Question

19£®ÈçͼËùʾ£¬Ð±ÃæABÇã½Ç¦È=30¡ã£¬µ×¶ËAµãÓëбÃæÉÏBµãÏà¾às=10m£¬¼×¡¢ÒÒÁ½ÎïÌå´óС²»¼Æ£¬ÓëбÃæ¼äµÄ¶¯Ä¦²ÁÒòÊýΪ¦Ì=$\frac{\sqrt{3}}{2}$£¬Ä³Ê±¿Ì¼×´ÓAµãÑØбÃæÒÔv₁=10m/sµÄ³õËٶȻ¬ÏòB£¬Í¬Ê±ÒÒÎïÌå´ÓBµãÒÔv₂=7.25m/sµÄ³õËٶȻ¬ÏòA£¬È¡ÖØÁ¦¼ÓËÙ¶Èg=10m/s²£¬×î´ó¾²Ä¦²ÁÁ¦µÈÓÚ»¬¶¯Ä¦²ÁÁ¦£®Çó£º
£¨1£©¼×ÎïÌåÑØбÃæÉÏ»¬µÄ¼ÓËٶȴóС£»
£¨2£©¼×¡¢ÒÒÁ½ÎïÌå¾­¶à³¤Ê±¼äÏàÓö£®

Answer 1

·ÖÎö £¨1£©¶Ô¼×½øÐÐÊÜÁ¦·ÖÎö£¬¸ù¾ÝÅ£¶ÙµÚ¶þ¶¨ÂÉÇó³ö»¬¿éÉÏ»¬µÄ¼ÓËٶȣ»
£¨2£©½áºÏËÙ¶Èʱ¼ä¹«Ê½Çó³öËٶȼõΪÁãµÄʱ¼ä£¬Çó³öÉÏ»¬µÄ×î´óλÒÆ£¬¸ù¾ÝÅ£¶ÙµÚ¶þ¶¨ÂÉÇó³öÒÒÏ»¬µÄ¼ÓËٶȣ¬¸ù¾ÝλÒƹ«Ê½Çó³öÏ»¬µÄλÒÆ£¬´Ó¶øµÃ³öABÁ½µã¼äµÄ¾àÀ룻ȻºóÔÙ½áºÏ¼¸ºÎ¹ØϵºÍÔ˶¯Ñ§µÄ¹«Ê½¼´¿ÉÇó³öÏàÓöµÄʱ¼ä£®

½â´ð ½â£º£¨1£©»¬¿é¼×ÑØбÃæÏòÉÏÔ˶¯Ê±£¬¼ÓËٶȴóСΪa₁£º
ma₁=mg£¨sin 30¡ã+¦Ìcos 30¡ã£©
ËùÒÔ£ºa₁=10¡Á£¨0.5+$\frac{\sqrt{3}}{2}¡Á\frac{\sqrt{3}}{2}$£©=12.5 m/s²£¬
£¨2£©É軬¿éÒÒÑØбÃæÏòÏÂÔ˶¯Ê±£¬¼ÓËٶȴóСΪa₂£º
ma₂=mg£¨sin 30¡ã-¦Ìcos 30¡ã£©
´úÈëÊý¾ÝµÃ£ºa₂=-2.5 m/s²£¬
»¬¿é¼×¾­t₁=$\frac{{v}_{1}}{{a}_{1}}=\frac{10}{12.5}=0.8$ sËٶȼ´¼õΪÁ㣮
´Ë¹ý³ÌÖÐÏòÉϵÄλÒÆ£º${x}_{1}={v}_{1}{t}_{1}-\frac{1}{2}{a}_{1}{t}_{1}^{2}=10¡Á0.8-\frac{1}{2}¡Á10¡Á{0.8}^{2}=4$m
Îï¿éÒÒÏ»¬Ê±µÄλÒÆ´óСΪ£ºx₂=s-x₁=10-4=6m
ÒÒµÄλÒÆ£º${x}_{2}={v}_{2}{t}_{2}-\frac{1}{2}{a}_{2}{t}_{2}^{2}$
´úÈëÊý¾ÝµÃ£ºt₂=1s£¾0.8s
ËùÒԼס¢ÒÒÁ½ÎïÌå¾­¶à³¤Ê±¼äÏàÓöµÄʱ¼äÊÇ1s£®
´ð£º£¨1£©¼×ÎïÌåÑØбÃæÉÏ»¬µÄ¼ÓËٶȴóСÊÇ12.5m/s²£»
£¨2£©¼×¡¢ÒÒÁ½ÎïÌå¾­1sʱ¼äÏàÓö£®

µãÆÀ ½â¾ö±¾ÌâµÄ¹Ø¼üÀíÇåÎïÌåÔÚÕû¸ö¹ý³ÌÖеÄÔ˶¯¹æÂÉ£¬½áºÏÅ£¶ÙµÚ¶þ¶¨ÂɺÍÔ˶¯Ñ§¹«Ê½×ÛºÏÇó½â£¬ÖªµÀ¼ÓËÙ¶ÈÊÇÁªÏµÁ¦Ñ§ºÍÔ˶¯Ñ§µÄÇÅÁº£®