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 of it meets these two cars at an interval of `4` minutes, will be.
A. `40 km//hr`
B. `45 km//hr`
C. `10 km//hr`
D. `15 km//hr`

Answer 1

Correct Answer - B
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, vec v_(BA) = vec v_B - vec 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 `vec v_C` relative to ground then the velocity of car `C` relative to `A` and `B` will be `vec v_(rel) = vec v_C - vec v`
But as `vec v` is opposite to `v_C`, 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 = (d)/(v_(rel)) rArr (4)/(60) = (5)/(v_C + 30)`
`rArr v_C = 45 km//hr`.