Mathematics 9709 · AS & A Level · Representation of data

Representation of data — practice question

A small ball $B$ is launched from $O$ with speed $U\,\text{m s}^{-1}$ at an angle of $\theta\degree$ above the horizontal. Two seconds later, $B$ hits a smooth wall inclined at $60\degree$ to the horizontal. At that instant, the speed of $B$ is $18\,\text{m s}^{-1}$ and its direction of motion is perpendicular to the wall (see Fig. 1). $B$ rebounds from the wall with speed $V\,\text{m s}^{-1}$, again moving perpendicular to the wall. After $0.8\,\text{s}$, $B$ meets the wall again at a lower point $A$ (see Fig. 2).
(i)[5]

Find $U$ and $\theta$.

(ii)[4]

By analysing the motion of $B$ after the rebound, find $V$.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: Hence, $U\cos\theta = 18\cos30 = 9\sqrt3$

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