## Question 5:

| Answer | Mark | Guidance |
|--------|------|----------|
| **Either** consider height: Attempt to substitute for $u$ and $a$ in $s = ut + \frac{1}{2}at^2$ | M1 | Accept $g$ as $g$, $\pm9.8$, $\pm9.81$, $\pm10$; $u = 30$; $s \leftrightarrow c$ |
| $y = 30\sin 35\ t - 4.9t^2$ | A1 | Derivation need not be shown |
| Need $y = 0$ for time of flight $T$ | B1 | |
| giving $T = \dfrac{30\sin 35}{4.9}\ (= 3.511692\ldots)$ | A1 | cao. Any form. May not be explicit |
| **Or** consider time to top: Attempt to substitute for $u$ and $a$ in $v = u + at$ | M1 | Accept $g$ as $g$, $\pm9.8$, $\pm9.81$, $\pm10$; $u = 30$; $s \leftrightarrow c$ |
| $v = 30\sin 35 - 9.8t$ | A1 | Derivation need not be shown |
| Need $v = 0$ and to double for time of flight $T$ | B1 | |
| giving $T = \dfrac{30\sin 35}{4.9}\ (= 3.511692\ldots)$ | A1 | cao. Any form. May not be explicit |
| **then** $x = 30\cos 35\ T$ | M1 | Accept $s \leftrightarrow c$ if consistent with above |
| so $x = 30\cos 35\times\dfrac{30\sin 35}{4.9}\ (= 86.29830\ldots)$ | F1 | FT for their time. Condone consistent $s \leftrightarrow c$ error (which could lead to correct answer here) |
| Required time for sound is $x/343$ | M1 | FT from their $x$ |
| Total time is $3.511692\ldots + 0.251598\ldots = 3.76329\ldots$ so $3.76\ \text{s}$ (3 s.f.) | A1 | cao following fully correct working throughout question |
| | **8** | |