求第(2)小题第②问解答过程
2个回答
展开全部
作AE⊥BC于E
∵在△ABC中,AB=AC,AE⊥BC
∴E为BC中点,CE=(1/2)BC=2√5
AC²=AE²+EC²
得AE=4√5
以点E为原点,EC为X轴正方向,EA为Y轴正方向建立平面直角坐标系
则E(0,0),C(2√5,0),B(-2√5,0),A(0,4√5)
Q((√5/5)vt,4√5-(2/5)(√5)vt),P((-√5/5)t,4√5-(2/5)(√5)t)
CP² = ((√5/5)t+2√5)²+(4√5-(2/5)(√5)t)²
=t²-12t+100
BQ² =((√5/5)vt+2√5)²+(4√5-(2/5)(√5)vt)²
=v²t²-12vt+100
由CP=BQ得:t²-12t+100 = v²t²-12vt+100
t²-12t+36 = v²t²-12vt+36
(vt-6)² = (t-6)²
vt-6 = ±(t-6)
v1=1(舍),v2=(12/t)-1
∵v>1,即(12/t)-1>1,即0<t<6
又∵vt≤10,得12-t≤10,t≥2
∴v = (12/t)-1(2≤t<6)
∵在△ABC中,AB=AC,AE⊥BC
∴E为BC中点,CE=(1/2)BC=2√5
AC²=AE²+EC²
得AE=4√5
以点E为原点,EC为X轴正方向,EA为Y轴正方向建立平面直角坐标系
则E(0,0),C(2√5,0),B(-2√5,0),A(0,4√5)
Q((√5/5)vt,4√5-(2/5)(√5)vt),P((-√5/5)t,4√5-(2/5)(√5)t)
CP² = ((√5/5)t+2√5)²+(4√5-(2/5)(√5)t)²
=t²-12t+100
BQ² =((√5/5)vt+2√5)²+(4√5-(2/5)(√5)vt)²
=v²t²-12vt+100
由CP=BQ得:t²-12t+100 = v²t²-12vt+100
t²-12t+36 = v²t²-12vt+36
(vt-6)² = (t-6)²
vt-6 = ±(t-6)
v1=1(舍),v2=(12/t)-1
∵v>1,即(12/t)-1>1,即0<t<6
又∵vt≤10,得12-t≤10,t≥2
∴v = (12/t)-1(2≤t<6)
本回答被提问者采纳
已赞过
已踩过<
评论
收起
你对这个回答的评价是?
推荐律师服务:
若未解决您的问题,请您详细描述您的问题,通过百度律临进行免费专业咨询