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

Options

A. `y= (x^3)/(3 v_0^3)`
B. `y= (x^2)/(2 v_0^2)`
C. `y= x/v_0`
D. `y= sqrt(x/v_0)`

Answer

A

Explanation

`(dv_Y)/(dt)=2t`
`:. v_y=t^2 or (dy)/(dt)=t^2`
or `y=t^3/3`
and `x=v_0t rArr t=x/v`
Substituting in Eq. (i) we have,
`y=x^3/(3v_0^3)`