Question

Èçͼ£¬ÔÚµÈÑüÈý½ÇÐÎABCÖУ¬AB=AC=10cm£¬¡ÏABC=30¡ã£¬ÒÔBCËùÔÚÖ±ÏßΪxÖᣬÒÔBC±ßÉϵĸßËùÔÚµÄÖ±ÏßΪyÖὨÁ¢Æ½ÃæÖ±½Ç×ø±êϵ£®
£¨1£©ÇóÖ±ÏßACµÄ½âÎöʽ£»
£¨2£©ÓÐÒ»¶¯µãPÒÔ1cm/sµÄËٶȴӵãB¿ªÊ¼ÑØxÖáÏòÆäÕý·½ÏòÔ˶¯£¬ÉèµãPµÄÔ˶¯ÎªtÃ루µ¥Î»£ºs£©£®¢Ùµ±tΪºÎֵʱ£¬¡÷ABPÊÇÖ±½ÇÈý½ÇÐΣ»¢ÚÏÖÓÐÁíÒ»µãQÓëµãPͬʱ´ÓµãB¿ªÊ¼£¬ÒÔ1cm/sµÄËٶȴӵãB¿ªÊ¼ÑØÕÛÏßBACÔ˶¯£¬µ±µãQµ½´ïµãCʱ£¬P¡¢QÁ½µãͬʱֹͣÔ˶¯£®ÊÔд³ö¡÷BPQµÄÃæ»ýS¹ØÓÚtµÄº¯Êý½âÎöʽ£¬²¢Ð´³ö×Ô±äÁ¿µÄÈ¡Öµ·¶Î§£®

Answer 1

£¨1£©¡ßAB=AC=10cm£¬¡ÏABC=30¡ã£¬
¡àOA=5cm£¬BO=CO=5

3

cm£¬
¡àµãAµÄ×ø±êΪ£¨0£¬5£©£¬µãCµÄ×ø±êΪ£¨5

3

£¬0£©£¬
ÉèÖ±ÏßACµÄ½âÎöʽΪy=kx+b£¬
½«µãA¡¢µãCµÄ×ø±ê´úÈë¿ÉµÃ£º

5 3 k+b=0 b=5

£¬
½âµÃ£º

k=- 3 3 b=5

¹ÊÖ±ÏßACµÄ½âÎöʽΪ£ºy=-

3

3

x+5£»
£¨2£©

¢Ùµ±¡ÏAPB=90¡ãʱ£¬µãPÓëµãOÖغÏʱ£¬´ËʱBP=5

3

£¬
¼´¿ÉµÃt=5

3

£»
µ±¡ÏBAP=90¡ãʱ£¬µãPλÓÚP₁´¦£¬
´ËʱBP₁=

AB

cos¡ÏABO

=

20 3

3

£¬
¼´¿ÉµÃt=

20 3

3

£®
×ÛÉϿɵõ±t=5

3

»ò

20 3

3

ʱ£¬¡÷ABPΪֱ½ÇÈý½ÇÐΣ®
¢Úµ±µãQλÓÚAB¶Îʱ£¬0£¼t£¼10£¬

¹ýµãQ×÷QD¡ÍOBÓÚµãD£¬BQ=t£¬BP=t£¬¡ÏABO=30¡ã£¬
ÔòQD=

1

2

BQ=

1

2

t
´ËʱS_¡÷BPQ=

1

2

BP¡ÁQD=

1

2

t¡Á

1

2

t=

1

4

t²£»
µ±µãQλÓÚAC¶Îʱ£¬10¡Üt£¼20£¬

´ËʱBP=t£¬CQ=20-t£¬¡ÏACO=30¡ã£¬
ÔòQD=

1

2

CQ=

1

2

£¨20-t£©=10-

1

2

t£¬
S_¡÷BPQ=

1

2

BP¡ÁQD=

1

2

t¡Á£¨10-

1

2

t£©=-

1

4

t²+5t£®