question_answer

Two men leave a place with an interval oft between them. They arrive at one end of a bridge of length L with time interval of T and reach the other end of the bridge at the same time. How far is the nearer end of the bridge from their starting point? Assume that they are moving with uniform speeds.

Answer:

  Let they move with uniform speeds \[{{V}_{1}}\]and\[{{V}_{2}}.\] For case CA: \[\frac{s+L}{{{V}_{1}}}-\frac{x+L}{{{V}_{2}}}=t\] \[\Rightarrow \frac{1}{{{V}_{1}}}-\frac{1}{{{V}_{2}}}=\frac{t}{x+L}\]                         ……(1) For case CB: \[\frac{L}{{{V}_{1}}}-\frac{L}{{{V}_{2}}}=T\] \[\Rightarrow \frac{1}{{{V}_{1}}}-\frac{1}{{{V}_{2}}}=\frac{T}{L}\]                                             ………(2) Equating (1) and (2) we get, \[x=L\left( \frac{t-T}{T} \right)\]