解题方法
1 . 研究表明:正反粒子碰撞会湮灭.某大学科研团队在如下图所示的长方形区域
内(包含边界)进行粒子撞击实验,科研人员在A、O两处同时释放甲、乙两颗粒子.甲粒子在A处按
方向做匀速直线运动,乙粒子在O处按
方向做匀速直线运动,两颗粒子碰撞之处记为点P,且粒子相互碰撞或触碰边界后爆炸消失.已知
长度为6分米,O为
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/14/104470b8-b534-4e46-871e-a4a76e3a8a7d.png?resizew=198)
(1)已知向量
与
的夹角为
,且
足够长.若两颗粒子成功发生碰撞,当
点距碰撞点
处多远时?两颗粒子运动路程之和的最大,并求出最大值;
(2)设向量
与向量
的夹角为
(
),向量
与向量
的夹角为
(
),甲粒子的运动速度是乙粒子运动速度的2倍.请问
的长度至少为多少分米,才能确保对任意的
,总可以通过调整甲粒子的释放角度
,使两颗粒子能成功发生碰撞?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe6d728b430549f00bb9c0a7bf8bf7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75578eb4a8555e6cfb6d743a509a612f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/14/104470b8-b534-4e46-871e-a4a76e3a8a7d.png?resizew=198)
(1)已知向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe6d728b430549f00bb9c0a7bf8bf7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75578eb4a8555e6cfb6d743a509a612f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)设向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe6d728b430549f00bb9c0a7bf8bf7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef2723673c90347f6dd58346278c7fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a135466eb8ca64d002d0fad36176d1c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75578eb4a8555e6cfb6d743a509a612f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fc9656d8286c4d6fa309d6ae347c89e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1c6f686681d7640cd71ed82b9f07e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/481e744af0f65e797a35d976c20f2dac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
您最近一年使用:0次