What is the Correct Approach for Calculating Connected Rates of Change?

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The discussion revolves around a homework problem related to calculating connected rates of change, specifically in part ii) concerning the rate of change of depth. The original poster expresses confusion about their logic being deemed incorrect. A response suggests checking arithmetic, specifically the multiplication of 4 and 14, indicating a potential calculation error. The poster acknowledges the mistake, highlighting the importance of careful arithmetic in solving such problems. Overall, the conversation emphasizes the need for accuracy in mathematical calculations when determining rates of change.
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Homework Statement



CRoC.jpg

Homework Equations

The Attempt at a Solution


CRoC Solution.jpg
My problem is with part ii)
To me, my logic seems sound for the rate of change of depth but apparently it's wrong.
Does anyone see what I'm missing?
Thanks
 
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AntSC said:

Homework Statement



View attachment 93778

Homework Equations

The Attempt at a Solution


View attachment 93779My problem is with part ii)
To me, my logic seems sound for the rate of change of depth but apparently it's wrong.
Does anyone see what I'm missing?
Thanks

In part ii) check your arithmetic. What is 4 ⋅ 14?
 
Oops! Thanks. Working too fast.
 
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?

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