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A particle is moving with velocity vecv...

A particle is moving with velocity ` vecv = k( y hat(i) + x hat(j)) `, where `k` is a constant . The genergal 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
`vec (v) = K ( y hat(i) + x hat(j))`
`v_(x) = Ky rArr ( dx)/( dt) = Ky , (dy)/( dt) = Kx = v_(y)`
`( dy)/( dx) = (x)/(y) rArr ydy = xdx`
`rArr y^(2) = x^(2) + c`
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