Multiple choice

A boat having a speed of $5\ \text{km/h}$. in still water, crosses a river of width $1\ \text{km}$ along the shortest possible path in $15 \ :\text{minutes}$. The speed of the stream in $\text{km/h}$

  1. $1$
  2. $3$
  3. $4$
  4. $\sqrt {41}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Shortest path means the boat moves perpendicular to the stream. Speed of boat in still water (Vb) = 5 km/h. Distance = 1 km, Time = 15 min = 0.25 h. Resultant speed = 1 / 0.25 = 4 km/h. Since Vb^2 = Vs^2 + Resultant^2, 5^2 = Vs^2 + 4^2, so Vs^2 = 25 - 16 = 9, Vs = 3 km/h.

AI explanation

The boat crosses the 1 km river in 15 minutes (0.25 hours), so its effective velocity across the river is 1 / 0.25 = 4 km/h. Because this path is the shortest possible, the 4 km/h velocity represents the boat's perpendicular component, which is derived from the still water speed (5 km/h) using the Pythagorean theorem. The stream speed squared equals the still water speed squared minus the perpendicular speed squared, giving v_stream = sqrt(5^2 - 4^2) = 3 km/h.

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