6 In this question you should take \(\boldsymbol { g \) to be \(\mathbf { 1 0 } \mathrm { ms } ^ { \boldsymbol { - } \mathbf { 2 } }\).} Piran finds a disused mineshaft on his land and wants to know its depth, \(d\) metres.
Local records state that the mineshaft is between 150 and 200 metres deep.
He drops a small stone down the mineshaft and records the time, \(T\) seconds, until he hears it hit the bottom. It takes 8.0 seconds. Piran tries three models, \(\mathrm { A } , \mathrm { B }\) and C .
In model A, Piran uses the formula \(d = 5 T ^ { 2 }\) to estimate the depth.

1. Find the depth that model A gives and comment on whether it is consistent with the local records. Explain how the formula in model A is obtained. In model B, Piran uses the speed-time graph in Fig. 6. \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{4c8c96cf-5184-46e4-9c45-a8a80d0a6ff8-5_762_1176_1087_424} \captionsetup{labelformat=empty} \caption{Fig. 6}
   \end{figure}
2. Calculate the depth of the mineshaft according to model B. Comment on whether this depth is consistent with the local records.
3. Describe briefly one respect in which model B is the same as model A and one respect in which it is different. Piran then tries model C in which the speed, \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), is given by $$\begin{aligned} & v = 10 t - t ^ { 2 } \text { for } 0 \leqslant t \leqslant 5
   & v = 25 \text { for } 5 < t \leqslant 8 \end{aligned}$$
4. Calculate the depth of the mineshaft according to model C. Comment on whether this depth is consistent with the local records.
5. Describe briefly one respect in which model C is similar to model B and one respect in which it is different.