Question

Velocity of the river with respect to ground is given by $v_0$. Width of the river is $d$. A swimmer swims (with respect to water) perpendicular to the current with acceleration $a=2t$ (where $t$ is time) starting from rest from the origin $O$ at $t=0$. The equation of trajectory of the path followed by the swimmer is

• A. $y=\frac{x^3}{3v_0^3}$
• B. $y=\frac{x^3}{2v_0^2}$
• C. $y=\frac{x}{v_0}$
• D. $y=\sqrt{\frac{x}{v_0}}$

Answer 1

The correct option is A $y=\frac{x^3}{3v_0^3}$

From the given data we have,
$\frac{d{v}_y}{dt}=2t$
$\therefore v_y=t^2$ or $\frac{dy}{dt}=t^2$
or $y=\frac{t^3}{3}$ .....$\left(i\right)$
and $x=v_{0}t\Rightarrow t=\frac{x}{v}$
Substituting in Eq. (i) we have,
$y=\frac{x^3}{3v_0^3}$