To determine the time taken for the stone to reach its maximum height, we need to consider the motion of the stone and the acceleration due to gravity.
When the stone is thrown vertically upward, its initial velocity is 30 m/s. The stone will continue to rise until it reaches its maximum height, at which point its velocity becomes zero before it starts descending.
At the maximum height, the final velocity (v) is zero. The acceleration due to gravity (g) is approximately 9.8 m/s², directed downward. We can use the following kinematic equation to find the time taken to reach the maximum height:
v = u + at
Substituting the known values, we have:
0 = 30 m/s + (-9.8 m/s²) * t
Rearranging the equation to isolate t, we get:
9.8 m/s² * t = 30 m/s
t = 30 m/s / 9.8 m/s²
t ≈ 3.06 seconds
Therefore, it takes approximately 3.06 seconds for the stone to rise to its maximum height.