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
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I don't always throw a ball in the air but when I do I usually go over some very complicated mathematics to prove that any ball you throw in the air will reach its maximum height faster than it does to reach the ground from its maximum height ;)
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/applied-project-which-is-faster-going-up-or-coming-down-question-5
I think a ball will come down fater from its maximum height than to go up.
Because of gravitational froce which will promotenthe ball to come down and will stop it to go up..