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

Kinematics of motion in a straight line — practice question

Particle $A$ is launched vertically upward from point $O$ at a speed of $80\,\text{m s}^{-1}$. After 1 second, a second particle, $B$, which has the same mass as $A$, is launched vertically upward from $O$ at a speed of $100\,\text{m s}^{-1}$. At a time $T\,\text{s}$ after the first particle is launched, the two particles meet and merge to form particle $C$.
(a)[4]

Show that the value of $T$ is $3.5$.

(b)[1]

Find the height above $O$ where the particles collide.

(c)[5]

Find the time from $A$ being projected until $C$ returns to $O$.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Displacement formulae $s_A=80T-\tfrac12gT^2$ and $s_B=100(T-1)-\tfrac12g(T-1)^2$ are both correct

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