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SL Math IA Help - Long jump

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Hi, 

So I started my math IA on long jump but I'm pretty lost on what to do. I took a burst of my jump and put the photos together using photoshop. I originally wanted to find the equation of which I jumped, my angle of takeoff, and the speed of my takeoff and then compare it to some 'optimal' values that would make me jump a certain distance, basically talking about how I can improve my jump based on my takeoff angle and speed. Is it possible to set an 'optimal' distance and then change my angle of take off and speed to achieve this distance? I already found the equation of my parabola and my angle of takeoff. However, that only uses quadratics and simple trig, which I'm also afraid is too easy and not enough. Idk how to make my math harder.

Secondly, since I took a burst and not a video of my jump, I don't know how long the jump took, so I run into that problem when finding my speed. Can this be fixed? 

Thanks. 

 

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