Physics

Problem

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

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^2}{2v_0^2}

(C)

y = \frac{x}{v_0}

(D)

y = \sqrt{\frac{x}{v_0}}

Intuitive explanation

The key is recognizing that the swimmer's motion has two independent components: perpendicular to the current (where acceleration varies with time) and parallel to it (where the river carries them at constant $v_0$ ). Find the swimmer's velocity and position perpendicular to the current by integrating the time-dependent acceleration, then use the constant drift from the river current to eliminate time and relate the two position coordinates—that's your trajectory equation.

Intuitive explanation

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