Question

A particle is moving with velocity $\vec{v} = k\left(y\hat{i} + x\hat{j}\right),$ where $k$ is a constant. The general equation for its path is

• A. $y = x^2 +$ constant
• B. $y^2 = x +$ constant
• C. $xy =$ constant
• D. $y^2 = x^2 +$ constant

Answer 1

Answer: (D)

$y^2 = x^2 +$ constant

Answer 2

$\vec{v} = K\,y\hat{i} + K\,x\hat{j}$ $\frac{dx}{dt} = Ky, \quad \frac{dy}{dt} = Kx$ $\frac{dy}{dx} = \frac{dy}{dt} \times \frac{dt}{dx} = \frac{Kx}{Ky}$ $y \,dy = x\, dx$ $y^{2} = x^{2} + c.$