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gibson:teaching:spring-2018:math445:lab11 [2018/04/26 08:59]
gibson
gibson:teaching:spring-2018:math445:lab11 [2018/05/01 06:20]
gibson
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 $ dy/dt = v_y $  $ dy/dt = v_y $ 
  
-$ dv_x/dt = -\frac{\mu}{m} v_x \sqrt{v_x^2 + v_y^2}$ ​+$ dv_x/dt = -\frac{\alpha}{m} v_x \sqrt{v_x^2 + v_y^2}$ ​
  
-$ dv_y/dt = -\frac{\mu}{m} v_y \sqrt{v_x^2 + v_y^2} - g$+$ dv_y/dt = -\frac{\alpha}{m} v_y \sqrt{v_x^2 + v_y^2} - g$
  
-The constant $g = 9.81 m/s^2$ is the acceleration due to gravity. The constant $\mu = \rho_{air} C_D A/2$ in the air resistance term depends on physical characteristics of the projectile and the air. The following code will calculate $\mu$ for a standard baseball, given either value of $\rho_{air}$.+The constant $g = 9.81 m/s^2$ is the acceleration due to gravity. The constant $\alpha = \rho_{air} C_D A/2$ in the air resistance term depends on physical characteristics of the projectile and the air. The following code will calculate $\alpha$ for a standard baseball, given either value of $\rho_{air}$.
  
 <​code>​ <​code>​
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 m = 0.145; ​      % mass of baseball in kg (145 gm m = 0.145; ​      % mass of baseball in kg (145 gm
  
-mu = rho_air*C_D*A/​2;​ % coefficient of nonlinear |v|^2 term, in mks units+alpha = rho_air*C_D*A/​2;​ % coefficient of nonlinear |v|^2 term, in mks units
 </​code>​ </​code>​
  
gibson/teaching/spring-2018/math445/lab11.txt ยท Last modified: 2018/05/01 06:23 by gibson