题目
题型:不详难度:来源:
(1)现机器人在平面直角坐标系的坐标原点,且面对x轴正方向.试给机器人下一个指令,使其移动到点(4,4).
(2)机器人在完成该指令后,发现在点(17,0)处有一小球 正向坐标原点作匀速直线滚动.已知小球滚动的速度为机器人直线行走速度的2倍,若忽略机器人原地旋转所需的时间,问机器人最快可在何处截住小球?并给出机器人截住小球所需的指令(结果用反三角函数表示).
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013339-10155.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013339-47661.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013339-65098.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013340-55033.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013340-16887.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013339-47661.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013339-65098.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013339-47661.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013339-65098.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013340-15700.gif)
(2)设机器最快在点P(x,0)处截住小球,则因为小球速度是机器人速度的2倍,所以在相同时间内有
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013340-41688.gif)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013341-65854.gif)
因为要求机器人最快地去截住小球,即小球滚动距离最短,所以x =7,
故机器人最快可在点P(7,0)处截住小球,
又设Q(4,4),机器人在Q点旋转的角度为
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013341-83219.gif)
则PQ|
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013341-83845.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013341-86878.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013341-40120.gif)
(法一):由
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013341-86878.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013342-82014.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013342-11017.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013342-82014.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013342-39033.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013342-19506.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013343-39782.gif)
(法二):
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013343-43530.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013343-19253.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013343-98945.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013344-47091.gif)
故,所给的指令为(5,
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013340-55033.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013340-16887.gif)
核心考点
试题【如图,根据指令(γ,θ)(γ≥0,-180°<θ≤180°),机器人在平面上能完成下列动作:先原地旋转角度θ(θ为正时,按逆时针方向旋转θ,θ为负时,按顺】;主要考察你对极坐标与直角坐标等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013336-76892.gif)
A.P在曲线C上,Q不在曲线C上 | B.P、Q都不在曲线C上 |
C.P不在曲线C上,Q在曲线C上 | D.P、Q都在曲线C上 |
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013332-23438.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013326-16573.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013326-69545.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013327-71958.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013327-79919.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013327-36632.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013327-88882.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013328-70589.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013328-91781.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013327-36632.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013322-75995.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013322-91694.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013322-75995.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013322-91694.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013322-61204.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013322-71392.gif)
③
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013323-27175.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013323-91076.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108013319-16402.png)