A river flows toward the east at the speed Vr and has the width d. A swimmer wis

Question

A river flows toward the east at the speed Vr and has the width d. A swimmer wishes to cross the river for the time t and so that his direction of the motion relative to the ground should be northward. What should be the swimmers speed in still water? Derive algebraic formula in terms of Vr, d, and t A river flows toward the east at the speed Vr and has the width d. A swimmer wishes to cross the river for the time t and so that his direction of the motion relative to the ground should be northward. What should be the swimmers speed in still water? Derive algebraic formula in terms of Vr, d, and t

Explanation / Answer

here,

the x component of the velocity of the swimmer , vx = Vr

the y component of the velocity of the swimmer , vy = d/t

then the velocity of the swimmer , v = sqrt( vx^2 + vy^2)

v = sqrt(Vr^2 + d^2/t^2)

the algebric formula for the swimmer speed is sqrt( Vr^2 + d^2/t^2)

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