Standard +0.8 This is a non-standard projectiles problem requiring insight to connect the angle of the position vector (15°) with the projectile equations at t=2s. Students must recognize that tan(15°) = y/x and substitute parametric equations, then solve the resulting equation involving tan(30°) and g. More conceptually demanding than routine 'find range/max height' questions.
A particle \(P\) is projected with speed \(V\) m s\(^{-1}\) at an angle of \(30°\) above the horizontal from a point \(O\) on horizontal ground. At the instant \(2\) s after projection, \(OP\) makes an angle of \(15°\) above the horizontal. Calculate \(V\). [4]
A particle $P$ is projected with speed $V$ m s$^{-1}$ at an angle of $30°$ above the horizontal from a point $O$ on horizontal ground. At the instant $2$ s after projection, $OP$ makes an angle of $15°$ above the horizontal. Calculate $V$. [4]
\hfill \mbox{\textit{CAIE M2 2014 Q1 [4]}}