Quick check from College Physics, 2.7 Falling Objects

Falling Objects: quick check

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?

Answer it in your own words before you look.

Answer
We know that initial position $y_{0} = 0$ , final position $y = −30 . 0 m$ , and $a = - g = - 9 . {80 m/s}^{2}$ . We can then use the equation $y = y_{0} + v_{0} t + \frac{1}{2} {at}^{2}$ to solve for $t$ . Inserting $a = - g$ , we obtain
$\begin{array}{l} y & = & 0 + 0 - \frac{1}{2} {gt}^{2} \\ t^{2} & = & \frac{2 y}{- g} \\ t & = & \pm \sqrt{\frac{2 y}{- g}} = \pm \sqrt{\frac{2 (- 30.0 m)}{- 9.80 m {/s}^{2}}} = \pm \sqrt{6.12 s^{2}} = 2.47 s \approx 2.5 s \end{array}$
2.88

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.

How did it go?