Insights Quaternions in Projectile Motion

AI Thread Summary
The discussion focuses on the application of quaternions in analyzing projectile motion, highlighting their derivation and alternative methods. Two worked examples illustrate the practical use of quaternions, including one that addresses projectile range on a slope. The approval process for using AAPT materials was described as straightforward, with AAPT representatives being supportive of the renewed interest in archived articles. Overall, the thread emphasizes the effectiveness of quaternions in simplifying complex motion calculations. The insights provided contribute to a deeper understanding of both quaternions and projectile motion.
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Nicely written! Great job!

How hard was it to get the AAPT to approve your use of their material?
 
Thanks for your kind comment. AAPT (or their representatives) were very helpful - I think they were happy for a long-archived article in AJP to get some renewed attention. Certainly there was something of a process to be followed (as you would expect) but at the end of the day the permission granted was very generous in extent.
 
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Hello everyone, Consider the problem in which a car is told to travel at 30 km/h for L kilometers and then at 60 km/h for another L kilometers. Next, you are asked to determine the average speed. My question is: although we know that the average speed in this case is the harmonic mean of the two speeds, is it also possible to state that the average speed over this 2L-kilometer stretch can be obtained as a weighted average of the two speeds? Best regards, DaTario
This has been discussed many times on PF, and will likely come up again, so the video might come handy. Previous threads: https://www.physicsforums.com/threads/is-a-treadmill-incline-just-a-marketing-gimmick.937725/ https://www.physicsforums.com/threads/work-done-running-on-an-inclined-treadmill.927825/ https://www.physicsforums.com/threads/how-do-we-calculate-the-energy-we-used-to-do-something.1052162/
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