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小 發表於 2023-3-25 02:44 AM (第 401 天)
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As with applications of differentiation questions, the hardest part is to actually formulate the equation that you want to (often implicitly) differentiate.
Anyhow, usually we first write down the constants and variables that we do know and want to find. Let's say the point on the ground vertically under L is O. We know/want to find:
Constants: MO=10, d(LO)/dt =-0.5 (minus sign here as the length of LO is decreasing),
Variables (at required time): LO=25, d(ML)/dt=?
So surely we want a relation between MO, ML and LO, and then differentiate it to get the d(blah)/dt's, right?
But that's not hard to find - MO, ML, LO forms a right angled triangle, so, please do it.
Then we differentiate w.r.t. t, plug in all the numerical values for various quantities, and we're done.
I'll stop here and let you work for a bit. There are still a few tight bends to navigate.
Feel free to ask if you get stuck anywhere.
[ 本帖最後由 風之男 於 2023-3-25 02:46 AM 編輯 ]
