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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


  1. v2+2

  2. 2v

  3. v

  4. v22


Solution

The correct option is D

v22


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+x22x2cos45

=2x2x22

y=x22

dydt=dxdt22v22

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