To solve the problem of determining the height attained by the stone and the time taken to reach there, we can use the principles of kinematics.
Firstly, let's summarize the given data:
- The acceleration, [tex]\(a\)[/tex], is [tex]\(8 \, m/s^2\)[/tex]. This is in the downward direction, due to gravity.
- The initial velocity, [tex]\(u\)[/tex], is [tex]\(0 \, m/s\)[/tex] since the stone is starting from rest.
- The initial height, [tex]\(h_0\)[/tex], is [tex]\(0\)[/tex] as it starts from the ground level.
Since the initial vertical velocity ([tex]\(u\)[/tex]) is [tex]\(0\)[/tex], the stone does not have any upward motion initially. Therefore, the stone immediately begins to accelerate downward due to gravity with no initial upward distance covered. Hence, we can determine the following:
- The height attained by the stone is zero [tex]\(0 \, m\)[/tex]. This is because it hasn't moved upwards; it just starts falling down from the initial height which is zero.
- The time taken to reach the maximum height, which is also zero, is [tex]\(0 \, seconds\)[/tex] because there is no upward journey taking place, only a downward fall that begins instantaneously.
So, the height attained by the stone is [tex]\(0 \, m\)[/tex] and the time taken to reach this height is [tex]\(0 \, seconds\)[/tex].
