Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line

Kinematics of motion in a straight line — practice question

Particles $P$ and $Q$ are launched vertically upwards from level ground at the same moment. Their initial speeds are $12\,\text{m s}^{-1}$ and $7\,\text{m s}^{-1}$ respectively, and $t$ seconds after launch their heights above the ground are $h_P$ and $h_Q$ respectively. On the way back down to the ground, each particle comes to rest.
(i)[3]

Determine the values of $t$ for which the particles are moving in opposite directions.

(ii)[5]

At a particular moment, $P$ and $Q$ are above the ground and $3h_P = 8h_Q$. Determine the velocities of $P$ and $Q$ at this moment.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Use $0=u-gt$ to determine the times when the particles are at maximum height

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