Question

A particle is moving in $x-y$ plane along a path $y=x^2+x.$ The ratio $v_y/v_x$, when the particle is at $(2,6)$ is,

$\text{where}\left\{{}_{v_x\to x-\text{component of velocity}}^{v_y\to y-\text{component of velocity}}\right\}$

• A. $13$
• B. $5$
• C. $10$
• D. $4$

Answer 1

The correct option is B $5$

Equation of trajectory of the particle is,
$y=x^2+x$

Differentiating the above equation, with respect to time.

$\frac{dy}{dt}=2x.\frac{dx}{dt}+\frac{dx}{dt}$
$\Rightarrow \frac{\frac{dy}{dt}}{\frac{dx}{dt}}=(2x+1)=\frac{v_y}{v_x}$

Now, $\text{at}(2,6)$
$\frac{v_y}{v_x}=(2\times 2+1)=5$

Hence, $\left(B\right)$ is the correct answer.