A) 40 km/hr
B) 45 km/hr
C) 30 km/hr
D) 15 km/hr
Correct Answer: B
Solution :
The two car (say A and B) are moving with same velocity, the relative velocity of one (say B) with respect to the other \[A,\,{{\overrightarrow{v}}_{BA}}={{\overrightarrow{v}}_{B}}-{{\overrightarrow{v}}_{A}}=v-v=0\] So the relative separation between them (= 5 km) always remains the same. Now if the velocity of car (say C) moving in opposite direction to A and B, is \[{{\overrightarrow{v}}_{C}}\] relative to ground then the velocity of car C relative to A and B will be \[{{\overrightarrow{v}}_{rel.}}={{\overrightarrow{v}}_{C}}-\overrightarrow{v}\] But as \[\overrightarrow{v}\] is opposite to vC So \[\,{{v}_{rel}}={{v}_{c}}-(-30)=({{v}_{C}}+30)\,km/hr.\] So, the time taken by it to cross the cars A and B \[t=\frac{d}{{{v}_{rel}}}\,\,\,\,\Rightarrow \,\,\,\frac{4}{60}=\frac{5}{{{v}_{C}}+30}\,\,\] \[\Rightarrow \,\,\,{{v}_{C}}=45\,km/hr.\]
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