To determine the time it takes for the stone to reach its maximum height, we need to use the equations of motion. When the stone reaches its maximum height, its final velocity will be zero.
The initial velocity of the stone is given as 0.2 m/s, and the final velocity is 0 m/s. We can use the following equation to find the time taken to reach the maximum height:
Final velocity (v) = Initial velocity (u) + Acceleration (a) × Time (t)
In this case, the acceleration (a) is equal to the acceleration due to gravity (g) acting in the opposite direction (-9.8 m/s², as the stone is moving upward). We can rearrange the equation to solve for time:
0 = 0.2 m/s - 9.8 m/s² × t
Simplifying the equation:
9.8 m/s² × t = 0.2 m/s
t = 0.2 m/s / 9.8 m/s²
t ≈ 0.0204 seconds
Therefore, the stone will reach its maximum height after approximately 0.0204 seconds.