question_answer

Two cars are moving in the same direction with the same speed\[\text{3}0\text{ km}{{\text{h}}^{-\text{1}}}\]. They are separated by a distance of 5 km. What is the speed of a car moving in the opposite direction if it meets these two cars at an interval of 4 minutes.

Answer:

                Let car C be moving in opposite direction to A and B, with velocity \[{{\vec{v}}_{c}}\]relative to ground. Then relative velocity of car C relative to A and B will be                                 \[{{\vec{v}}_{rel}}={{\vec{v}}_{c}}-\vec{v}\]. As, \[\vec{v}\]is opposite to \[{{\vec{v}}_{c}}\] So, \[{{\text{v}}_{\text{rel}}}={{\text{v}}_{\text{c}}}-\left( -\text{3}0 \right)=({{\text{v}}_{\text{c}}}+\text{3}0)\text{km}{{\text{h}}^{-\text{1}}}\]Hence, time taken by car C to cross the cars A and B will be \[\text{t }=\frac{s}{{{v}_{rel}}}\]or \[\frac{4}{60}=\frac{5}{{{v}_{c}}+30}\] or \[{{\text{v}}_{\text{c}}}=\text{45 km}{{\text{h}}^{-\text{1}}}\]