7 At time $t = 0$, a small ball $A$ is projected vertically upwards with speed $8 \mathrm {~ms} ^ { - 1 }$ from a fixed point on horizontal ground.\\
The ball hits the ground again for the first time at time $t = T _ { 1 }$ seconds.\\
Ball $A$ is modelled as a particle moving freely under gravity.
\begin{enumerate}[label=(\alph*)]
\item Show that $T _ { 1 } = 1.63$ to 3 significant figures.

After the first impact with the ground, $A$ rebounds to a height of 2 m above the ground.\\
Given that the mass of $A$ is 0.1 kg ,
\item find the magnitude of the impulse received by $A$ as a result of its first impact with the ground.

At time $t = 1$ second, another small ball $B$ is projected vertically upwards from another point on the ground with speed $5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$

Ball $B$ is modelled as a particle moving freely under gravity.\\
At time $t = T _ { 2 }$ seconds ( $T _ { 2 } > 1$ ), $A$ and $B$ are at the same height above the ground for the first time.
\item Find the value of $T _ { 2 }$
\end{enumerate}

\hfill \mbox{\textit{Edexcel M1 2024 Q7}}