مشاهدة النسخة كاملة : مسألة على المعدلات الزمنية المرتبطة


unusualboy9999
02-09-2011, 02:02 AM
السلام عليكم ورحمة الله
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جزاكم الله عنّا كل خير

-يستند سلم طوله 6.5 متر بأحد طرفيه على أرض أفقية وبطرفه الآخر على حائط رأسى فإذا انزلق الطرف السفلى للسلم مبتعدا عن الحائط بمعدل 30 سم/دقيقة عندما يكون على بعد 2.5 متر من الحائط.اوجد عندئذ معدل إنخفاض الطرف العلوى للسلم.ثم أوجد بعد الطرف العلوى للسلم عن الأرض عندما يتحرك الطرف العلوى والطرف السفلى بنفس المعدل.

شكراً جزيلاً

الاستاذ على الدين يحيى
02-09-2011, 03:17 PM
من فيثاغورس : س^2 + ص^2 = 6.5 ............. (1)
بأخذ إشتقاق الطرفين بالنسبة للزمن ن :
2 س ( د س / د ن ) + 2 ص ( د ص / د ن ) = 0 .............. (2)
بالتعويض عن ص = 2.5 فى (1) نجد أن س = 0.25
بالتعويض فى (2) عن س = 0.25 ، د س / د ن = 30
نجد أن : د ص / د ن = - 6 سم / د ( وهو المطلوب أولاً )
عندما د ص / د ن = - د س / د ن عوض فى (2)
نجد أن س = ص
عوض فى (1)
نجد أن ص = 1 / 2 × جذر 13 ( وهو المطلوب ثانياً )

unusualboy9999
02-09-2011, 06:33 PM
متشكر جدا أستاذنا الفاضل

winamin
05-15-2022, 05:14 PM
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