A stone is projected vertically with a speed of 10 m/s from a point 8 metres above the ground. Find the maximum height reached. \([g = 10 ms^{-2}]\).

We can solve this problem using the equations of motion for a particle moving vertically under gravity. The key idea is that at the maximum height, the vertical velocity of the stone will be zero. We can use the following equation to find the time taken by the stone to reach the maximum height: \[-u/g = -10/10 = -1\] where u is the initial velocity and g is the acceleration due to gravity. The time taken to reach the maximum height is 1 second. We can now use the following equation to find the maximum height reached: \[h = u t - \frac{1}{2} g t^{2} = 10\times 1 - \frac{1}{2}\times 10\times 1^{2} = 5\] where h is the maximum height reached. Therefore, the maximum height reached by the stone is 5 metres above the initial height of 8 metres, which gives us a total height of 13 metres. Hence, the answer is option (A) 13 metres.