Further Math A2s 3.1.3 Projectile trajectories

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A particle P is projected with speed $u \mathrm{~ms}^{-1}$ at an angle $\theta$ above the horizontal from a point O on a horizontal plane and moves freely under gravity. During its flight P passes through the point which is a horizontal distance 3 a from O and a vertical distance $\frac{3}{8} a$ above the horizontal plane. It is given that $\tan \theta=\frac{1}{3}$ .

Show that $u^{2}=8 a g$ .
A particle Q is projected with speed $V \mathrm{~ms}^{-1}$ at an angle $\alpha$ above the horizontal from O at the instant when P is at its highest point. Particles P and Q both land at the same point on the horizontal plane at the same time.

Use equation of trajectory: $y=x \tan \alpha-\frac{g x^{2}}{2 u^{2}} \sec ^{2} \alpha$ :
$\frac{3}{8} a=3 a \times \frac{1}{3}-g \times \frac{(3 a)^{2}}{2 u^{2}}\left(1+\frac{1}{9}\right)$ $\frac{5}{8} a=\frac{5 g a}{u^{2}}, \quad u^{2}=8 g a$
At least one step of working.
AG

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CAIE A-Level Further Math A2 3.1.3 Projectile Motion Questions

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CAIE A-Level Further Math A2 3.1.3 Projectile Motion Questions question 1