Multiple choice

Velocity of boat in still water is 13m/s. If water flowes in a river with a velocity of 5 m/s, what is the difference in times taken by him to cross the river in the shortest path and in the shortest time. If the width of the river is 156m.

  1. $1 sec$
  2. $\dfrac{13}{12}sec$
  3. $\dfrac{\sqrt3}{2}sec$
  4. $\sqrt3 sec$
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A Correct answer
Explanation

The shortest-time crossing takes 156/13 = 12 seconds. To follow the shortest path, the boat's effective crossing speed is sqrt(13^2 - 5^2) = 12 m/s, so the time is 13 seconds. The difference is 1 second.

AI explanation

For the shortest time, the boat heads straight across at 13 m/s, giving a time of 156 divided by 13, which is 12 seconds. For the shortest path, the boat heads upstream to cancel drift, so its across-river velocity is sqrt(13 squared minus 5 squared) equals sqrt(144) equals 12, giving a time of 156 divided by 12, which is 13 seconds. The difference is 13 minus 12, which is 1 second.

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