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Two bodies cross each other with a speed of $10 m / s$ as they move toward each other, but when they move away from each other, they cross each other at a speed of $6 m / s$ . The speed of both bodies are [[1]] $m / s$ and ____ $m / s$ .

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Detailed Solution

Two bodies cross each other with a speed of

10 m / s

as they move toward each other, but when they move away from each other, they cross each other at a speed of

6 m / s

. The speed of both bodies are

8 m / s

and

2 m / s

.
Let the speed of both bodies be

v_{1}

and

v_{2}

When both bodies move toward each other, their relative speed is given as

v_{1} + v_{2} = 10

………(1) When both bodies move away from each other, their relative speed is given as

v_{1} - v_{2} = 6

………..(2)
Adding equation (1) and (2)

v_{1} + v_{2} + v_{1} - v_{2} = 10 + 6

\Rightarrow 2 v_{1} = 16

\Rightarrow v_{1} = 8 m / s

Putting

v_{1}

in equation (1):

8 + v_{2} = 10

\Rightarrow v_{2} = 2 m / s

Hence, the velocity of both bodies are

8 m / s

and

2 m / s

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