Question

a man swims perpendicular with respect to river flow with a constant acceleration (in y direction) and river is flowing with a constant velocity in the x direction the trajectory of man seems from ground will be ​

Answer 1

Given:

A man swims perpendicular with respect to river flow with a constant acceleration (in y direction). River is flowing with a constant velocity in the x direction.

To find:

Trajectory of man as seen from the ground.

Calculation:

Let Velocity of man be u (in the Y axis ) and Velocity of river be v (in the X axis).

So, distance travelled in Y axis in time t :

$y = ut + \dfrac{1}{2} a {t}^{2} \: \: \: ......(1)$

So, distance travelled in X axis in time t :

$x = vt \: \: \: .........(2)$

Putting value of t from eq.(2) into eq.(1) ;

$\therefore \: y = ut + \dfrac{1}{2} a {t}^{2}$

$= > \: y = u( \dfrac{x}{v} ) + \dfrac{1}{2} a {( \dfrac{x}{v}) }^{2}$

$\boxed{ = > \: y = \dfrac{ux}{v} + \dfrac{a {x}^{2} }{2 {v}^{2} } }$

So, Equation of Trajectory is a parabola ;

Hence ,the man will move in a parabolic trajectory when seen from ground.