| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | SUVAT in 2D & Gravity |
| Type | Vertical projection: time at height |
| Difficulty | Moderate -0.3 This is a straightforward two-part SUVAT question with vertical motion under gravity. Part (a) requires finding maximum height using v²=u²+2as (standard technique), and part (b) requires solving a quadratic equation for times when height equals 2m. Both are routine M1 applications with no conceptual challenges, making it slightly easier than average. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.02h Motion under gravity: vector form |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(u = 10.5, v = 0, a = -g\) use \(v^2 = u^2 + 2as\) | M1 | |
| \(0 = 110.25 - 19.6s \Rightarrow s = 5.625\) | M1 A1 | |
| ball starts from 0.6 m, so it reaches 6.225 m above ground level | A1 | |
| (b) \(s = 2 - 0.6 = 1.4, u = 10.5, a = -g\), use \(s = ut + \frac{1}{2}at^2\) | M1 | |
| \(10.5t - 4.9t^2 > 1.4\) i.e. \(7t^2 - 15t + 2 < 0\) | M1 A1 | |
| \((7t - 1)(t - 2) < 0\) leading to \(\frac{1}{7} < t < 2\) | M1 A1 | |
| ball is above ground for \(\frac{13}{7}\) (≈ 1.86) seconds | A1 | (10 marks) |
**(a)** $u = 10.5, v = 0, a = -g$ use $v^2 = u^2 + 2as$ | M1 |
$0 = 110.25 - 19.6s \Rightarrow s = 5.625$ | M1 A1 |
ball starts from 0.6 m, so it reaches 6.225 m above ground level | A1 |
**(b)** $s = 2 - 0.6 = 1.4, u = 10.5, a = -g$, use $s = ut + \frac{1}{2}at^2$ | M1 |
$10.5t - 4.9t^2 > 1.4$ i.e. $7t^2 - 15t + 2 < 0$ | M1 A1 |
$(7t - 1)(t - 2) < 0$ leading to $\frac{1}{7} < t < 2$ | M1 A1 |
ball is above ground for $\frac{13}{7}$ (≈ 1.86) seconds | A1 | (10 marks)6. A boy kicks a football vertically upwards from a height of 0.6 m above the ground with a speed of $10.5 \mathrm {~ms} ^ { - 1 }$. The ball is modelled as a particle and air resistance is ignored.
\begin{enumerate}[label=(\alph*)]
\item Find the greatest height above the ground reached by the ball.
\item Calculate the length of time for which the ball is more than 2 m above the ground.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q6 [10]}}