Mathematics 9709 · AS & A Level · Energy, work and power

Energy, work and power — practice question

A block of mass $60\,\text{kg}$ is drawn up a hill along the line of greatest slope by a force of magnitude $50\,\text{N}$ acting at an angle $\alpha^\circ$ above the hill. The block moves through points $A$ and $B$ with speeds $8.5\,\text{m s}^{-1}$ and $3.5\,\text{m s}^{-1}$ respectively (see diagram). The separation $AB$ is $250\,\text{m}$ and $B$ is $17.5\,\text{m}$ above the level of $A$. The resistance to motion of the block is $6\,\text{N}$.
(main)[11]

Find the value of $\alpha$.

Worked solution & mark scheme

This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: Determining change in PE or KE: $\Delta PE = 60g \times 17.5$ or $\Delta KE = \tfrac12 60(8.5^2-3.5^2)$

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