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A particle is moving with velocity vec(v...

A particle is moving with velocity `vec(v)=K(yhati + xhatj)`, where K is a constant. The general equation for its path is:

A

`y^(2)=x^(2)` + constant

B

`y=x^(2)` + constant

C

`y^(2) = x + ` constant

D

xy =constant

Text Solution

Verified by Experts

The correct Answer is:
A
Given `(dx)/(dt)hati+(dy)/(dt)hatj=K(yhati+xhatj)`

`:.dx/dt=Ky` and `(dy)/(dt)=Kx`
`implies dx/dt=y/x` and xdx=ydv or integrating `x^(2)=y^(2)+c`
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