### Part (a)

| Answer/Working | Marks | Guidance |
|---|---|---|
| Energy A to B $\frac{1}{2} \times 0.2v^2 - \frac{1}{2} \times 0.2u^2 = 0.2g \times 0.1$ | M1A1 | |
| $v^2 - u^2 = 0.2g$ | | |
| $v^2 = u^2 + 1.96$ * | A1 cso | (3) |

### Part (b)

| Answer/Working | Marks | Guidance |
|---|---|---|
| $mg\cos\theta(-R) = m\frac{v^2}{r}$ | M1 | Attempt NL2 at B. Normal contact force is zero here so need not be seen in the equation |
| $R = 0 \Rightarrow g \times \frac{4}{5} = \frac{(u^2 + 1.96)}{0.5}$ | A1 | Fully correct equation with $R = 0$ and substitution for $v^2$ |
| $0.4g = u^2 + 1.96$ | | |
| $u^2 = 1.96$, $u = 1.4$ or 1.40 | DM1, A1 | (4) Solve for a numerical value for $u^2$ or $u$ Correct value for $u$, must be 1.4 |

### Part (c)

| Answer/Working | Marks | Guidance |
|---|---|---|
| Vert speed $= v\sin\theta = \frac{3}{5}\sqrt{0.4g}$ ($= 1.1879...$) or $\frac{21\sqrt{2}}{25}$ | M1 | Attempt the vertical speed, ($v\sin\theta$ or $v\cos\theta$, with their value for $v$ (not their value of $u$) and an attempt at a numerical value for the trig function. |
| $0.4 = \frac{3}{5}\sqrt{0.4g}t + \frac{1}{2}gt^2$ | M1A1ft | Correct equation, follow through their vertical speed |
| $4.9t^2 + 1.1879...t - 0.4 = 0$ | | |
| $t = \frac{-1.1879 \pm \sqrt{1.1879^2 + 4 \times 4.9 \times 0.4}}{9.8}$ | | |
| $t = 0.1891...$ ($t > 0$) | A1 | |
| Horiz speed $= v\cos\theta = \frac{4}{5}\sqrt{0.4g}$ | M1 | Attempt the horizontal speed, (trig function used to be different to that used for the vertical) with their value for $v$ and an attempt at a numerical value for the trig function. Allow if value of $u$ is used, provided there is an attempt to resolve. |
| Horiz distance $= \frac{4}{5}\sqrt{0.4g} \times 0.1891... = 0.2995$ | A1 | |
| $OC = 0.3 + 0.2995... = 0.5995...$ $OC = 0.60$ or 0.600 m | A1ft | (7) [14] |

**Key Notes:**
- (a)M1: Energy equation from A to B: A difference of KE terms = loss of GPE mass m, 0.2 or already cancelled. Must be clearly an energy equation and not uniform acceleration.
- (a)A1: Completely correct equation mass $m$, 0.2 or already cancelled.
- (a)A1cso: Rearrange to the GIVEN form mass $m$, 0.2 or previously cancelled.
- (b)M1: Attempt NL2 at B. Normal contact force is zero here so need not be seen in the equation
- (b)A1: Fully correct equation with $R = 0$ and substitution for $v^2$
- (b)DM1: Solve for a numerical value for $u^2$ or $u$
- (b)A1: Correct value for $u$, must be 1.4
- (c)M1: Attempt the vertical speed, $v\sin\theta$ or $v\cos\theta$, with their value for $v$ (not their value of $u$) and an attempt at a numerical value for the trig function.
- (c)M1: Use $s = ut + \frac{1}{2}at^2$ with their vertical speed. Must have attempted to resolve the speed.
- (c)A1ft: Correct equation, follow through their vertical speed
- (c)A1: Correct value of $t$ (no ft here)
- (c)M1: Attempt the horizontal speed, (trig function used to be different to that used for the vertical) with their value for $v$ and an attempt at a numerical value for the trig function. Allow if value of $u$ is used, provided there is an attempt to resolve.
- (c)A1: Correct horizontal distance
- (c)A1ft: Add their horizontal distance to 0.3. Answer must be 2 or 3 sf.

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