sample_exam_questions_1

sample_exam_questions_1 - CE 335 Old exam questions(with...

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CE 335 Old exam questions (with solutions following) for Chapters 1-4 1] Write a Matlab function that determines whether any given year is a leap year in the Gregorian calendar. It should return 1 if the positive integer year is a leap year and 0 otherwise. (Leap years are divisible by 4 but not by 100, unless they are divisible by 400; thus, 2000 and 2008 are leap years, but 1900, 2009, or 2100 are not.) (Possibly useful built-in function: if a and b are integers, rem(a, b) returns the remainder of a ÷ b.) The first line of the function should be function is_leap_year = leap(year) 2] Consider a free-falling bungee jumper whose velocity is given by (1) dv/dt = g - (c d /m)v 2 The drag coefficient c d is actually not constant but increases as the bungee jumper falls because air is more dense lower in the atmosphere. We suppose that (2) dc d /dz = c d /H where H is a scale height of the atmosphere. (Note that v = dz/dt.) Suppose that g = 10 m s -2 , m = 60 kg, and H = 8 × 10 3 m. The initial conditions at t = 0 s are v = 0 m s -1 and c d = 0.2 kg m -1 . We want to estimate v at some later time(s). (a) Show how you would apply Euler's method to solve this problem (i.e. write an approximate expression for v(t + Δ t) in terms of the values of variables at the current time t). (b) Write a Matlab script to estimate v at t = 10 s using Euler's method with a timestep Δ t of 1 s. 3]

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sample_exam_questions_1 - CE 335 Old exam questions(with...

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