Homework 21 Solution

# Homework 21 Solution - Lecture 21 MEEN 357 Homework...

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Lecture 21 MEEN 357 Homework Solution 1 Lecture-21-Homework-Solution-2009.doc RMB 1. A crazy man jumps out of an airplane over Aggieland. In the coordinate system fixed to the airplane, the ordinary differential equations governing his decent are 22 2 2 d d x dx dx dy mc dt dt dt dt ⎛⎞⎛⎞ =− + ⎜⎟⎜⎟ ⎝⎠⎝⎠ (21.1) and 2 2 d d y dy dx dy m g dt dt dt dt + (21.2) where 80 kg m = is the mass, 5.38 Nsec /m d c = is the drag coefficient and 2 9.81 m/sec g = is the gravitational constant. If the man jumps with an initial horizontal velocity of 130 m/sec and an initial vertical velocity of 0 from an initial height of 0 in his coordinate system, plot the trajectory , i.e., his x and y positions, of the man for 5 seconds. Solution: The first step is to write the two coupled second order ordinary differential equations (21.1) and (21.2) in normal form. As with our many examples, you define the column vector x by 1 2 3 4 x x dx x dt x y x dy dt ⎡⎤ ⎢⎥ == ⎣⎦

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Homework 21 Solution - Lecture 21 MEEN 357 Homework...

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