I am wondering how to solve a kinematics exercise with a differential equation. I want to respect other author's copyright and the solution to their exercises, so I won't put the word problem here but if its okay I'll come up with a similar problem and ask for help solving that and then I'll be able to solve the problem from my textbook.
Otherwise, I think this will be taken down.
This is based on Giancoli Physics: Principles with Applications 7th edition, chapter 2 Describing Motion: Kinematics in One Dimension, page 45, problem 53, level III, which means a Challenge problem.
Douglas Giancoli states on page 43 (with Grammarly corrections applied to the quote), "The Problems at the end of each Chapter are ranked I, II, or III according to estimated difficulty, with level I Problems being easiest. Level III is meant as challenges for the best students."
This is a similar problem that I think could be reframed as a differential equation. A falling stone takes 0.2718 s (I'm choosing a time based on the digits of Euler's number) to travel past a window 2.718 m tall. From what height above the top of the window did the stone fall?
I think this could be modeled as an initial value problem for a second-order differential equation. It also might be a differential algebraic equation or a delay-differential equation that could be solved with DSolve. Once I figure out how to abstract the problem, I can make the computer do the calculations, get the result, and interpret the answer in the context of the problem.
My question is, what question should I ask in Computer-Based Maths step 1? Computer-Based Maths step 2 is abstract, which I think will be an ODE, and step 3, I think, will be DSolve and step 4 will be writing a conclusion.