Distance between a Clock's hands when the distance is increasing most rapidly

WMDhamnekar · 2025-12-07T14:57:05-0600

Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question)

Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

berkeman · 2025-12-07T19:40:02-0600

WMDhamnekar said:

Answer: Making assumption that both the hands moves at constant angular velocities, the answer is SQRT(7) But don't you think this assumption is somewhat doubtful and wrong?

The hands move with constant and different angular velocities. At what point of their movement do you think the difference in their tip velocity vectors is the max? How did you approach this question?

Distance between a Clock's hands when the distance is increasing most rapidly

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