Solution to Test Paper 3

& 0=24\textrm{.}5-9\textrm{.}8t \\ & t=\frac{24\textrm{.}5}{9\textrm{.}8}=2\textrm{.}5\text{ seconds} \\ \end{align}

& {{0}^{2}}={{24\textrm{.}5}^{2}}+2\times (-9\textrm{.}8)\times s \\ & s=\frac{{{24\textrm{.}5}^{2}}}{2\times 9\textrm{.}8}=30\textrm{.}625\text{ m} \\ & \\ & \text{OR} \\ & \\ & s=\frac{1}{2}(24\textrm{.}5+0)\times 2\textrm{.}5=30\textrm{.}625\text{ m} \\ \end{align}

& T-4900=500\times 0\textrm{.}6 \\ & T=300+4900=5200\text{ N} \\ \end{align}

& 4800-4900=500a \\ & a=\frac{-100}{500}=-0\textrm{.}2\text{ m}{{\text{s}}^{\text{-2}}} \\ & 0\textrm{.}\text{2 m}{{\text{s}}^{-\text{2}}}\quad \text{downwards} \\ \end{align}

& 5\times 9\textrm{.}8\sin 42{}^\circ -14\textrm{.}6=5a \\ & a=\frac{18\textrm{.}22}{5}=3\textrm{.}64\text{ m}{{\text{s}}^{\text{-2}}} \\ \end{align}

& 2=\frac{1}{2}\times 3\textrm{.}64{{t}^{2}} \\ & t=\sqrt{\frac{4}{3\textrm{.}64}}=1\textrm{.}05\text{ seconds} \\ \end{align}

& Q\cos 40{}^\circ =8\times 9\textrm{.}8\sin 40{}^\circ \\ & Q=\frac{8\times 9\textrm{.}8\sin 40{}^\circ }{\cos 40{}^\circ }=65\textrm{.}8\text{ N} \\ \end{align}

& Q\cos 40{}^\circ +F=8\times 9\textrm{.}8\sin 40{}^\circ \\ & Q\sin 40{}^\circ +8\times 9\textrm{.}8\cos 40{}^\circ =R \\ & Q\cos 40{}^\circ =8\times 9\textrm{.}8\sin 40{}^\circ \\ & \text{ }-0\textrm{.}3(Q\sin 40{}^\circ +8\times 9\textrm{.}8\cos 40{}^\circ ) \\ & Q=\frac{8\times 9\textrm{.}8\sin 40{}^\circ -0.\textrm{.}\times 8\times 9\textrm{.}8\cos 40{}^\circ }{\cos 40{}^\circ +0.\times \sin 40{}^\circ } \\ & \text{ }=33\textrm{.}8\text{ N} \\ \end{align}

& -(1+0\textrm{.}05t)=1-0\textrm{.}1t \\ & 0\textrm{.}05t=2 \\ & t=40 \\ \end{align}