Kevin S. Huang

2012: Problem 1

Topic: Kinematics
Concepts: Free fall

Solution:

Let $T$ be the time between when drops are released from the faucet. We are given that a drop takes time $2T$ to fall to the sink so

h=\frac{1}{2}g(2T)^2

The drop in the air has fallen for time $T$ so it is located a distance $d$ below the faucet with

d=\frac{1}{2}gT^2=\frac{h}{4}

Thus, it is at height

h_1=h-d=\frac{3h}{4}=\frac{3(10\,\mathrm{cm})}{4}=7.5\,\mathrm{cm}

so the answer is D.