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Two identical tall jars are filled to the brim with water. The first jar has a small side hole at a depth h/3 below the water surface, and the second jar has a small side hole at a depth 2h/3, where h is the height of the jar. Water from the first jar lands a horizontal distance R1 from the base and water from the second jar lands a distance R2 from the base. Which relation between R1 and R2 is correct?
- R1 > R2
- R1 < R2
- R1 = 2R2
- R1 = R2
Correct answer: R1 = R2
Solution
The horizontal range from a side hole at depth d is R = 2*sqrt(d*(h-d)). This expression is symmetric about d = h/2, so holes at d and (h-d) give the same range. Since h/3 and 2h/3 are symmetric about h/2, R1 = R2.
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