To calculate the required initial velocity for an object to reach a maximum height of 9.0 m, we can use the equations of motion for vertical motion.
The equation for the maximum height reached by an object can be derived from the equation:
v² = u² + 2as
Where: v is the final velocity (0 m/s at the maximum height), u is the initial velocity, a is the acceleration due to gravity (-9.8 m/s²), and s is the vertical displacement (9.0 m).
Plugging in the values, we have:
0² = u² + 2(-9.8 m/s²)(9.0 m)
Simplifying the equation, we get:
0 = u² - 176.4 m²/s²
Rearranging the equation to solve for u, we have:
u² = 176.4 m²/s² u = √(176.4 m²/s²) u ≈ 13.29 m/s
Therefore, the required initial velocity for the object at the ground level is approximately 13.29 m/s for it to reach a maximum height of 9.0 m.