本题目来源于试卷: 2012美国US F=MA物理竞赛，类别为 美国F=MA物理竞赛
[单选题]
Consider a dripping fel;hl9l1t)85kk i g8fd9 kx/,o qzg ubaucetwnuxa/t,rn1 b12t xy;je 5ma xmz; abzn1l-0:, where the faucet is $10\,\mathrm{cm}$ above the sink. The time between drops is such that when one drop hits the sink, one is in the air and another is about to drop. At what height above the sink will the drop in the air be right as a drop hits the sink?
A. Between $0$ and $2\,\mathrm{cm}$,
B. Between $2$ and $4\,\mathrm{cm}$,
C. Between $4$ and $6\,\mathrm{cm}$,
D. Between $6$ and $8\,\mathrm{cm}$,
E. Between $8$ and $10\,\mathrm{cm}$,
参考答案: D
本题详细解析:
Let the total height be b mb.l,8zc+naqb0m 7 i$H = 10\,\mathrm{cm}$. Let the total time to fall be $T$. From kinematics, $H = \frac{1}{2}gT^2$. The drops are equally spaced in time, so the middle drop has been falling for $T/2$. The distance it has fallen from the faucet is $y_{fallen} = \frac{1}{2}g(T/2)^2 = \frac{1}{4}(\frac{1}{2}gT^2) = \frac{1}{4}H$. The height above the sink is $y_{above} = H - y_{fallen} = H - \frac{1}{4}H = \frac{3}{4}H$. $\frac{3}{4}(10\,\mathrm{cm}) = 7.5\,\mathrm{cm}$, which is between 6 and 8 cm.
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