Question

a boat which a speed of 5 km/hr in still water crosses a river of width 1km along the shortest possible path in 15 minutes calcute the velocity of river water in km/hr

Answer 1

a boat which a speed of $5\mathrm{km/hr}$ in still water crosses a river of width $1\mathrm{km}$ along the shortest possible path in 15 minutes calculate the velocity of river water in $\mathrm{km/hr}$

Velocity-addition formula:

if a boat is moving relative to the water velocity $v$ and water is on a river that is flowing with velocity $u$ , then the velocity of the boat relative to the shore equals the vector sum:

$\vec{s} = \vec{v} + \vec{u}$

Time will be minimal if $s$ is perpendicular to the shores.

Pythagorean theorem

$$u ^ {2} = v ^ {2} - s ^ {2}$$

velocity of the boat relative to the shore equals:

$$s = \frac {1 k m}{1 5 m i n} = 4 \frac {k m}{h}$$

Therefore:

$$u = \sqrt {v ^ {2} - s ^ {2}} = 3 \frac {k m}{h}$$

Answer: $3 \frac{km}{h}$