题目
题型:高考真题难度:来源:
①失事船的移动路径可视为抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024084032-65961.png)
②定位后救援船即刻沿直线匀速前往救援;
③救援船出发t小时后,失事船所在位置的横坐标为7t。
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024084032-80191.png)
(2)问救援船的时速至少是多少海里才能追上失事船?
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024084033-98726.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024084033-71409.png)
由|AP|=
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024084033-47144.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024084034-58147.png)
由tan∠OAP=
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024084034-59633.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024084034-30063.png)
故救援船速度的方向为北偏东arctan
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024084034-51284.png)
(2)设救援船的时速为v海里,经过t小时追上失事船,此时位置为(7t,12t2)
由vt=
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024084035-55013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024084035-85089.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024084035-18153.png)
所以v2≥144×2+337=252,即v≥25
因此,救援船的时速至少是25海里才能追上失事船
核心考点
试题【海事救援船对一艘失事船进行定位:以失事船的当前位置为原点,以正北方向为y轴正方向建立平面直角坐标系(以1海里为单位长度),则救援船恰好在失事船正南方向12海里A】;主要考察你对抛物线等知识点的理解。[详细]
举一反三
过抛物线y2=4x上一点A(1,2)作抛物线的切线,分别交x轴于点B,交y轴于点D,点C(异于点A)在抛物线上,点E在线段AC上,满足
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024084019-68668.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024084019-86482.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024084019-95844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024084020-29800.png)
λ1+λ2=1,线段CD与EF交于点P.
(1)设
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024084020-17865.png)
(2)当点C在抛物线上移动时,求点P的轨迹方程.
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024084020-27131.png)
(1 )若
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024083942-59275.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024083943-32890.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024083943-91640.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024083943-39401.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024083943-54957.png)
(2)若随机变量
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024083944-14984.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024083944-99681.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024083944-34513.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024083944-52004.png)
(3)过平面外一点与该平面成
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024083945-34045.png)
(4)点
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024083945-42966.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024083945-72988.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024083945-58094.png)
(5)在同一坐标系中函数
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024083945-86223.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024083946-90943.png)
则正确命题的序号是( ).