22. 几千年的沧桑沉淀,凝练了西樵山的美,清幽秀丽的自然风光,文化底蕴厚重的旅游,古朴自然的民俗风情.自明清以来,文人雅士,群贤毕至,旅人游子,纷至沓来,使秀美的西樵山成为名嗓南粤的旅游热点.如图,游客从某旅游景区的景点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
处下山至
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
处有两种路径,一种是从
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
沿直线步行到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
,另一种是先从
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
乘景区观光车到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
,然后从
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
沿直线步行到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
.现有甲、乙两位游客从
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
处下山,甲沿
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
匀速步行,速度为50米/分钟,在甲出发2分钟后,乙从
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
乘观光车到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
处停留20分钟后,再从
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
匀速步行到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
.假设观光车匀速直线运行的速度为250米/分钟,山路
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
长为2340米,经测量,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71d54878886657b672c4bcd2bc746553.png)
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94a67c529d3e81a79c4e4409953d316f.png)
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/5/48236c39-dff2-43d0-868b-ebb3222b9263.png?resizew=179)
(1)求观光车路线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
的长;
(2)问乙出发多少分钟后,乙在观光车上与甲的距离最短?
(3)为使两位游客在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
处互相等待的时间不超过3分钟,乙步行的速度应控制在什么范围内?