Question

A boat having a speed of $5$ km/hr. in still water, crosses a river of width $1$ km along the shortest possible path in $15$ minutes. The speed of the river in Km/hr

• A. $1$
• B. $3$
• C. $4$
• D. $\sqrt{41}$

Answer 1

The correct option is B $3$

The shortest path is given to be $1$ Km.
Now it takes $15$ minutes i.e. $\frac{1}{4}$ Hrs to cross the river.
Thus, Component of velocity perpendicular to the river current is

$speed=\frac{distance}{time}=\frac{1}{1/4}=4km/hr$

Now, it is given that the velocity of the boat is $5$ km/hr.
Thus, the component of velocity along the current is

$\sqrt{5^2-4^2}=3km/hr$

This is the value of the river current in the opposite direction.