Problem 1
An object falls from rest through height H with constant gravity g. Find speed after falling distance x and time to fall H. Use the stated ideal model: quantities are constant or vary only as specified, with no extra drag, losses, or external influences. State a sign convention, keep units consistent, and use a classical approximation only where appropriate. (a) Set up the governing equation from a fundamental law. (b) Solve for the requested quantity under the stated conditions. (c) Check the result using a suitable limit, sign, or unit test, and report both the expression and its physical meaning.
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problems.proof.analysis
The boxed expressions answer the parts in order. Signs, conditions of validity, and constants follow the conventions in the statement.