In this video I go over Question 5 of the Applied Project: Which is Faster, Going Up or Coming Down? In this question, I look at the general case of physical properties and determine if a ball reaches its maximum height faster or slower than for the…
In this video I go over Question 5 of the Applied Project: Which is Faster, Going Up or Coming Down? In this question, I look at the general case of physical properties and determine if a ball reaches its maximum height faster or slower than for the ball to reach the ground after reaching its maximum height. Since we can't solve for the time explicitly from the height equation, we can however solve it indirectly. This is done by determining whether the height function is positive or negative (or zero) when we plug in the time being equal to two times the time it takes to reach the maximum height.
In turns out that our Question 4 video is in fact correct in that ascent is always faster than descent! Although in this applied project, a linear model was used for the air resistance, it turns out that any model will yield the same result, that is ascent is faster. The following paper illustrates this proof so take a look through it if you are interested in learning more.
Fred Brauer, "What Goes Up Must Come Down, Eventually," The American Mathematical Monthly, Volume 108, Number 5. (May, 2001), pages 437-440. URL: http://www.cems.uvm.edu/~tlakoba/AppliedUGMath/FallingBall_01.pdf
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhs9LhJrn90fMK8A1WQ
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/applied-project-which-is-faster-going-up-or-coming-down-question-5
Related Videos:
Applied Project: Which is Faster, Going Up or Coming Down? Question 4: https://youtu.be/xsZ00yxiVqI
Applied Project: Which is Faster, Going Up or Coming Down? Question 3: https://youtu.be/DM5WFRv2Hh8
Applied Project: Which is Faster, Going Up or Coming Down? Question 2: https://youtu.be/irZGAdB6HPk
Applied Project: Which is Faster, Going Up or Coming Down? Question 1: https://youtu.be/VFH4Pc5cA-M
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