## Question 7(a):

| Answer/Working | Mark | Guidance Notes |
|---|---|---|
| Horizontal distance | M1 | Equation with correct terms, condone sign errors |
| $2ut = 80$ | A1 | Correct equation |
| Vertical distance or vertical speed | M1 | Equation with correct terms, condone sign errors |
| $0 = ut - \frac{1}{2}gt^2$ | A1 | Correct equation in $t$. Alternatives include $-u = u - gt$ or $0 = u - g\frac{1}{2}t$ |
| Solve for $u$ $\left(\text{e.g. } u \times \frac{80}{2u} = \frac{1}{2}g\frac{80^2}{4u^2}\right)$ | DM1 | Dependent on the two previous M marks |
| $u = 14$ * | A1* | Obtain **given answer** correctly |
| **Note:** If they consistently have $u$ horizontal and $2u$ vertically, then mark as a misread: M1A0M1A0M1A1 | | |
| **Total: 6 marks** | | |

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## Question 7(b):

| Answer/Working | Mark | Guidance Notes |
|---|---|---|
| $v^2 = (7\sqrt{17})^2 - 28^2$ | M1 | Form an equation in $v$ only ($v$ is vertical component) |
| $\Rightarrow v = 7$ (or $-7$) | A1 | Second value not needed |
| Use of *suvat* to find the required time. Check logic: time speed is $< 7\sqrt{17}$ or time speed is $> 7\sqrt{17}$? | DM1 | Dependent on the first M mark. Complete method to obtain the required time, condone sign errors |
| $7 = 14 - gt \Rightarrow t = \frac{5}{7} = 0.71\ldots$ | A1 | Obtain a relevant value of $t$ |
| Total time $= 2 \times \frac{5}{7} = 1.4$ or $1.43$ (s) | A1 | For the required time to 2 sf or 3 sf. A0 for $\frac{10}{7}$; follows the use of an approximate value for $g$ |
| **Total: 5 marks** | | |

### Question 7(b) Alternative 1:

| Answer/Working | Mark | Guidance Notes |
|---|---|---|
| $\frac{1}{2}m(28^2 + 14^2) - \frac{1}{2}m(7\sqrt{17})^2 = mgh$ | M1 | Form an equation in $h$ only |
| $\Rightarrow h = 7.5$ | A1 | Correct only |
| Use of *suvat*; check logic: time speed is $< 7\sqrt{17}$ or time speed is $> 7\sqrt{17}$? | DM1 | Dependent on the first M mark. Complete method to obtain the required time, condone sign errors |
| $7.5 = 14t - \frac{1}{2} \times 9.8t^2 \Rightarrow t = \frac{5}{7},\ t = \frac{15}{7}$ | A1 | Obtain at least one relevant value of $t$ |
| Total time $= \frac{20}{7} - \left(\frac{15}{7} - \frac{5}{7}\right) = 1.4$ or $1.43$ (s) | A1 | For the required time to 2 sf or 3 sf. A0 for $\frac{10}{7}$; follows the use of an approximate value for $g$ |

### Question 7(b) Alternative 2:

| Answer/Working | Mark | Guidance Notes |
|---|---|---|
| Use $7\sqrt{17}$ to form an equation in $t$ only | M1 | |
| $\Rightarrow 7\sqrt{17} = \sqrt{(14 - gt)^2 + 28^2}$ | A1 | Or equivalent |
| Solve to find the required time; check logic: time speed is $< 7\sqrt{17}$ or time speed is $> 7\sqrt{17}$? | DM1 | Dependent on the first M mark. Complete method to obtain the required time, condone sign errors |
| $147 = 2gt - g^2t^2 \Rightarrow t = \frac{5}{7},\ t = \frac{15}{7}$ | A1 | Obtain at least one relevant value of $t$ |
| Total time $= \frac{20}{7} - \left(\frac{15}{7} - \frac{5}{7}\right) = 1.4$ or $1.43$ (s) | A1 | For the required time to 2 sf or 3 sf. A0 for $\frac{10}{7}$; follows the use of an approximate value for $g$ |
| **Total: 5 marks** | | |

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