gibson:teaching:spring-2016:math445:lab12
====== Differences ====== This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision | ||
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gibson:teaching:spring-2016:math445:lab12 [2016/04/27 13:36] gibson |
gibson:teaching:spring-2016:math445:lab12 [2016/05/03 06:50] (current) gibson |
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| $ dy/dt = v_y $ | $ dy/dt = v_y $ | ||
| - | $ dv_x/dt = -\mu v_x \sqrt{v_x^2 + v_y^2}$ | + | $ dv_x/dt = -\frac{\mu}{m} v_x \sqrt{v_x^2 + v_y^2}$ |
| - | $ dv_y/dt = -g - \mu v_y \sqrt{v_x^2 + v_y^2}$ | + | $ dv_y/dt = -\frac{\mu}{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 $\mu = 1/2 \rho_{air} C_D A/m$ 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 $\mu = \rho_{air} C_D A/2$ 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 $\rho_{air}$. |
| <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*m); % coefficient of nonlinear |v|^2 term, in mks units | + | mu = rho_air*C_D*A/2; % coefficient of nonlinear |v|^2 term, in mks units |
| </code> | </code> | ||
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| **Problem 4:** Do the same as problem 3 for the home run in Denver. | **Problem 4:** Do the same as problem 3 for the home run in Denver. | ||
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| + | **Problem 5:** What are your answers for the minimal speed and optimal angle in the more familiar units of miles per hour and degrees, for both Boston and Denver? | ||
gibson/teaching/spring-2016/math445/lab12.1461789362.txt.gz · Last modified: 2016/04/27 13:36 by gibson
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