Question

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

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

Answer 1

The correct option is A $y^2=x^2+$ contant

As$v=k(yi+xi)$

$vₓ=\frac{Kyso{d}_x}{dt}=Ky$

$vy=\frac{K_{x}sody}{dt}=K_x$

dividing both equations

$\frac{dy}{dx}=\frac{dy}{dt}$divide$\frac{dx}{dt}=\frac{Kx}{Ky}=\frac{x}{y}$

$ydy=xdx$

integrating the equation

$\frac{y^2}{2}=\frac{x^2}{2}+c$