Projectiles in Resisted Motion
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A stone is thrown from a height of 1m with a velocity of \((3\mathbf{i} + 2\mathbf{j} + 6\mathbf{k})\ \text{ms}^{-1}\), where \(\mathbf{i},\mathbf{j}\) and \(\mathbf{k}\) are unit vectors in the east, north and vertically up directions respectively. The acceleration of the stone due to gravity, air resistance and wind is \((4\mathbf{i} + 2\mathbf{j} - 2\mathbf{k})\ \text{ms}^{-2}\). Assuming a flat ground and the origin on the ground level directly below the point of projection, calculate the maximum height reached by the stone.
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