g(0) = the gravitational acceleration at the earth’s surface (= 9.81 m/s2) and R = the earth’s radius (= 6.37 x 106 m). Decompose this second order differential equation into two first order differential equations (Hint: dx/dt = v). If v (t = 0) = 1400 m/s, use the midpoint method to solve this system of ODE to determine: (i) Maximum height that would be obtained if a step size (or time step) of 100s is used (ii) Maximum height that would be obtained if a step size (or time step) of 50s is used * Tabulate your solution at each step and linearly interpolate to estimate the max. height of the projectile. [1] Chapra, S.C & Canale, R.P, Numerical Methods for Engineers, McGraw-Hill 5th ed. (2006) Week 11

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