Question

A man can swim in still water at 10kmph . The river flows 5kmph .if he crosses the river in shortest time his resultant velocity is ;
a)15kmph b)5kmph c)5root5kmph d)none

Answer 1

(c)
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Answer 2

Answer:

The resultant velocity is $5\sqrt{5}$ km/h.  Option c) is correct.

Explanation:

• The resultant velocity is calculated by the vector sum of the individual velocities.
• For the shortest time, man should swim vertically opposite point from starting point.

The formula for calculating resultant velocity is:

$V_{R}=\sqrt{V_{mw}^{2}+ V_{w}^{2 }$

where, $V_{mw}$ is the velocity of the man with respect to water.

           $V_{w}$ is the velocity of the water.

Step 1:

Given the value of $V_{mw}$ equal to $10$ km/h.

The value of $V_{w}$ is $5$ km/h.

Step 2:

The resultant velocity, $V_{R} =$ $\sqrt{10_{}^{2}+ 5_}^{2 }$

                                           $= 5\sqrt{5}$ km/h.

So, the resultant velocity is $5\sqrt{5}$ km/h.

Option c) is correct.