Answer to Question #147134 in Physics for Rajanikanth R

Question

Anne and Vera are standing by the train tracks and waiting for the train to pass. The train is moving with a constant velocity. At the moment when the front of the train is aligned with where they are standing, Anne starts moving with the constant velocity in the same direction as the train, and Vera starts moving in the opposite direction with the same velocity as Anne. They stop moving when the rear of the train passes by them. Anne passed 45 meters and Vera passed 30 meters. What is the length of the train?

Answer 1

$$l=(v+u)t=(v-u)t'\\t=\frac{s}{u},t'=\frac{s'}{u}\\l=(v+u)\frac{s}{u}=(v-u)\frac{s'}{u}\\l=\left(\frac{v}{u}+1\right)s=\left(\frac{v}{u}-1\right)s'\\\frac{\left(\frac{v}{u}+1\right)}{\left(\frac{v}{u}-1\right)}=\frac{s'}{s}=\frac{45}{30}=1.5\\\frac{v}{u}=5$$

The length of the train is

$$l=(5+1)30=180\ m$$