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Physics/Calculated Free Fall Time Higher Than Expected

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Question
I am 16 years old and I'm part of an AP Physics C class. Data and calculations done for a recent experiment have stumped everyone in the class, including the teacher. In this experiment, a tennis ball is dropped from a height of 4.64 meters. The average time it took for this object to hit the ground was 0.77 seconds. The next step was to calculate the amount of time it should have taken, given no air resistance. This seemed simple enough, the equation is .5at^2=d, then solve for t. The problem here is that the value of t calculated from this formula is 0.97 seconds, which is higher than the actual value while it should be lower. What is wrong with this math? The second problem I have is that we are supposed to calculate the air resistance by getting the area between the theoretical and actual velocity over time curves. This in itself is simple, it's just an integral. But does this really determine air resistance? The end result would be a measurement of meters, and that doesn't sound correct.

There's one more question I have, although it's not really problem related and you're not really obligated to answer. I'm taking AP Physics C as an independent study, which means it's supposed to be me and two others working on our own with the teacher. Unfortunately, we've been grouped with the Physics B class. At this point, it feels like it will just be a repeat of last year's class. The course did not at all prepare me for the exam, and I'd like to do better this year. Since collegeboard.org seems to be useless for this purpose, is there anything I could possibly do to make sure I learn the material for the test? And to make the course a little more enjoyable and hopefully more of the "independent study" that it's supposed to be, can you think of any larger projects that I could do with my two classmates? Something that could take a full week to complete. One idea was to construct a floating arm trebuchet. Thank you for any input you provide for the problem and/or for my predicament.

Answer
You say the average time was 0.77s.  How many measurements were taken and what were the values?   The timing mechanism must be off since you can't possibly get a time less than 0.97s.  In this case you can't calculate any air resistance unless the measured time is greater than the theoretical time.  
Building a trebuchet might be a good project.  Just be careful where you throw things.  

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Richard J. Raridon

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I can answer most questions in undergraduate physics courses, including electricity and magnetism, atomic and nuclear, mechanics and optics.

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I have taught undergraduate physics courses

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Sigma Xi, AAAS, SE section of APS

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BA in math, MA in physics, PhD in physical chemistry

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