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Two cars are moving in the same directio...

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 of it meets these two cars at an interval of `4` minutes, will be.

A

40 km/hr

B

45 km/hr

C

30 km/hr

D

0 km/hr

Text Solution

Verified by Experts

As the two cars (say A and B) are moving with
same velocity, the relative velocity of one
(say B) with respect to the other A,
`vecV_(BA) = vecV_(B) - vecV_(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` vecV_(C)` relative to ground then the velocity of car C relative to A and B will be ` vec V _("rel") = vecV_(C) - vecV `
But as ` vecV ` is opposite to ` V_(C)` .
` V_("rel") = V_(C) - (-30) = (V_(C) + 30)` km/hr
So, the time taken by it to cross the cars A and B is
` t = (d)/(V_("rel"))`
` rArr (4)/(60) = (5)/(V_(C) + 30) rArr V_(C) = 45 ` km/hr
Hence correct answer is (B)
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