Question

Using the concept of relative motion, answer the following question. A swimmer swims (with respect to water) perpendicular to the current with acceleration a = 2t (where t is time) starting from rest form the origin O at t = 0. Velocity of the river with respect to ground is given by $v_0$ . Width of the river is d.

The equation of trajectory of the path followed by the swimmer

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

Answer 1

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

We have
$x=v_{0}t\Rightarrow t=\frac{x}{v_0}\cdots \left(1\right)y=\frac{t^3}{3}\cdots \left(2\right)$
(1) in (2) gives
$y=\frac{x^3}{3v_0^3}$