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A boat which has a speed of 5 Km/h in still water crosses a river of width 1 km along the shortest possible path in 15 min. The velocity of the river water in km/h is
- a)3
- b)√41
- c)1
- d)4
Correct answer is option 'A'. Can you explain this answer?
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A boat which has a speed of 5 Km/h in still water crosses a river of w...
To find the velocity of the river water, we can use the concept of relative velocity. Let's assume that the boat is moving perpendicular to the river's flow.
Let's say the velocity of the river water is v km/h.
The boat's speed in still water is 5 km/h.
Since the boat is moving perpendicular to the river's flow, the effective speed of the boat is the vector sum of its speed in still water and the velocity of the river water.
Let's consider the time it takes for the boat to cross the river. It is given as 15 minutes, which is equivalent to 15/60 = 1/4 hours.
In this time, the boat covers the width of the river, which is 1 km.
Using the concept of relative velocity, we can write the equation:
Boat's effective speed * Time taken = Distance covered
(5 + v) * (1/4) = 1
Simplifying the equation:
5 + v = 4
v = 4 - 5
v = -1 km/h
Since the velocity of the river water cannot be negative, the answer is not possible.
Therefore, there is no valid answer for the velocity of the river water in this scenario.
Let's say the velocity of the river water is v km/h.
The boat's speed in still water is 5 km/h.
Since the boat is moving perpendicular to the river's flow, the effective speed of the boat is the vector sum of its speed in still water and the velocity of the river water.
Let's consider the time it takes for the boat to cross the river. It is given as 15 minutes, which is equivalent to 15/60 = 1/4 hours.
In this time, the boat covers the width of the river, which is 1 km.
Using the concept of relative velocity, we can write the equation:
Boat's effective speed * Time taken = Distance covered
(5 + v) * (1/4) = 1
Simplifying the equation:
5 + v = 4
v = 4 - 5
v = -1 km/h
Since the velocity of the river water cannot be negative, the answer is not possible.
Therefore, there is no valid answer for the velocity of the river water in this scenario.
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A boat which has a speed of 5 Km/h in still water crosses a river of width 1 km along the shortest possible path in 15 min. The velocity of the river water in km/h isa)3b)√41c)1d)4Correct answer is option 'A'. Can you explain this answer?
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