Optimizing Distance from a Cannon: Simplifying the Quadratic Formula

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The discussion revolves around optimizing the angle for maximum distance from a cannon using the quadratic formula. The correct angle is identified as theta = 70.5 degrees, but the user questions whether there's a simpler method to avoid complex algebra. It is clarified that solving the quadratic is unnecessary since the range (r) is always increasing, indicating no solutions exist for certain parameter conditions. The conversation emphasizes understanding the relationship between parameters rather than focusing solely on algebraic solutions. Overall, the thread highlights the importance of recognizing when algebraic solutions may not be applicable in optimization problems.
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Homework Statement


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Homework Equations


Hint given in problem statement
Quadratic formula

The Attempt at a Solution


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The correct answer is theta = 70.5 degrees. I'd like to know if I'm on the right track. Do I simply solve for theta? Is there a better approach that circumvents all of this messy algebra? Much appreciated!
 
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Last edited:
kalpalned said:
Is there a better approach that circumvents all of this messy algebra?
You do not need to solve the quadratic. If r is always increasing the quadratic has no solutions. What condition on the parameters leads to that?
 

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