问题 问答题

一修路工在S=100m的隧道中,突然发现一列火车出现在离右道口200m处,修路工恰在无论向右还是向左跑均能安全脱离危险的位置.问这位置离左出口的距离多少?他奔跑的速度至少是火车速度的多少倍?

答案

要脱离危险必须使人在火车到达隧道口前跑出隧道.设人所在位置离左出口为xm,知图所示,则离右出口为(100-x)m.

v为人的速度,v为车的速度.

从左出口人恰能脱离危险时有:

x
v人
=
300
v车

从右出口人恰能脱离危险时有:

100-x
v人
=
200
v车

由上式可得:x=60m,即人离左出口60m,

v人
v车
=
60
300
=
1
5

即人的最小速度是火车速度的

1
5

答:该位置离出口60m;人的速度为火车速度的

1
5
倍.

单项选择题 A1型题
单项选择题

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