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:

Where y = upward distance (m), t = time (s), y = upward velocity (m/s), g = gravitational constant (= 9.81 m/s²), cd = drag coefficient (kg/m), and m = mass (kg). Note that the drag coefficient is related to more fundamental parameters by

C_d = ½ pAC_d

Where r = air density (kg/m³), A = area (m²), and Cd = the dimensionless drag coefficient. Use the following parameter values for your calculation: d = 22 cm, m = 0.4 kg, r = 1.3 kg/m³ and C_d = 0.52.

Transcribed Image Text:

dy dt dv Cd dt =-g-mulul