question_answer

Two cars are travelling in the same direction at 60 kmph and are 30 km apart. A third car travelling at 30 kmph crosses one of the cars at a certain moment. Find the time elapsed before it crosses the second car. Solve the problem if the first two cars are travelling in the opposite directions.

Answer:

  When car 3 travels in the same direction as car 1 and car 2 it cannot cross. When car 3 travels in opp. direction w.r.t. car 1 and car 2 as shown in figure then: Relative speed of car 1 or car 2 w.r.t. car 3 \[=60+30=90\,kmph.\] \[=O{{C}^{2}}=O{{P}^{2}}+P{{C}^{2}}=\sqrt{{{40}^{2}}+{{30}^{2}}}=\sqrt{2500}\]time elapsed to cross \[=\frac{30}{90}=\frac{1}{2}hr\,\,or\,\,20\,\,\min \] Relative speed of car 3 w.r.t car \[1=60+30=90\text{ }kmph.\] \[\overline{AD}\] time elapsed to cross \[\frac{30}{90}=\frac{1}{2}hr\,or\,\,20\,\min .\]