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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


A

v22

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B

v2+2

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C

2v

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D

v

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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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