Kinematic Equations for Objects in Free Fall

A chunk of ice breaks off a glacier and falls 30.0 meters before it hits the water. Assuming it falls freely (there is no air resistance), how long does it take to hit the water?

Solution

We know that initial position $y_{0}=0$, final position $y=-30.0 \mathrm{~m}$, and $a=-g=-9.80 \mathrm{~m} / \mathrm{s}^{2} .$ We can then use the equation $y=y_{0}+v_{0} t+\frac{1}{2} a t^{2}$ to solve for $t .$ Inserting $a=-g$, we obtain

$\begin{aligned}&y=0+0-\frac{1}{2} g t^{2} \\ &t^{2}=\frac{2 y}{-g} \\ &t \quad=\pm \sqrt{\frac{2 y}{-g}}=\pm \sqrt{\frac{2(-30.0 \mathrm{~m})}{-9.80 \mathrm{~m} / \mathrm{s}^{2}}}=\pm \sqrt{6.12 \mathrm{~s}^{2}}=2.47 \mathrm{~s} \approx 2.5 \mathrm{~s} \end{aligned}$

where we take the positive value as the physically relevant answer. Thus, it takes about 2.5 seconds for the piece of ice to hit the water.