3 The diagram shows the three points A, B and C that lie along a line of greatest slope on a rough plane which is inclined at an angle of \(25 ^ { \circ }\) to the horizontal.
\includegraphics[max width=\textwidth, alt={}, center]{0a790ad0-7eda-40f1-9894-f156766ae46f-3_392_1136_383_242} A block of mass 6 kg is placed at B and is projected up the plane towards C with an initial speed of \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The block travels 3.5 m before coming instantaneously to rest at C , before sliding back down the plane. When the block is sliding back down the plane it attains its initial speed at A , which lies \(x \mathrm {~m}\) down the plane from B . It is given that the work done against resistance throughout the motion is 4 joules per metre.

1. Use an energy method to determine the following.
   1. The value of \(u\)
   2. The value of \(x\) A student claims that half of the energy lost due to resistances is accounted for by friction between the block and the plane, and the other half by air resistance.
2. Assuming that the student's claim is correct, determine the coefficient of friction between the block and the plane.