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Re:谁能解释一下,具体怎么做??谢谢了

Posted by gogdizzy at 2007-04-23 17:07:12 on Problem 2666
In Reply To:谁能解释一下,具体怎么做??谢谢了 Posted by:caonimama at 2006-10-04 10:51:15
走的是个弧线,考虑极坐标
可以把速度2u分解为两个方向,一个沿径向(为了和母船都与爆炸点等距,大小为V1=u)
另一个沿切向,大小为V2=sqrt(3)u

画图分析,在中间某个任意极短的时间dt里,子船沿切向走了V2*dt的距离。这个距离可以用另一种方式表示,假设从开始到现在经过了t的时间,那么此时与爆炸点的距离(也就是半径)应该是d+V1*t,子船在dt时间走过的切向角度为da,则另一种表示方法就是(d+V1*t)*da
所以V2*dt=(d+V1*t)*da,dt,da分别是对时间t和角度a的微分。
整理一下并替换V1,V2得到:dt/(d+u*t)=da/(sqrt(3)*u)
两边积分,初始条件t=0,a=0,结束条件,t=所求的,a=a。

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