Question

一列隊(duì)伍長(zhǎng)L=80m，行進(jìn)速度v=3.6km/h，為了傳達(dá)一個(gè)命令，通訊員從隊(duì)伍排尾跑步趕到隊(duì)伍排頭，其速度v^′=3m/s，然后又立即用跟隊(duì)伍行進(jìn)速度相同大小的速度返回排尾．
求：（1）通訊員從離開隊(duì)伍到重回到排尾共用多少時(shí)間？
（2）通訊員歸隊(duì)處跟離隊(duì)處相距多遠(yuǎn)？

Answer 1

分析：求這位通訊員往返一次的時(shí)間，就要分別求出這位通訊員從隊(duì)尾到排頭以及從排頭返回隊(duì)尾所用的時(shí)間．從隊(duì)尾到排頭，應(yīng)用隊(duì)伍長(zhǎng)除以它們的速度差求出時(shí)間，從排頭返回隊(duì)尾應(yīng)用隊(duì)伍長(zhǎng)除以它們的速度和求出時(shí)間．然后把求出的兩個(gè)時(shí)間加起來(lái)即為通訊員往返一次的時(shí)間．

解答：解：（1）在通訊員從隊(duì)伍排尾跑步到隊(duì)伍排頭的過(guò)程中通訊員相對(duì)于隊(duì)伍的速度大小為V=v′-v=2m/s，故通訊員從隊(duì)伍排尾跑步到隊(duì)伍排頭所需的時(shí)間為t₁=

l

v

=40s
在通訊員從隊(duì)伍排頭跑步到隊(duì)伍排尾的過(guò)程中通訊員相對(duì)于隊(duì)伍的速度大小為V′=v'+v=2m/s，故通訊員從隊(duì)伍排頭跑步到隊(duì)伍排尾所需的時(shí)間為t₂=

l

V′

=40s
故通訊員從離開到重回排尾一共所需時(shí)間t=t₁+t₂=80s．
（2）通訊員歸隊(duì)處跟離隊(duì)處的距離即為隊(duì)伍這段時(shí)間運(yùn)動(dòng)的位移：x=vt=80m
答：（1）通訊員從離開隊(duì)伍到重回到排尾共用80s；（2）通訊員歸隊(duì)處跟離隊(duì)處相距80m

點(diǎn)評(píng)：此題的解答思路是：先求出通訊員走到排頭用的時(shí)間，再求通訊員返回隊(duì)尾所用的時(shí)間，最后求通訊員從離開隊(duì)尾到回到隊(duì)尾所用的時(shí)間，解決問(wèn)題．