First slide

Relative motion based problems

Question

Wind is blowing to east along two parallel railway tracks. Two trains moving with the same speed in opposite direction have the steam track of one double that of the other. The speed of each train is

Easy

A

Equal to that of the wind
B

Three times that of the wind
C

Double that of the wind
D

Half that of the wind

Solution

Let V and u be the speed of train and wind respectively Also let train -1 is running due east and train-2 is running due west.
For train-1 , length of steam track in a given time t ,
l₁ = vt - ut = (v-u) t
and for train - 2 , l₂ = vt + ut = (v+u)t
since l₂ = 2l₁ , we can write
(v+u)t = 2 x (v - u) t ⇒V = 3u

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