gibson:teaching:fall-2014:math445:lab8
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gibson:teaching:fall-2014:math445:lab8 [2014/12/04 07:29] gibson |
gibson:teaching:fall-2014:math445:lab8 [2015/04/24 14:25] gibson |
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| - | ====== Math 445: Home run ====== | + | ====== Math 445 HW3: Home run ====== |
| It is easy to determine the trajectory of a projectile subject to gravity if you neglect air resistance. It is much more difficult to solve if you include air resistance, especially if the | It is easy to determine the trajectory of a projectile subject to gravity if you neglect air resistance. It is much more difficult to solve if you include air resistance, especially if the | ||
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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's unlikely 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, $x=120$. |
| <code> | <code> | ||
| yfence = interp1(x(:,1), x(:,2), 120); | yfence = interp1(x(:,1), x(:,2), 120); | ||
| </code> | </code> | ||
| + | **Problem 3:** For the optimal sea level home run, make a plot that shows the $x,y$ trajectory of the homerun hit with the minimal speed and optimal angle, which you determined in problem 2. Now add another curve that shows what the path of the ball would be if there were no air resistance. Use a solid line for the curve with air resistance, and a dashed line for the curve without. | ||
| + | **Problem 4:** Do the same as problem 3 for the home run in Denver. | ||
gibson/teaching/fall-2014/math445/lab8.txt ยท Last modified: 2015/04/24 14:25 by gibson
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