Question

17£®ÔÚƽֱµÀ·ÉÏ£¬¼×Æû³µÒÔËÙ¶ÈvÔÈËÙÐÐÊ»£®µ±¼×Æû³µË¾»ú·¢ÏÖÇ°·½¾àÀëΪd´¦µÄÒÒÆû³µÊ±£¬Á¢¼´ÒÔ´óСΪa₁µÄ¼ÓËÙ¶ÈÔȼõËÙÐÐÊ»£¬Óë´Ëͬʱ£¬ÒÒÆû³µË¾»úÒ²·¢ÏÖÁ˼×Æû³µ£¬Á¢¼´´Ó¾²Ö¹¿ªÊ¼ÒÔ´óСΪa₂µÄ¼ÓËÙ¶ÈÑؼ×Æû³µÔ˶¯µÄ·½ÏòÔȼÓËÙÔ˶¯£¬ÏÂÁÐ˵·¨ÕýÈ·µÄÊÇ£¨¡¡¡¡£©

• A£® ¼×¡¢ÒÒÁ½Æû³µÖ®¼äµÄ¾àÀëÒ»¶¨²»¶Ï¼õС
• B£® ¼×¡¢ÒÒÁ½Æû³µÖ®¼äµÄ¾àÀë¿ÉÄÜÏȲ»¶Ï¼õС¡¢ºó²»¶ÏÔö´ó
• C£® Èôv£¾$\sqrt{2£¨{a}_{1}+{a}_{2}£©d}$£¬ÔòÁ½Æû³µÒ»¶¨²»»áÏàײ
• D£® Èôv£¼$\sqrt{2£¨{a}_{1}+{a}_{2}£©d}$£¬ÔòÁ½Æû³µÒ»¶¨²»»áÏàײ

Answer 1

·ÖÎö Á½³µÔÚËÙ¶ÈÏàµÈÇ°£¬¾àÀëÔ½À´Ô½Ð¡£¬ËÙ¶ÈÏàµÈʱ£¬Èô²»Ïàײ£¬Ôò¾àÀëÔ½À´Ô½´ó£®ÁÙ½çÇé¿öÊÇËÙ¶ÈÏàµÈʱ£¬Ç¡ºÃÏàײ£¬½áºÏÔ˶¯Ñ§¹«Ê½Çó³ö²»ÏàײµÄÌõ¼þ£®

½â´ð ½â£ºAB¡¢Á½³µÔÚËÙ¶ÈÏàµÈÇ°£¬¾àÀëÔ½À´Ô½Ð¡£¬Èô²»Ïàײ£¬ËÙ¶ÈÏàµÈºó£¬¾àÀëÔ½À´Ô½´ó£¬ËùÒԼס¢ÒÒÁ¾Æû³µÖ®¼äµÄ¾àÀë¿ÉÄÜÏȲ»¶Ï¼õС¡¢ºó²»¶ÏÔö´ó£¬¹ÊA´íÎó£¬BÕýÈ·£»
CD¡¢µ±Á½³µËÙ¶ÈÏàµÈʱ£¬ÓÐ$v-{a}_{1}^{\;}t={a}_{2}^{\;}t$£¬½âµÃ£º$t=\frac{v}{{a}_{1}^{\;}+{a}_{2}^{\;}}$£¬Á½³µÇ¡ºÃ²»ÏëײʱÓУº$vt-\frac{1}{2}{a}_{1}^{\;}{t}_{\;}^{2}=d+\frac{1}{2}{a}_{2}^{\;}{t}_{\;}^{2}$£¬½âµÃ$v=\sqrt{2£¨{a}_{1}^{\;}+{a}_{2}^{\;}£©d}$£¬Èô$v£¼\sqrt{2£¨{a}_{1}^{\;}+{a}_{2}^{\;}£©d}$£¬Á½³µÒ»¶¨²»»áÏàײ£¬¹ÊC´íÎó£¬DÕýÈ·£»
¹ÊÑ¡£ºBD

µãÆÀ ½â¾ö±¾ÌâµÄ¹Ø¼üÖªµÀÁ½³µÇ¡ºÃ²»ÏàײµÄÁÙ½çÇé¿ö£¬¼´ËÙ¶ÈÏàµÈʱ£¬Ç¡ºÃ²»Ïàײ£®½áºÏÔ˶¯Ñ§¹«Ê½Áé»îÇó½â£®