| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2018 |
| Session | October |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Projectiles |
| Type | Speed at specific time or position |
| Difficulty | Standard +0.3 This is a standard M2 projectiles question requiring systematic application of kinematic equations. Part (a) uses velocity components at t=2s to find initial conditions (routine reverse-working), part (b) applies standard displacement formulas, and part (c) requires solving a quadratic for times when height equals h. All techniques are textbook exercises with no novel insight required, making it slightly easier than average. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.02h Motion under gravity: vector form3.02i Projectile motion: constant acceleration model |
4. At time $t = 0$ a ball is projected from a fixed point $A$ on horizontal ground to hit a target. The ball is projected from $A$ with speed $u \mathrm {~m} \mathrm {~s} ^ { - 1 }$ at an angle $\theta ^ { \circ }$ to the horizontal. At time $t = 2 \mathrm {~s}$ the ball hits the target. At the instant when it hits the target, the ball is travelling downwards at $30 ^ { \circ }$ below the horizontal with speed $12 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. The ball is modelled as a particle moving freely under gravity and the target is modelled as the point $T$.
\begin{enumerate}[label=(\alph*)]
\item Find
\begin{enumerate}[label=(\roman*)]
\item the value of $\theta$,
\item the value of $u$.
The height of $T$ above the ground is $h$ metres.
\end{enumerate}\item Find the value of $h$.
\item Find the length of time for which the ball is more than $h$ metres above the ground during the flight from $A$ to $T$.
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\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2018 Q4 [13]}}