A length of piping connects the rain gutters on a house roof to the drain in the ground. The house is 3 stories, or about 8 meters in height. If a hole forms in the pipe at the midpoint, approximately what will the velocity of the water be as it escapes through the hole? Ignore water flow and use kinematics.
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Correct Answer: B. 9 m/s
The water will exit at a velocity which is proportional to the height it has fallen, according to the equation v = sqrt(2gh). This can be derived from the basic equation for velocity and displacement, v2 = 2a * s, where a is acceleration, and s is displacement (or in this case height). Thus, the height the water has fallen in this problem is 4 meters, and v = 8.85m/s, which we round up to 9.
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