Practice question · Multiple choice
A ladder slides down a wall. Its top falls faster and faster while the base moves out at a steady speed. Why does a constant horizontal rate produce an accelerating vertical one?
Hints
- Write the constraint linking x and y, then differentiate both sides with respect to time.
- As the ladder nears the floor, y approaches 0. What must dy/dt do?
Show the answer
B. Because x² + y² = L² ties them, and dy/dt grows as y shrinks
Why
The constraint does the work: differentiating x² + y² = L² ties the two rates, and as y → 0 the vertical rate must blow up. The model predicts infinite speed, which the physical ladder answers by leaving the wall, a good reminder that a constraint holds only while its assumptions do.
Practise Related Rates and Implicit Differentiation
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