Mathematics 9709 · AS & A Level · Probability

Probability — practice question

A particle $P$ is launched from point $O$ on horizontal ground with speed $20\,\text{m s}^{-1}$ at an angle of $30^\circ$ above the horizontal. $P$ then rebounds when it first hits the ground at point $A$.
(i)[3]

Find how long after projection $P$ first strikes the ground, and determine the distance $OA$.

(ii)[5]

When $P$ bounces at $A$, the horizontal component of $P$'s velocity is unchanged. Immediately after the bounce, the vertical component of velocity is $8\,\text{m s}^{-1}$. $P$ hits the ground a second time at $B$, where it comes to rest. Calculate the first and last times after projection at which the speed of $P$ is $18\,\text{m s}^{-1}$.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Applies vertical-motion equation: $-20\sin30 = 20\sin30 - gt$

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