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\includegraphics[max width=\textwidth, alt={}, center]{4acdc4d7-01f0-496f-9390-de5f136bc5f9-4_559_1057_1025_543} A small ball of mass 0.2 kg is projected with speed \(11 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) up a line of greatest slope of a roof from a point \(A\) at the bottom of the roof. The ball remains in contact with the roof and moves up the line of greatest slope to the top of the roof at \(B\). The roof is rough and the coefficient of friction is \(\frac { 1 } { 2 }\). The distance \(A B\) is 5 m and \(A B\) is inclined at \(30 ^ { \circ }\) to the horizontal (see diagram).

1. Show that the speed of the ball when it reaches \(B\) is \(5.44 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), correct to 2 decimal places. The ball leaves the roof at \(B\) and moves freely under gravity. The point \(C\) is at the lower edge of the roof. The distance \(B C\) is 5 m and \(B C\) is inclined at \(30 ^ { \circ }\) to the horizontal.
2. Determine whether or not the ball hits the roof between \(B\) and \(C\). {www.ocr.org.uk}) after the live examination series.
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