7 A sphere, of mass 0.2 kg , moving on a smooth horizontal surface, collides with a fixed wall. Before the collision the sphere moves with speed \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of \(60 ^ { \circ }\) to the wall. After the collision the sphere moves with speed \(\nu \mathrm { m } \mathrm { s } ^ { - 1 }\) at an angle of \(\theta ^ { \circ }\) to the wall. The velocities are shown in the diagram below.
\includegraphics[max width=\textwidth, alt={}, center]{86817115-46a1-4702-8a33-8f9b05d69bb9-08_303_762_735_625} The coefficient of restitution between the wall and the sphere is 0.7 7

1. Assume that the wall is smooth. 7
2. 1. Find the value of \(v\) Give your answer to two significant figures.
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3. (ii) Find the value of \(\theta\) Give your answer to the nearest whole number.
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4. (iii) Find the magnitude of the impulse exerted on the sphere by the wall.
   Give your answer to two significant figures.
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5. In reality the wall is not smooth.
   Explain how this would cause a change in the magnitude of the impulse calculated in part (a)(iii).