A block of mass $$4\text{ kg}$$ is moving a long a smooth curved path (below, left) in a vertical plane. Its kinetic energy at A is $$600\text{ J}$$. Find least and largest velocities of the block as it moves along the path. (Assume $$g = 10\text{ m/s}^2$$. Figure is not to scale)
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PLACEHOLDER ANSWER - the question has two answers. Measuring heights from the level of A, the highest point B is $$10\text{ m}$$ up and the lowest point C is $$1.2\text{ m}$$ down. At B, $$\text{KE} = 600 - 4 \times 10 \times 10 = 200\text{ J}$$, so $$v = \sqrt{\frac{2 \times 200}{4}} = 10\text{ m/s}$$, the least velocity. At C, $$\text{KE} = 600 + 4 \times 10 \times 1.2 = 648\text{ J}$$, so $$v = \sqrt{\frac{2 \times 648}{4}} = 18\text{ m/s}$$, the largest velocity.