Two circular pipes both have radii of 3.5 meters. They both steadily eject water horizontally, and the water from each pours onto a measuring grid 5 meters below. The stream from the first pipe lands on the measuring grid 20 cm away from a position directly below the pipe mouth, and the stream from the second pipe lands 5 cm away from a position directly below its pipe mouth. How long would it take the second pipe to pour out as much water as the first pours out in 1 minute?Question 48 Answer Choices A. 2 minutes B. 4 minutes C. 8 minutes D. 16 minutes
Question
Two circular pipes both have radii of 3.5 meters. They both steadily eject water horizontally, and the water from each pours onto a measuring grid 5 meters below. The stream from the first pipe lands on the measuring grid 20 cm away from a position directly below the pipe mouth, and the stream from the second pipe lands 5 cm away from a position directly below its pipe mouth. How long would it take the second pipe to pour out as much water as the first pours out in 1 minute?Question 48 Answer Choices A. 2 minutes B. 4 minutes C. 8 minutes D. 16 minutes
Solution
The distance the water lands from the pipe is directly proportional to the speed at which the water is ejected from the pipe. This is because the water from both pipes falls the same vertical distance, so the horizontal distance it travels depends on how fast it's moving horizontally when it leaves the pipe.
The water from the first pipe lands 20 cm away from directly below the pipe, while the water from the second pipe lands 5 cm away. This means the water from the first pipe is moving 20/5 = 4 times as fast as the water from the second pipe when it leaves the pipe.
Since the pipes have the same radius, the volume of water they eject is proportional to the speed of the water. This means the first pipe ejects water 4 times as fast as the second pipe.
Therefore, it would take the second pipe 4 times as long to eject the same amount of water as the first pipe. So if the first pipe takes 1 minute to eject a certain amount of water, the second pipe would take 4 minutes to eject the same amount.
So the answer is B. 4 minutes.
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