June 2023 Paper 1 Q1
1 A ball is thrown vertically upwards with a speed of \(8\,\mathrm{m\,s^{-1}}\).
Find the times at which the ball is 3 m above the point of projection. [2]
| Scheme | Marks | AO |
|---|---|---|
| using suvat with upwards positive \(u = 8,\ a = -9.8,\ s = 3\) \(s = ut + \frac{1}{2}at^2\) \(3 = 8t - 4.9t^2\) Solve \(4.9t^2 - 8t + 3 = 0\) | M1 | 3.4 |
| \(t = 0.584,\ 1.05\) s | A1 | 1.1b |
| [2] |
Notes
M1: Using suvat equation(s) leading to a value for \(t\). Allow sign errors
A1: both values needed. ISW if an inequality is given as the final answer
Exact roots are \(\frac{40 \pm \sqrt{130}}{49}\)