Numerical Methods for Engineers
Numerical Methods for Engineers
7th Edition
ISBN: 9780073397924
Author: Steven C. Chapra Dr., Raymond P. Canale
Publisher: McGraw-Hill Education
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Chapter 25, Problem 25P

Use the following differential equations to compute the velocity and position of a soccer ball that is kicked straight up in the air with an initial velocity of 40 m/s:

d y d t = v d v d t = g c d m v | v |

where y = upward distance (m), t = time (s), v = upward velocity (m/s), g = gravitational constant ( = 9.81  m/s 2 ) , c d = drag coefficient (kg/m), and m = mass (kg). Note that the drag coefficient is related to more fundamental parameters by

c d = 1 2 ρ A C d

where ρ = air density (kg/m3), A = area (m2), and C d = the dimensionless drag coefficient. Use the following parameter values for your calculation: d = 22  cm, m = 0.4  kg,  ρ = 1 .3 kg/m 3  and  C d = 0.52 .

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