Question

14£®ÈçͼËùʾ£¬ÔÚxOyÖ±½Ç×ø±êϵÄÚ£¬0¡Üx¡Üd¼°x£¾d·¶Î§ÄÚ´æÔÚ´¹Ö±ÓÚxOyƽÃæÇҵȴó·´ÏòµÄÔÈÇ¿´Å³¡¢ñ¡¢¢ò£¬·½ÏòÈçͼÖÐËùʾ£¬Ö±Ïßx=dÓëxÖá½»µãΪA£®×ø±êÔ­µãO´¦´æÔÚÁ£×ÓÔ´£¬Á£×ÓÔ´ÔÚxOyƽÃæÄÚÏòx£¾OÇøÓòµÄ¸÷¸ö·½Ïò·¢ÉäËٶȴóС¾ùΪv₀µÄͬÖÖÁ£×Ó£¬Á£×ÓÖÊÁ¿Îªm£¬µçºÉÁ¿Îª-q£¬ÆäÖÐÑØ+x·½ÏòÉä³öµÄÁ£×Ó£¬Ôڴų¡IÖеÄÔ˶¯¹ì¼£Óëx=dÏàÇÐÓÚP£¨d£¬-d£©µã£¬²»¼ÆÁ£×ÓÖØÁ¦£»
£¨1£©Çó´Å¸ÐӦǿ¶ÈµÄ´óС£»
£¨2£©Çó´ÓAµã½øÈë´Å³¡¢òµÄÁ£×ÓÔڴų¡ÖÐÔ˶¯µÄ×Üʱ¼ä£»
£¨3£©½ö³·È¥´Å³¡¢ò£¬Ëæ¼´ÔÚxOyƽÃæÄÚ¼ÓÉÏ·¶Î§×ã¹»´óµÄÔÈÇ¿µç³¡£¬´ÓOµãÑØOP·½ÏòÉä³öµÄÁ£×Ó£¬½«ÑØOPÖ±ÏßÔ˶¯µ½Pµã£¬ºóÁ£×Ó¾­¹ýQ£¨x_Q£¬-d£©µã£¬ÇóÔÈÇ¿µç³¡µÄµç³¡Ç¿¶È¼°x_QµÄÖµ£®

Answer 1

·ÖÎö £¨1£©Á£×Ó´ÓO¡úP×öÔÈËÙÔ²ÖÜÔ˶¯£¬ÓÉÌâÒâ»­³ö¹ì¼££¬Çó³ö¹ì¼£°ë¾¶£¬¸ù¾ÝÂåÂ××ÈÁ¦ÌṩÏòÐÄÁ¦£¬ÁÐʽÇó½âB£®
£¨2£©¸ù¾Ý¼¸ºÎ֪ʶÇó³ö¹ì¼£¶ÔÓ¦µÄÔ²ÐĽǣ¬À´Çó½âÔ˶¯Ê±¼ä£®
£¨3£©½ö³·È¥´Å³¡¢ò£¬Á£×Ó½«ÑØOPÖ±ÏßÔ˶¯µ½Pµã£¬µç³¡Á¦ÓëÂåÂ××ÈÁ¦Æ½ºâ£¬ÁÐʽÇó³öµç³¡Ç¿¶ÈE£®P¡úQ£¬Á£×Ó×öÀàƽÅ×Ô˶¯£¬ÔËÓÃÔ˶¯µÄ·Ö½â·¨Çó½âx_QµÄÖµ£®

½â´ð ½â£º£¨1£©´ÓO¡úP£¬Á£×ÓÔ˶¯¹ì¼£Èçͼ£¬Óɼ¸ºÎ¹ØϵÓÐ
¡ÏO₁=90¡ã
¹ì¼£°ë¾¶Îª R=d
ÓÉÅ£¶ÙµÚ¶þ¶¨Âɵà qv₀B=m$\frac{{v}_{0}^{2}}{R}$
ÕûÀíµÃ B=$\frac{m{v}_{0}}{qd}$
£¨2£©´ÓAµã½øÈë´Å³¡¢òµÄÁ£×Ó£¬¹ì¼£Èçͼ£¬ÔòR=d£¬OA=R=d£¬Ôò¡÷OO₂AΪµÈ±ßÈý½ÇÐΣ¬¡ÏO₂=60¡ã
ͬÀí¡ÏO₄=60¡ã£¬¡ÏO₃=120¡ã
Óɹ«Ê½t=$\frac{¦È}{360¡ã}$•$\frac{2¦Ðm}{qB}$£¬¦È=¡ÏO₂+¡ÏO₄+£¨360¡ã-¡ÏO₃£©=360¡ã
ÔòµÃ t=$\frac{2¦Ðd}{{v}_{0}}$
£¨3£©Á£×ӹ켣Èçͼ£¬´ÓO¡úP£¬Á£×Ó×öÖ±ÏßÔ˶¯£¬±ØÓÐ qv₀B=qE
µÃ E=$\frac{m{v}_{0}^{2}}{qd}$£¬µç³¡·½Ïò´¹Ö±ÓÚOPÓëxÖḺ·½Ïò¼äµÄ¼Ð½ÇΪ45¡ã£®
P¡úQ£¬Á£×Ó×öÀàƽÅ×Ô˶¯£¬Ôò
  PQsin45¡ã=v₀t₁£»
  PQcos45¡ã=$\frac{1}{2}a{t}_{1}^{2}$£»
ÓÖ PQ=x_Q-d
ÓÉÅ£¶ÙµÚ¶þ¶¨ÂɵÃqE=ma
ÕûÀíµÃ x_Q=£¨2$\sqrt{2}$+1£©d
´ð£»
£¨1£©´Å¸ÐӦǿ¶ÈµÄ´óСΪ$\frac{m{v}_{0}}{qd}$£»
£¨2£©´ÓAµã½øÈë´Å³¡¢òµÄÁ£×ÓÔڴų¡ÖÐÔ˶¯µÄ×Üʱ¼äΪ$\frac{2¦Ðd}{{v}_{0}}$£»
£¨3£©½ö³·È¥´Å³¡¢ò£¬Ëæ¼´ÔÚxOyƽÃæÄÚ¼ÓÉÏ·¶Î§×ã¹»´óµÄÔÈÇ¿µç³¡£¬´ÓOµãÑØOP·½ÏòÉä³öµÄÁ£×Ó£¬½«ÑØOPÖ±ÏßÔ˶¯µ½Pµã£¬ºóÁ£×Ó¾­¹ýQ£¨x_Q£¬-d£©µã£¬ÔÈÇ¿µç³¡µÄµç³¡Ç¿¶ÈΪ$\frac{m{v}_{0}^{2}}{qd}$£¬µç³¡·½Ïò´¹Ö±ÓÚOPÓëxÖḺ·½Ïò¼äµÄ¼Ð½ÇΪ45¡ã£®x_QµÄֵΪ£¨2$\sqrt{2}$+1£©d£®

µãÆÀ ½â¾ö±¾ÌâµÄ¹Ø¼üÒªÄܸù¾Ý´øµçÁ£×ÓµÄÊÜÁ¦Çé¿ö£¬È·¶¨ÆäÔ˶¯Çé¿ö£¬ÔËÓÃÁ¦Ñ§µÄ»ù±¾¹æÂɽâ´ð£®½âÌâʱ£¬ÒªÕýÈ·»­³öÁ£×ÓµÄÔ˶¯¹ì¼££¬Óɼ¸ºÎ֪ʶÇó½â¹ì¼£°ë¾¶ºÍÔ²ÐĽǣ®