这里好冷清,再出两个数学/物理题,活跃一下气氛1. 一个边长为1的正方形,四个顶点有四只小虫ABCD。同一时刻小虫以同样的速度开始爬动。A的目标是B,B的目标是C,C的目标是D,D的目标是A。问四只小虫相遇时它们爬行的距离是多远。如果是正三角形呢,正五边形呢?一般的正n边形呢(边长为1)?
2. 一条长为L=1m的弹簧,一只小虫位于弹簧的一端,小虫以v1=1cm/s的速度向弹簧另一端爬,同时弹簧以v2=1m/s的速度拉伸,问小虫能否爬到弹簧的另一端,如果能,这个时候弹簧有多长?(注:小虫的长度为0,不老不死,上题也是,弹簧可以无限拉伸)
1。永远不能相遇,或者题目给的不对
2。缺少条件
unless think in this way:
at moment t.
relative move to string is .01-(t+int(ds)|t)/L
L is string length at t, which is 1+t
it's a double integral problem. but think in extreme condition.
if the worm is not a dot but a length, one side will remain at origin and the other side will reach at end line at 100 sec time.
so the answer can be from 100 sec to infinity depends what kind of motion worm move together with string.
unless think in this way:
at moment t.
relative move to string is .01-(t+int(ds)|t)/L
L is string length at t, which is 1+t
it's a double integral problem. but think in extreme condition.
if the worm is not a dot but a length, one side will remain at origin and the other side will reach at end line at 100 sec time.
so the answer can be from 100 sec to infinity depends what kind of motion worm move together with string.