A block $$\(B\)$$ of mass $$\(4 \mathrm{~kg}\)$$ is pushed up a line of greatest slope of a smooth plane inclined at $$\(30^{\circ}\)$$ to the horizontal by a force applied to $$\(B\)$$, acting in the direction of motion of $$\(B\)$$. The block passes through points $$\(P\)$$ and $$\(Q\)$$ with speeds $$\(12 \mathrm{~m} \mathrm{~s}^{-1}\)$$ and $$\(8 \mathrm{~m} \mathrm{~s}^{-1}\)$$ respectively. $$\(P\)$$ and $$\(Q\)$$ are $$\(10 \mathrm{~m}\)$$ apart with $$\(P\)$$ below the level of $$\(Q\)$$ At the instant the block reaches $$\(Q\)$$, the force pushing the block up the slope is removed. Find the time taken, after this instant, for the block to return to $$\(P\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_s20_qp_43 Year：2020 Question No：5(c)
Answer:
\(-4 g \sin 30=4 a\)
\(a=-5\)
\(-10=8 t-\frac{1}{2} \times 5 t^{2}\)
\(t=4.16 \mathrm{~s}\)
\(a=-5\)
\(-10=8 t-\frac{1}{2} \times 5 t^{2}\)
\(t=4.16 \mathrm{~s}\)
Knowledge points:
4.2.4 use appropriate formulae for motion with constant acceleration in a straight line. （Questions may involve setting up more than one equation, using information about the motion of different particles.）
4.4.3 solve simple problems which may be modelled as the motion of a particle moving vertically or on an inclined plane with constant acceleration Including, for example, motion of a particle on a rough plane where the acceleration while moving up the plane is different from the acceleration while moving down the plane.
Solution:
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