Question

19£®Ä³ÎïÀíÐËȤС×éÓÃƵÉÁÕÕÏàµÄ·½·¨£¨Ã¿¸ôÏàµÈʱ¼äÅÄÉãÒ»ÕÅÕÕƬ£©Ñо¿Ð¡Îï¿éÑØбÃæÏòÏÂ×öÖ±ÏßÔ˶¯µÄÓйØÎÊÌ⣮ÏÂͼÊÇËûÃÇij´ÎʵÑéʱÅÄÉãµÄƵÉÁÕÕƬ£®
£¨1£©ÏÂÁÐËĸöͼÏóÖУ¬Ò»¶¨²»ÄÜ·´Ó³Ð¡Îï¿éÔ˶¯Çé¿öµÄÊÇC£®

£¨2£©ÒªÊ¹Ð¡Îï¿éÔÚбÃæÉÏÔ˶¯µÄƽ¾ùËÙ¶ÈÔö´ó£¬¿É²ÉÓõķ½·¨ÓÐÔö´óбÃæÇã½Ç¦È£¨Ð´³öÒ»ÖÖ¼´¿É£©£®
£¨3£©Ö»ÓÃÃë±íºÍ¿Ì¶È³ßÒ²¿É²â³öСÎï¿éÑØбÃæÏòÏÂ×öÖ±ÏßÔ˶¯Ä³¶Î¾àÀëµÄƽ¾ùËٶȣ¬ÎªÁ˼õС²âÁ¿Îó²î£¬Ð±ÃæµÄб½Ç¦ÈÓ¦½ÏС£¨Ñ¡Ìî¡°½Ï´ó¡±»ò¡°½ÏС¡±£©Ð©£®
£¨4£©Èô°ÑСÎï¿éij´ÎÑØбÃæÏòÏÂ×öÖ±ÏßÔ˶¯µÄ¾àÀëAC·Ö³ÉÏàµÈÁ½¶ÎABºÍBC£¬ÇÒÒÑÖªÎï¿éÔÚÕâÁ½¶ÎµÄƽ¾ùËٶȷֱðΪv₁ºÍv₂£¬ÔòAC¶ÎµÄƽ¾ùËÙ¶ÈΪ$\frac{2{v}_{1}{v}_{2}}{{v}_{1}+{v}_{2}}$£®£¨±í´ïʽÖеÄ×Öĸ·ûºÅÖ»Äܺ¬ÓÐv₁¡¢v₂£©

Answer 1

·ÖÎö £¨1£©Ê×ÏÈ·ÖÎöС³µµÄÔ˶¯Çé¿ö£¬ÔÙÃ÷ȷͼÏó¸÷ÎïÀíÁ¿Ö®¼äµÄº¯Êý¹Øϵ£¬È»ºó¸ù¾ÝͼÏóÌصã½øÐÐÅжϣ»
£¨2£©Â·³ÌÒ»¶¨£¬ÒªÊ¹Ð¡³µµÄƽ¾ùËٶȱä´ó£¬ÓÉËٶȹ«Ê½v=$\frac{s}{t}$¿ÉÖª¾ÍÒª¼õÉÙÏ»¬Ê±¼ä£¬¿É´ÓÏÂÁз½·¨¿¼ÂÇ£ºÔö´óбÃæ½Ç¶È¡¢»òÔÚ¸ü¹â»¬µÄбÃæÉÏʵÑ飻
£¨3£©ÊµÑéÖÐбÃæÇã½ÇԽС£¬Ð¡³µËٶȱ仯ԽÂý£¬Ð¡³µÔ˶¯Ê±¼äÔ½³¤£¬±ãÓÚʱ¼äµÄ²âÁ¿£»
£¨4£©ÓÉËٶȹ«Ê½µÄ±äÐι«Ê½Çó³öÎïÌåµÄÔ˶¯Ê±¼ä£¬È»ºóÇó³ö×Ü·³ÌÓë×Üʱ¼ä£¬×îºóÇó³öÕû¸ö·³ÌµÄƽ¾ùËٶȣ®

½â´ð ½â£º
£¨1£©ÓÉͼ¿ÉÖª£¬Ð¡Îï¿é×ö¼ÓËÙÖ±ÏßÔ˶¯£¬ABÁ½Í¼ÊÇv-tͼÏó£¬ÊǼÓËÙÔ˶¯Í¼Ïó£¬CͼÊÇs-tͼÏóÊÇÔÈËÙÖ±ÏßÔ˶¯Í¼Ïó£¬DͼÊÇs-tͼÏóÊǼÓËÙÖ±ÏßÔ˶¯£¬Ò»¶¨²»ÄÜ·´Ó³Ð¡Îï¿éÔ˶¯Çé¿öµÄÊÇC£»
£¨2£©Ôö´óбÃæ½Ç¶È»ò¼õСбÃæºÍÎï¿é½Ó´¥Ãæ¼äµÄ´Ö²Ú³Ì¶È£¬¼õÉÙÏ»¬Ê±¼ä£¬ÓÉËٶȹ«Ê½v=$\frac{s}{t}$¿ÉÖª£¬ÔÚ·³ÌÒ»¶¨Ê±£¬¿ÉÒÔÔö´óС³µÆ½¾ùËٶȣ»
£¨3£©ÊµÑéÖÐʹÓõÄбÃæµÄƶȽÏС£¬ÆäÄ¿µÄÊDZãÓÚ²âÁ¿Ê±¼ä£»
£¨4£©Éè×Ü·³ÌÊÇ2s£¬ÔòÇ°Ò»°ëÓëºóÒ»°ë·³Ì¶¼ÊÇs£¬
¸ù¾Ýv=$\frac{s}{t}$¿ÉÖª£¬
Ç°Ò»°ë·³ÌµÄÔ˶¯Ê±¼ä£ºt₁=$\frac{s}{{v}_{1}}$£¬
ºóÒ»°ë·³ÌµÄÔ˶¯Ê±¼ä£ºt₂=$\frac{s}{{v}_{2}}$£¬
Õû¸ö·³ÌµÄƽ¾ùËٶȣºv=$\frac{2s}{{t}_{1}+{t}_{2}}$=$\frac{2s}{\frac{s}{{v}_{1}}+\frac{s}{{v}_{2}}}$=$\frac{2{v}_{1}{v}_{2}}{{v}_{1}+{v}_{2}}$£®
¹Ê´ð°¸Îª£º£¨1£©C£»£¨2£©Ôö´óбÃæÇã½Ç¦È£»£¨3£©½ÏС£»£¨4£©$\frac{2{v}_{1}{v}_{2}}{{v}_{1}+{v}_{2}}$£®

µãÆÀ ±¾ÌâΪ²âÁ¿ÎïÌåƽ¾ùËٶȡ¢Ì½¾¿ÎïÌåÔ˶¯Çé¿öµÄʵÑéÌ⣬ÆäÖУ¬¼ÆËãƽ¾ùËٶȣ¬ÒªÓÃ×Ü·³Ì³ýÒÔ×Üʱ¼ä£¬ÒªÕÆÎÕʵÑéÖмõСÎó²îµÄ·½·¨¼°²âÁ¿Ï°ë¶Î·³Ìʱ¼äµÄ·½·¨£¬ÕâÊDZ¾ÌâµÄÄѵ㣮