A swimmer crosses a flowing stream of width ω to and fro in time t1 The time taken to cover the same distance up and down the stream is t2. If t3 is the time the swimmer would take to swim a distance 2ω in still water, then

Question

A swimmer crosses a flowing stream of width ω to and fro in time t1 The time taken to cover the same distance up and down the stream is t2. If t3 is the time the swimmer would take to swim a distance 2ω in still water, then (A) t12=t2t3 (B) t22=t1t3 (C) t23=t1t2 (D) t3=t1+t2

Tardigrade Admin · Accepted Answer

Let v be the river velocity and u the velocity of swimmer in still water. Then t1=2((W/√u2-v2)) t2=(W/u+v)+(W/u-v)=(2uW/u2-v2) and t3 = (2W/u) Now we can see th t21=t2t3

Q. A swimmer crosses a flowing stream of width $ω$ to and fro in time $t_{1}$ The time taken to cover the same distance up and down the stream is $t_{2}$ . If $t_{3}$ is the time the swimmer would take to swim a distance $2 ω$ in still water, then

$t_{1}^{2} = t_{2} t_{3}$

$t_{2}^{2} = t_{1} t_{3}$

$t_{2}^{3} = t_{1} t_{2}$

$t_{3} = t_{1} + t_{2}$

Let $v$ be the river velocity and $u$ the velocity of swimmer in still water. Then

$t_{1} = 2 (\frac{W}{u ^{2} - v ^{2}})$

$t_{2} = \frac{W}{u + v} + \frac{W}{u - v} = \frac{2 u W}{u ^{2} - v ^{2}} an d t_{3} = \frac{2 W}{u}$

Now we can see th $t_{1}^{2} = t_{2} t_{3}$

Q. A swimmer crosses a flowing stream of width ω to and fro in time t1​ The time taken to cover the same distance up and down the stream is t2​. If t3​ is the time the swimmer would take to swim a distance 2ω in still water, then

t12​=t2​t3​

t22​=t1​t3​

t23​=t1​t2​

t3​=t1​+t2​