Puzzling Wells

Firstly, recall the SUVAT equation $s=ut+\frac{1}{2}at^{2}$ . Since $u$ , the initial velocity, is $0$ , so we have $s=\frac{1}{2}at^{2}$ . Now it is simply a case of inputing $g$ ( $9.8ms^{-2}$ ) for $a$ and $10$ for $t$ , yielding $\frac{1}{2}\times 9.8\times 10^{2}=490$ m. So the solution is $\boxed{490}$ .

Note that, if the SUVAT equation above isn't known by heart, it can be derived as follows:

$s=v\times t$

The final velocity of the stone is given by $v=at$ (since its intial velocity is $0$ ). Since it's acceleration is constant (always equal to $g$ ), its average velocity is given by $v=\frac{1}{2}\times at$ .

By substituting $\frac{1}{2}\times at$ for $v$ , we obtain $s=\frac{1}{2}at^{2}$ , as required since $u=0$ .

recall that dv/dt =g. Integrating twice yields the equation y = v(0)t + 0.5gt^2. Inputing v(0) = 0 and t = 10, the final answer is y = 490m.

Comment: the unit for the answer should be specified in the question for clarity!