Question

3£®ÈçͼËùʾ£¬BCΪ°ë¾¶R=0.8mµÄ$\frac{1}{4}$Ô²»¡¹Ì¶¨ÔÚˮƽµØÃæÉÏ£¬ABΪˮƽ¹ìµÀ£¬Á½¹ìµÀÔÚB´¦ÏàÇÐÁ¬½Ó£»AB¹ìµÀÉϵĻ¬¿éPͨ¹ý²»¿ÉÉ쳤µÄÇáÉþÓëÌ×ÔÚÊúÖ±¹â»¬Ï¸¸ËµÄ»¬¿éQÁ¬½Ó£»P¡¢Q¾ù¿ÉÊÓΪÖʵãÇÒÔ²»¡¹ìµÀCµãÓëÊúÖ±¸Ë¼ä¾àÀë×ã¹»Ô¶£¬¿ªÊ¼Ê±£¬PÔÚA´¦£¬QÔÚÓëAͬһˮƽÃæÉϵÄE´¦£¬ÇÒÉþ×Ó¸ÕºÃÉìÖ±´¦ÓÚˮƽ£¬¹Ì¶¨µÄС»¬ÂÖÔÚD´¦£¬DE=0.35m£¬ÏÖ°ÑQ´Ó¾²Ö¹ÊÍ·Å£¬µ±ÏÂÂäh=0.35mʱ£¬PÇ¡ºÃµ½´ïÔ²»¡¹ìµÀµÄBµã£¬ÇҸպöÔBÎÞѹÁ¦£¬²¢ÇÒ´ËʱÉþ×ÓͻȻ¶Ï¿ª£¬È¡g=10m/s²£®ÊÔÇó£º
£¨1£©ÔÚPµ½´ïB´¦Ê±£¬P¡¢QµÄËٶȴóС·Ö±ðΪ¶àÉÙ£»
£¨2£©»¬¿éP¡¢QÂäµØµÄʱ¼ä²î£®

Answer 1

·ÖÎö £¨1£©PÇ¡ºÃµ½´ïÔ²»¡¹ìµÀµÄB£¬ÇÒ¶ÔBÎÞѹÁ¦£¬ÖØÁ¦ÌṩÏòÐÄÁ¦£¬¸ù¾ÝÏòÐÄÁ¦¹«Ê½µÃv_p£¬Pµ½´ïBµãʱ£¬Éþ×ÓµÄËٶȵÈÓÚPµÄËٶȣ¬¸ù¾Ý¼¸ºÎ¹Øϵ֪ÉþÓëÊúÖ±·½Ïò¼Ð½ÇΪ45¡ã£¬v_Q=$\frac{{v}_{p}}{cos45¡ã}$£®
£¨2£©Éþ×ӶϺó£¬P×öƽÅ×Ô˶¯R=$\frac{1}{2}g{t}_{1}^{2}$£¬Q×öÊúÖ±ÏÂÅ×Ô˶¯R-h=v_Qt$+\frac{1}{2}g{{t}_{2}}^{2}$´Ó¶øÖª¸÷×ÔÔ˶¯Ê±¼ä£¬¡÷t=t₁-t₂£®

½â´ð ½â£º£¨1£©PÇ¡ºÃµ½´ïÔ²»¡¹ìµÀµÄB£¬ÇÒ¶ÔBÎÞѹÁ¦£¬ÖØÁ¦ÌṩÏòÐÄÁ¦£¬
¸ù¾ÝÏòÐÄÁ¦¹«Ê½µÃ£º
m_pg=m_p$\frac{{v}_{p}^{2}}{R}$
½âµÃ£ºv_p=$\sqrt{gR}$=$\sqrt{10¡Á0.8}$=2$\sqrt{2}$m/s
Pµ½´ïBµãʱ£¬Éþ×ÓµÄËٶȵÈÓÚPµÄËٶȣ¬¸ù¾Ý¼¸ºÎ¹Øϵ֪ÉþÓëÊúÖ±·½Ïò¼Ð½ÇΪ45¡ã£¬
v_Q=$\frac{{v}_{p}}{cos45¡ã}$=$\frac{2\sqrt{2}}{\frac{\sqrt{2}}{2}}$=4m/s
£¨2£©Éþ×ӶϺó£¬P×öƽÅ×Ô˶¯R=$\frac{1}{2}g{t}_{1}^{2}$¢Ù
Q×öÊúÖ±ÏÂÅ×Ô˶¯R-h=v_Qt$+\frac{1}{2}g{{t}_{2}}^{2}$¢Ú
¡÷t=t₁-t₂¢Û
Óɢ٢ڢ۵á÷t=0.3s
´ð£º£¨1£©ÔÚPµ½´ïB´¦Ê±£¬P¡¢QµÄËٶȴóС·Ö±ðΪ2$\sqrt{2}$m/s£¬4m/s
£¨2£©»¬¿éP¡¢QÂäµØµÄʱ¼ä²îΪ0.3s£®

µãÆÀ ´ËÌ⿼²ìÇúÏßÔ˶¯µÄ֪ʶ£¬»á¸ù¾ÝÔ˶¯µÄ·Ö½âÖªQµÄËٶȣ¬ÊìϤƽÅ×Ô˶¯ºÍÊúÖ±ÉÏÅ×Ô˶¯µÄ¹æÂɼ´¿É½â´ð£¬ÊôÓÚÖеÈÌâÄ¿£®