Applied Project: Which is Faster, Going Up or Coming Down? Question 4

In this video I go over Question 4 of the Applied Project: Which is Faster, Going Up or Coming Down? In this question I use the example of the ball in Question 3 to determine the time it takes for it to reach the ground after its maximum height. In this particular example, it is shown that it is in fact slightly faster for the ball to reach its maximum height than it is for it hit the ground after reaching its maximum height. This shows that my initial guess, from Question 1, that the times should be the same, to be proven incorrect.

This is actually a very interesting result. In this question, the time it takes until the ball hits the ground is determined numerically through the graph of the height function derived in Question 3. It turns out that finding an explicit answer for the time is not possible for this particular height function. I will explain this further in Question 5 in the next video, as well as go over a general case to show that the time is always faster to reach the maximum height. That is a very interesting video so stay tuned!

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