Multiple choice

A man rowing a boat in river making an angle of $45^{o}$ with the straight course reaches the opposite point from the starting point. If velocity of water is $V$, then velocity of the boat w.r.t water is:

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

To reach the opposite point, the boat's velocity component perpendicular to the river must cancel the river's velocity. Let v be the boat's speed w.r.t water. The boat is angled at 45 degrees. The component of v along the river is v*cos(45) and perpendicular is v*sin(45). To cross straight, v*sin(45) = V. So v*(1/sqrt(2)) = V, which means v = sqrt(2)V.

AI explanation

To counteract the stream velocity V and reach the exact opposite point, the boat's upstream velocity component relative to the water must equal V. Since the boat is pointed at a 45-degree angle to the straight course, this component is V_boat * cos(45 degrees) = V_boat / sqrt(2). Setting this equal to V gives V_boat = sqrt(2)V, meaning the velocity of the boat with respect to water is sqrt(2)V.

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