Question

Velocity of a boat in still water is $13m/s$. If the water in a river flows with a velocity of $5m/s$ and the width of the river is $156m$, what is the difference in time taken by the boat to cross the river in the shortest possible path and the shortest possible time? (in seconds)

Answer 1

Given $v_{br}=13m/s,v_r=5m/s$

Case 1 : For shortest path taken by boat
In this case, resultant velocity of boat $v_b$ is perpendicular to the flow.
$v_b^2=v_{br}^2-v_r^2={13}^2-5^2$ (from figure)
$\Rightarrow v_b=12m/s$
$\therefore t_1=\frac{156}{12}=13s$

Case 2 : Shortest time when it moves perpendicular
In this case, the velocity of boat w.r.t river $v_{br}$ is perpendicular to the flow.
$\therefore t_2=\frac{156}{13}=12s$
Difference$=t_1-t_2=13-12=1s$