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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 = x ^ 2 ` + constant

B

`y ^ 2 = x + ` constant

C

`xy ` = constant

D

` y ^ 2 = x ^ 2 + ` constant

Text Solution

Verified by Experts

Here, `vecv=K(yathi+x hatj)`
`vecv=Kyhati+Kxhatj .........(1)`
Also, `vecv=(dx)/(dt) hati+(dy)/(dt) hatj ........(ii)`
Equating equation (i) and (ii), we get
`(dx)/(dt)=Ky , (dy)/(dt)=Kx, Now, (dy)/(dx)=(dy)/(dt) xx (dt)/(dx) therefore (dy)/(dx)=(Kx)/(Ky)=x/y`
Integrating both sides of the above equation, we get `int ydy= int xdx rArr y^(2)/2 =x^(2)/2+" constant "or y^(2)=x^(2)+"constant"`
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