Two men A and B start with velocities v at the same time from the junction of two roads inclined at `45^@` to each other.If they travel by different roads,find the rate at which they are being separated.

Explanation

Let `A C=B C=x` and `A B=y`


In `triangle A C D` and `triangle D C B`,



`angle C A D=angle C B D `


`therefore angle A C D=angle D C B`


`text { or } angle A C D=frac{1}{2} times angle A C B `


`Rightarrow angle A C D=frac{1}{2} times 45^{circ} `


`Rightarrow angle A C D=frac{pi}{8} `


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