First slide

Relative motion in 2 dimension

Question

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

Moderate

A

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

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

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

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

Solution

Let v be the river velocity and u the velocity of swimmer in still water. Then
$\begin{array}{l} t_{1} = 2 (\frac{W}{\sqrt{u^{2} - v^{2}}}) \\ t_{2} = \frac{W}{u + v} + \frac{W}{u - v} = \frac{2 u W}{u^{2} - v^{2}} and t_{3} = \frac{2 W}{u} \end{array}$
Now we can see that $t_{1}^{2} = t_{2} t_{3}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App