Question

1£®ÈçͼËùʾ£¬Ôڹ⻬ˮƽÃæÉÏ£¬´æÔÚ×Å´¹Ö±Ö½ÃæÏòÍâµÄÔÈÇ¿´Å³¡¢ñ¡¢´¹Ö±Ö½ÃæÏòÀïµÄÔÈÇ¿´Å³¡¢ò£¬O¡¢M¡¢P¡¢QΪ´Å³¡±ß½çºÍxÖáµÄ½»µã£¬OM=MP=L£®Ò»ÖÊÁ¿Îªm¡¢´øµçºÉÁ¿Îª+qµÄ´øµçСÇò£¬´ÓÔ­µãO´¦£¬ÒÔËٶȴóСv₀ÓëxÖáÕýÏò³É45¡ãÉäÈëÇøÓò¢ñ£¬ÓÖ´ÓMµãÉä³öÇøÓò¢ñ£¨Á£×ÓµÄÖØÁ¦ºöÂÔ²»¼Æ£©£®
£¨1£©ÇóÇøÓò¢ñµÄ´Å¸ÐӦǿ¶È´óС£®
£¨2£©Èô´øµçСÇòÄÜÔٴλص½Ô­µãO£¬ÔòÔÈÇ¿´Å³¡¢òµÄ¿í¶ÈdÐèÂú×ãʲôÌõ¼þ£¿Ð¡ÇòÁ½´Î¾­¹ýÔ­µãOµÄʱ¼ä¼ä¸ôΪ¶àÉÙ£¿

Answer 1

·ÖÎö £¨1£©Ð¡ÇòÔڴų¡¢ñÇø×öÔÈËÙÔ²ÖÜÔ˶¯´ÓMµã´©³ö£¬¸ù¾Ý¶Ô³ÆÐÔ£¬´©³öʱÓëxÖá³É45¡ã£¬Óɼ¸ºÎ¹ØϵÇó³ö°ë¾¶r£¬ÔÙÓÉÂåÂØ×ÈÁ¦ÌṩÏòÐÄÁ¦¿ÉÒÔÇóµÃ´Å¸ÐӦǿ¶È£®
£¨2£©Èô´øµçСÇòÄÜÔٴλص½Ô­µãO£¬ÔòÁ£×ÓÔÚ¢òÇø×öÔÈËÙÔ²ÖÜÔ˶¯µÄÔ²ÐıØÔÚxÖáÉÏ£¬ÕâÑùÁ£×Ó´Ó¢òÇø´©³öʱ²ÅÄÜÉäµ½Mµã£¬Ôٻص½Oµã£®ÕâÑùÓɼ¸ºÎ¹Øϵ¿ÉÒÔÇó³öÁ£×ÓÔÚ¢òÇøÀï×öÔÈËÙÔ²ÖÜÔ˶¯µÄ°ë¾¶R£¬Ö»Óе±¹ì¼£Óë±ß½çÏàÇÐʱ£¬¿í¶È×îС£¬´Å³¡¢òÇø×îС¿í¶ÈÓɼ¸ºÎ¹ØϵÇó³ö£®ÖÁÓÚʱ¼ä°ÑÁ£×ÓÔÚÈý¸öÇøÓòµÄʱ¼äÏà¼Ó£¬¾ÍÄܵóö½á¹û£®

½â´ð ½â£º£¨1£©´øµçСÇò´ÓÔ­µãÓëxÖá³É45¡ã½Ç³ö·¢£¬Ôڴų¡¢ñÇø×öÔÈËÙÔ²ÖÜÔ˶¯´ÓMµã´©³ö£¬Ôò£º
             $q{v}_{0}{B}_{1}=\frac{m{{v}_{0}}^{2}}{r}$   ¢Ù
   Óɼ¸ºÎ¹Øϵ֪£ºL=2r cos45¡ã      ¢Ú
   ÁªÁ¢ÒÔÉÏÁ½Ê½µÃ£º${B}_{1}=\frac{\sqrt{2}m{v}_{0}}{qL}$  
£¨2£©¸ù¾Ý¶Ô³ÆÐÔ£¬´ÓMµã´©³öʱÓëxÖáÒ²³É45¡ã½Ç£¬È»ºó×öÔÈËÙÖ±ÏßÔ˶¯½øÈë´Å³¡¢òÇø£¬ÔÚ¢òÇøÔÙ
×öÔÈËÙÔ²ÖÜÔ˶¯£¬À뿪¢òÇøºó×öÔÈËÙÖ±ÏßÔ˶¯´ÓMµãÔٴνøÈë¢ñÇø£¬ÕâÑùÇ¡Ç¡´ÓOµã¾­¹ý£¬¹ì¼£ÈçͼËùʾ£º
    Óɼ¸ºÎ¹ØϵÓУºÁ£×ÓÔÚ¢òÇø×öÔÈËÙÔ²ÖÜÔ˶¯µÄ°ë¾¶Îª£º$R=\sqrt{2}L$   ¢Û
    ´øµçСÇòÄÜÔٴλص½Ô­µãO£¬ÔòÔÈÇ¿´Å³¡¢òµÄ¿í¶ÈdÐèÂú×㣺d¡ÝR+Rcos45¡ã      ¢Ü
    ÁªÁ¢µÃ£º$d¡Ý£¨\sqrt{2}+1£©L$¡¡¡¡¡¡
    Á£×ÓÔÚ¢ñÇøµÄʱ¼ä£º${t}_{1}=2¡Á\frac{1}{4}{T}_{1}=\frac{1}{2}¡Á\frac{2¦Ðr}{{v}_{0}}=\frac{\sqrt{2}¦ÐL}{{2v}_{0}}$    
    ÔÚÎÞ³¡ÇøµÄʱ¼ä£º${t}_{2}=2¡Á\frac{\sqrt{2}L}{{v}_{0}}=\frac{2\sqrt{2}L}{{v}_{0}}$  
    ÔÚ¢òÇøµÄʱ¼ä£º${t}_{3}=\frac{3}{4}{T}_{2}=\frac{3}{4}¡Á\frac{2¦ÐR}{{v}_{0}}=\frac{3\sqrt{2}¦ÐL}{2{v}_{0}}$
    Á£×ӻص½OµãµÄʱ¼äΪ£ºt=t₁+t₂+t₃=$\frac{2\sqrt{2}£¨¦Ð+1£©L}{{v}_{0}}$£®
´ð£º£¨1£©ÇøÓò¢ñµÄ´Å¸ÐӦǿ¶È´óСΪ$\frac{\sqrt{2}m{v}_{0}}{qL}$£®
£¨2£©Èô´øµçСÇòÄÜÔٴλص½Ô­µãO£¬ÔòÔÈÇ¿´Å³¡¢òµÄ¿í¶ÈdÐèÂú×ã$d¡Ý£¨\sqrt{2}+1£©L$£¬Ð¡ÇòÁ½´Î¾­¹ýÔ­µãOµÄʱ¼ä¼ä¸ôΪ$\frac{2\sqrt{2}£¨¦Ð+1£©L}{{v}_{0}}$£®

µãÆÀ ±¾ÌâµÄö¦µãÔÚÓÚҪʹÁ£×ÓÄܻص½Oµã£¬ÄÇôÁ£×ÓÔÚ¢òÇø×öÔÈËÙÔ²ÖÜÔ˶¯µÄÔ²ÐıØÔÚx ÖáÉÏ£¬¸ù¾ÝÔ²ÖÜÔ˶¯µÄ¶Ô³ÆÐÔÁ£×Ó´Ó¢òÇø´©³öºó×öÖ±ÏßÔ˶¯µ½Mµã£¬×öÔ²ÖÜÔ˶¯×îºó»Øµ½Oµã£®ËäÈ»¢òÇø´Å´Å¸ÐӦǿ¶Èδ֪£¬µ«ÓÉÓÚ×öÔ²ÖÜÔ˶¯µÄ°ë¾¶Óɼ¸ºÎ¹ØϵÄÜÇó³ö£¬ËùÒÔÔÚÿ¸öÇøÓòµÄʱ¼ä¾ùÄܱíʾ³öÀ´£®