Standard +0.8 This is a two-unknown projectile problem requiring simultaneous equations from both horizontal and vertical displacement at a given time. Students must resolve the 40m distance into components, apply SUVAT equations with gravity, and solve the resulting non-linear system—more demanding than standard single-unknown projectile questions but a recognized M2 exercise type.
3 A particle \(P\) is projected with speed \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of \(\theta ^ { \circ }\) above the horizontal from a point \(O\) on horizontal ground. At the instant 4 s after projection the particle passes through the point \(A\), where \(O A = 40 \mathrm {~m}\) and the line \(O A\) makes an angle of \(30 ^ { \circ }\) with the horizontal. Calculate \(V\) and \(\theta\).
3 A particle $P$ is projected with speed $V \mathrm {~m} \mathrm {~s} ^ { - 1 }$ at an angle of $\theta ^ { \circ }$ above the horizontal from a point $O$ on horizontal ground. At the instant 4 s after projection the particle passes through the point $A$, where $O A = 40 \mathrm {~m}$ and the line $O A$ makes an angle of $30 ^ { \circ }$ with the horizontal. Calculate $V$ and $\theta$.\\
\hfill \mbox{\textit{CAIE M2 Q3 [5]}}