A ball is projected with an initial speed of \(17 \text{m s}^{−1}\)
at an angle of \(25°\) below the horizontal from a point on the top of a vertical wall. The point of projection is \(8 \text{m}\) above horizontal ground. The ball hits a vertical fence which is at a horizontal distance of \(9 \text{m}\) from the wall (see diagram).

###### There are **5** marks available for part (i), **5** marks for part (ii) and **4** marks for part (iii).

###### In total, this question is worth **19.4%** of all available marks in the paper.

###### This is part of the set OCR A Level Problems.

\((\text{i})\) Calculate the height above the ground of the point where the ball hits the fence.

\((\text{ii})\) Calculate the direction of motion of the ball immediately before it hits the fence.

\((\text{iii})\) It is given that 30% of the kinetic energy of the ball is lost when it hits the fence. Calculate the speed of the ball immediately after it hits the fence.

**Input your answer to part \((\text{iii})\), correct to 3 significant figures.**

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