(i)[2]
Write the change in gravitational potential energy of the particle in terms of $x$.
(ii)[4]
Apply an energy method to determine $x$.
Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
A particle of mass $8\,\text{kg}$ is launched at a speed of $5\,\text{m s}^{-1}$ up the line of greatest slope on a rough plane inclined at an angle $\alpha$ to the horizontal, where $\sin \alpha = \frac{5}{13}$. Its motion is opposed by a constant friction force of magnitude $15\,\text{N}$. After moving a distance $x\,\text{m}$ up the plane, the particle is brought to instantaneous rest.