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Question

What are the speeds of two objects if, when they move uniformly towards each other, they get 6 m closer in each second and when they move uniformly in the same direction with the original speeds, they get 6.0 m closer in each 10 s?

A
3.3 m/s and 1.2 m/s
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B
5.2 m/s and 4.6 m/s
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C
3 m/s and 3 m/s
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D
3.3 m/s and 2.7 m/s
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Solution

The correct option is D 3.3 m/s and 2.7 m/s
Let VA and VB be the velocities of two objects moving uniformly.
Case 1: When objects are moving opposite to each other:
In this case the relative speed of object A w.r.t object B is given by VAB=VA(VB) (∵VA is in the opposite direction to that of object VB)
VAB=VA+VB
According to question :(VA+VB)×1 s=6 m
VA+VB=6 m/s (i)
Case 2: When objects are moving in same direction.
In this case the relative speed of object A w.r.t object B is given by VAB=VAVB
According to question:
(VAVB)×10 s=6 m
(VAVB)=0.6 m/s (ii)
Using (i) and (ii) we get VA=3.3 m/s and VB=2.7 m/s

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