Question

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

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

Answer 1

The correct option is B $y^2=x^2+constant$

$\frac{dx}{dt}=ky,\frac{dy}{dt}=kx$
Now, $\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}=\frac{x}{y}$
$\Rightarrow ydy=xdx$
Integrating both side
$y^2=x^2+c$