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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:
1
`vec(v)=K(yhat(i)+xhat(j)), v_(x)=ky, (dx)/(dt)=ky`
similarly `(dy)/(dt)=Kx`
Hence `(dy)/(dx)=x/yrArr y dy=x dx`,
by integrating `y^(2)=x^(2)+c`
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