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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

15 km/hr

Text Solution

Verified by Experts

The correct Answer is:
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,
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 `vec_C` relative to ground then the velocity of car C
relative to A and B will be `vec_(rel.)=vec_C-vecv`
But as `vecv` is oppsite 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.))implies(4)/(60)=(5)/(v_C+30)`
`impliesv_C=45(km)/(hr)`.
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