To find the maximum height reached by the stone, we can use the equations of motion. Since the stone is thrown vertically upward, we can consider the acceleration due to gravity (g) acting in the downward direction.
The initial velocity of the stone (u) is +20 m/s (positive because it is upward). The final velocity of the stone (v) at the maximum height is 0 m/s (at the topmost point, the stone momentarily comes to rest). The acceleration (a) is -9.8 m/s² (negative because it acts in the opposite direction to the initial velocity). The displacement (s) is the maximum height reached by the stone.
We can use the equation of motion:
v² = u² + 2as
Plugging in the known values:
0² = 20² + 2(-9.8)s
Simplifying the equation:
0 = 400 - 19.6s
Rearranging the equation to solve for s:
19.6s = 400
s = 400 / 19.6
s ≈ 20.41 meters
Therefore, the maximum height reached by the stone is approximately 20.41 meters.