Question

# Two men P, and Q 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, the rate at which they are being separated, is v√2+√2 √2v v v√2−√2

Solution

## The correct option is D v√2−√2 Let R, and S be the position of men P, and Q respectively at any time t.  Since velocities are same ⇒OR=OS=x Given  dxdt=v Let SR=y Now, in △ORS by cosine rule y2=x2+x2−2x2cos45∘ =2x2−x2√2 ⇒y=x√2−√2 dydt=dxdt√2−√2⇒v√2−√2

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