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gibson:teaching:fall-2014:math445:lab8 [2014/12/03 19:42]
gibson created
gibson:teaching:fall-2014:math445:lab8 [2014/12/03 19:43]
gibson
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-**Problem 2:** Determine the minimum initial ball speed and optimal angle that result in a home run, at sea level, and in Denver. You'll have to start with a guess and tweak it by stages. For a starting point, recall that a good fastball clocks at 90 mph or roughly 40 m/s, and that 45 degrees is $\theta =\pi/4 \approx 0.78.+**Problem 2:** Determine the minimum initial ball speed and optimal angle that result in a home run, at sea level, and in Denver. You'll have to start with a guess and tweak it by stages. For a starting point, recall that a good fastball clocks at 90 mph or roughly 40 m/s, and that 45 degrees is $\theta =\pi/4 \approx 0.78$.
  
 Note that Matlab'​s ode45 function will return the x,y positions of the trajectory points at discrete time intervals, and it'​sunlikely that any of these will line up exactly with the outfield fence. However you can use interpolation to get the ball height y at exactly at the fence, as follows. If you set up your Matlab code so that $x$ is //x(:,1)// and $y$ is //x(:,2)//, the following code will determine the height $y$ of the ball at the position of the fence, $x=120$. ​ Note that Matlab'​s ode45 function will return the x,y positions of the trajectory points at discrete time intervals, and it'​sunlikely that any of these will line up exactly with the outfield fence. However you can use interpolation to get the ball height y at exactly at the fence, as follows. If you set up your Matlab code so that $x$ is //x(:,1)// and $y$ is //x(:,2)//, the following code will determine the height $y$ of the ball at the position of the fence, $x=120$. ​
gibson/teaching/fall-2014/math445/lab8.txt ยท Last modified: 2015/04/24 14:25 by gibson