Question

A boat can travel at $13$ m/min in still water. The width of the river is $78m$ flowing with a velocity of $5i$ m/s($i$ - in East direction). How long the boat would take to cross the river if $a)$ it takes the shortest route. $b)$ takes the minimum time route.
($H:{\nu }_{sw}=13$ m/s ; $6.5$ min & $6$ min)

Answer 1

Given speed of boat in still water =13 m/min

speed of water =5 m/s

(a) To achieve minimum distance the boat must travel in the direction opposite to that of the flow of water.

So the net speed of boat$=5-\frac{13}{60}=4.78\text{m/s}$

We know $t=\frac{s}{v};\text{where s= 78 m (as the width of the river is 78})$

$t=\frac{78}{4.78}=16.31s$

(b) To achieve minimum time the boat must travel in the direction to that of the flow of water.

Thus speed of the boat=5.216 m/s

t=$\frac{78}{5.216}=14.95s$