Vectors Question 176
Question: Two cars are moving in the same direction with the same speed 30 km/hr. They are separated by a distance of 5 km, the speed of a car moving in the opposite direction if it meets these two cars at an interval of 4 minutes, will be
Options:
A) 40 km/hr
B) 45 km/hr
C) 30 km/hr
D) 15 km/hr
Correct Answer: B 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} $ Show Answer
Answer:
Solution:
$ \Rightarrow ,v _{C}=45,km/hr. $
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