A child of weight 330N is at point X at the top of a slide. The slide is at the edge of a swimming pool, as shown in Fig. 3.1. X child, weight 330 N surface of slide 4.0 m surface of water Y 1.1 m water in swimming pool Fig. 3.1 (not to scale) The child moves from rest to the lowest point of the slide that is a vertical distance of 4.0 m below X. The child continues moving towards point Y which is at the end of the slide and a vertical distance of 1.1 m above the lowest point. The kinetic energy of the child at Y is 540 J.

1. (a)Calculate the difference in the gravitational potential energy of the child at points X and Y.[2]
2. (b)An average frictional force of 52N acts on the child when moving from X to Y. By considering changes of energy, determine the distance moved by the child from X to Y.[2]
3. (c)(i)The child leaves the slide at point Y with a velocity that is at an angle of 41° to the horizontal. The path of the child through the air is shown in Fig. 3.2. velocity Z Y 41° path of child slide surface of water water in swimming pool Fig. 3.2 (not to scale) Point Z is the highest point on the path of the child through the air. Assume that air resistance is negligible. Calculate the speed of the child at: point Y[2]
4. (c)(ii)Calculate the speed of the child at: point Z.[2]

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