The swap — and the mass that cancels
Drop something, and stored energy becomes motion energy: . Now watch the on both sides — it cancels. Solve, and (v equals root two g h): the landing speed does not care what the mass is. Galileo dropped that fact off a tower four centuries ago, and it still lands.
These are two-step problems: bank the energy at the top, cash it at the bottom. Write the middle answer down with its units before moving on — and estimate first. One order-of-magnitude guess costs five seconds and catches almost every slipped root and missing g.
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