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I am working on projectile motion and optimization these days. Projectile motion uses the kinematic equations of free fall for the vertical direction together with the equations of constant velocity in the horizontal direction.

Maximum Range:if an object is launched at a certain initial speed, the angle theta of maximum range depends on the initial and final height. For example, the angle is 45 degrees for same level launching and landing. The angle decreases as the launching elevation becomes larger than the landing elevation.

Maximum Flight Time:the launching angle will be 90 degrees in the case but the range will be zero. the object is going straight up and will stay in the air the longest in comparison to other situation.

Now, what if I wanted to find the launching angle that produces the largest range and the longest flight time simultaneously? What would I go about that? Is that possible? Do I need to construct a function having two variables, the range and the flight time, and assign some weight factor to each? The weight would give relative importance to range and flight time. I am not sure how to get started on this...

For the previous simple cases (maximize either time or distance), it was simply about setting the first derivatives equal to zero.

thanks,

fog37

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# I Optimization in Projectile Motion

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