Question

2£®Ëæ×ÅÖйú±ùºø¶ÓÔÚÊÀ½ç±ÈÈüÖÐÈ¡µÃºÃ³É¼¨£¬ÈËÃǶԱùºøÔ˶¯Ô½À´Ô½¹Ø×¢£¬±ùºøÔÚˮƽ±ùÃæÉϵÄÒ»´Î»¬Ðпɼò»¯ÎªÈçϹý³Ì£ºÈçͼËùʾ£¬Ô˶¯Ô±Ê©Ò»Ë®Æ½ºãÁ¦½«¾²Ö¹ÓÚAµãµÄ±ùºø£¨ÊÓΪÖʵ㣩ÑØÖ±ÏßADÍƵ½Bµã·ÅÊÖ£¬×îºó±ùºøÍ£ÓÚDµã£¬ÒÑÖª±ùºøÓë±ùÃæ¼äĦ²ÁÒòÊýΪ¦Ì£¬±ùºøÖÊÁ¿Îªm£¬AB=CD=l£¬BC=4l£¬ÖØÁ¦¼ÓËÙ¶ÈΪg£¬Çó£º

£¨1£©±ùºøÔÚBµãµÄËÙÂÊ£»
£¨2£©±ùºøÔÚCD¶ÎÓëÔÚAB¶ÎÔ˶¯Ê±¼äÖ®±È£®

Answer 1

·ÖÎö £¨1£©¸ù¾Ý×°±ùºøÔÚBD¼äµÄÔ˶¯£¬ÓÉËÙ¶ÈλÒƹØϵÇó±ùºøÔÚBµãµÄËٶȣ»
£¨2£©¸ù¾ÝBµãËÙ¶ÈÓÉABλÒÆÇóµÃAB¶ÎµÄÔ˶¯Ê±¼ä£¬ÔÙ¸ù¾ÝCD¶ÎµÄλÒƺͼÓËٶȼ°Ä©ËÙ¶ÈÇóµÃCD¶ÎµÄÔ˶¯Ê±¼ä£®

½â´ð ½â£º£¨1£©±ùºø´ÓBµãµ½Dµã×öÔȼõËÙÖ±ÏßÔ˶¯£¬¼ÓËٶȴóСΪa₁=¦Ìg
¸ù¾ÝËÙ¶ÈλÒƹØϵÓУº
${v}_{B}^{2}=2{a}_{1}•5l$
½âµÃ±ùºøÔÚBµãµÄËÙÂÊv_B=$\sqrt{10¦Ìgl}$
£¨2£©Éè±ùºøÔÚAB¶ÎÔ˶¯¼ÓËٶȴóСΪa₂£¬ÓÉAB¼äÔȼÓËÙÔ˶¯ÓÐ
${v}_{B}^{2}=2{a}_{2}l$
¿ÉµÃ±ùºøÔÚAB¼äÔ˶¯µÄ¼ÓËÙ¶Èa₂=5¦Ìg
±ùºøÔÚCD¶ÎÔ˶¯Ê±¼äΪt₁£¬±ùºøÔÚAB¶ÎÔ˶¯Îªt₂¸ù¾ÝÔ˶¯Ñ§¹ØϵÓУº
$l=\frac{1}{2}{a}_{2}{t}_{2}^{2}=\frac{1}{2}{a}_{1}{t}_{1}^{2}$
±ùºøÔÚCD¶ÎÓëÔÚAB¶ÎÔ˶¯Ê±¼äÖ®±È$\frac{{t}_{1}}{{t}_{2}}$=$\sqrt{5}$
´ð£º£¨1£©±ùºøÔÚBµãµÄËÙÂÊΪ$\sqrt{10¦Ìgl}$£»
£¨2£©±ùºøÔÚCD¶ÎÓëÔÚAB¶ÎÔ˶¯Ê±¼äÖ®±ÈΪ$\sqrt{5}$£º1£®

µãÆÀ ½â¾ö±¾ÌâµÄ¹Ø¼üÊÇÄܸù¾ÝÔȱäËÙÖ±ÏßÔ˶¯µÄËÙ¶ÈλÒƹØϵºÍλÒÆʱ¼ä¹Øϵ·ÖÎö±ùºøµÄÔ˶¯£¬²»ÄÑÊôÓÚ»ù´¡Ì⣮