Standard +0.3 This is a straightforward projectiles question requiring resolution of velocity components and use of constant acceleration equations. Students need to find T from vertical motion (v = u sin 30° - gT = 0 at max height), then find velocity components at t = (2/3)T and combine using Pythagoras. All steps are standard A-level mechanics techniques with no novel insight required, making it slightly easier than average.
A particle \(P\) is projected with speed \(u\) at an angle of \(30°\) above the horizontal from a point \(O\) on a horizontal plane and moves freely under gravity. The particle reaches its greatest height at time \(T\) after projection.
Find, in terms of \(u\), the speed of \(P\) at time \(\frac{2}{3}T\) after projection. [5]
A particle $P$ is projected with speed $u$ at an angle of $30°$ above the horizontal from a point $O$ on a horizontal plane and moves freely under gravity. The particle reaches its greatest height at time $T$ after projection.
Find, in terms of $u$, the speed of $P$ at time $\frac{2}{3}T$ after projection. [5]
\hfill \mbox{\textit{CAIE Further Paper 3 2020 Q1 [5]}}