Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
A particle is fired from a point $O$ on level ground. Its initial speed is $20\text{ m s}^{-1}$ and it is directed upwards at an angle $\theta$ to the horizontal. The particle goes through the point that is $7\text{ m}$ above the ground and $16\text{ m}$ horizontally from $O$, and then lands on the ground at $A$.
(i)[4]
Starting from the equation of the particle’s trajectory together with the identity $\sec^2 \theta = 1 + \tan^2 \theta$, demonstrate that the two possible values of $\tan \theta$ are $\frac{3}{4}$ and $\frac{17}{4}$.
(ii)[3]
Determine the distance $OA$ for each of the two possible values of $\tan \theta$.
(iii)[2]
On the same diagram, sketch the two possible trajectories.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme.