a) $\left[ {{v^2} = {3^2} + 2 \times 2.5 \times 8} \right]$

Speed is $7{\text{ }}m{s^{ - 1}}$

b) $KE$ gain $ = {\raise0.5ex\hbox{$\scriptstyle 1$}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle 2$}}0.8\left( {{7^2} - {3^2}} \right){\text{ }}\left( { = 16} \right)$

$PE$ loss $ = 16 + 7$

$\left[ {0.8 \times 10 \times 8\sin \alpha  = 23} \right]$

Angle is ${21.1^ \circ }$ or ${0.368^ \circ }$

ALTERNATIVELY:

$F = 7/8$

$\left[ {0.8 \times 10\sin \alpha  - F = 0.8 \times 2.5} \right]$

$0.8 \times 10\sin \alpha  - 0.875 = 0.8 \times 2.5$

Angle is ${21.1^ \circ }$ or ${0.368^ \circ }$

c) ${5^2} = {3^2} + 2 \times 2.5s{\text{ }}\left( {s = 3.2} \right)$

$[WD/7 = 3.2/8$

or $WD = 0.875 \times 3.2$

or $WD = 8 \times 3.2 \times \left( {23/64} \right)$

$ - {\raise0.5ex\hbox{$\scriptstyle 1$}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle 2$}}0.8\left( {{5^2} - {3^2}} \right)]$

Work done is $2.8{\text{ }}J$