6. A parachutist drops from a helicopter $H$ and falls vertically from rest towards the ground. Her parachute opens 2 s after she leaves $H$ and her speed then reduces to $4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. For the first 2 s her motion is modelled as that of a particle falling freely under gravity. For the next 5 s the model is motion with constant deceleration, so that her speed is $4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ at the end of this period. For the rest of the time before she reaches the ground, the model is motion with constant speed of $4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.
\begin{enumerate}[label=(\alph*)]
\item Sketch a speed-time graph to illustrate her motion from $H$ to the ground.
\item Find her speed when the parachute opens.

A safety rule states that the helicopter must be high enough to allow the parachute to open and for the speed of a parachutist to reduce to $4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ before reaching the ground. Using the assumptions made in the above model,
\item find the minimum height of $H$ for which the woman can make a drop without breaking this safety rule.

Given that $H$ is 125 m above the ground when the woman starts her drop,
\item find the total time taken for her to reach the ground.
\item State one way in which the model could be refined to make it more realistic.\\
(1 mark)
\end{enumerate}

\hfill \mbox{\textit{Edexcel M1 2001 Q6 [15]}}