(i)[3]
By using the equation for the trajectory of a projectile, show that each angle of projection satisfies the equation $\tan^2\theta - 8\tan\theta + 4 = 0$.
(ii)[5]
Calculate the distance between the points where $P$ and $Q$ land on the plane.
Mathematics 9709 · AS & A Level · Probability
Probability — practice question
Particles $P$ and $Q$ are launched together from point $O$ on a horizontal plane with speed $40\ \text{m s}^{-1}$. At different times later on, both particles pass through point $A$, whose horizontal and vertically upward displacements from $O$ are $40\ \text{m}$ and $15\ \text{m}$ respectively.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Substitutes the values into the projectile equation to give $15 = 40\tan\theta - \dfrac{g40^2}{2 \times 40^2 \cos^2\theta}$” …
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