## Question 9(i):

| Answer | Marks | Guidance |
|--------|-------|----------|
| Vertical motion $u=0$ | B1 | Using $u=0$ in the vertical direction |
| $s = ut + \dfrac{1}{2}at^2$ | M1 | Using suvat equation(s) to find $t$; allow sign errors and incorrect value for $u$ |
| $-5 = 0 - \dfrac{9.8}{2}t^2$ | | |
| $t = \sqrt{\dfrac{10}{9.8}} = 1.01 \text{ s}$ | A1 [3] | Must follow from working where signs are consistent |

## Question 9(ii):

| Answer | Marks | Guidance |
|--------|-------|----------|
| $x = 14t$ | B1 | May be implied |
| $y = 5 - 4.9t^2$ | B1 | May be implied |
| So cartesian equation is $y = 5 - 4.9\left(\dfrac{x}{14}\right)^2\left[= 5-\dfrac{x^2}{40}\right]$ | M1, A1 [4] | Attempt to eliminate $t$; any form |

## Question 9(iii):

**EITHER:**

| Answer | Marks | Guidance |
|--------|-------|----------|
| When $y=2$: $y = 5 - \dfrac{x^2}{40} = 2$ | M1 | Using their equation of trajectory and $y=2$; **SC2** for $d < \sqrt{80}\ [=8.94]$; **SC1** for $d=\sqrt{80}\ [=8.94]$ |
| $\dfrac{x^2}{40} = 3$ | | |
| $x = \sqrt{120} = 10.9544...$ | A1 | Must be 11.0 or better |
| $[0<\,]d < 11.0 \text{ m}$ | E1 [3] | Allow "Fence must be less than 10.95 m from the origin"; FT their value |

**OR:**

| Answer | Marks | Guidance |
|--------|-------|----------|
| When $y=2$: $2 = 5 - 4.9t^2$ | M1 | Both steps required for M1; allow if origin taken to be at window height and top of wall is 3m below the window; signs must be consistent for A1 |
| $t = 0.782$ | A1 | Must be 11.0 or better |
| When $t=0.782$: $x = 14\times0.782 = 10.95$ | A1 | |
| $[0<\,]d < 11.0 \text{ m}$ | [3] | Allow "Fence must be less than 10.95 m from the origin" |