To find the maximum height attained and the time of flight, we can use the equations of motion for vertical motion.
- Maximum Height (H): The maximum height reached by the stone can be calculated using the formula: H = (v^2 - u^2) / (2g) where: H is the maximum height, v is the final velocity (which is 0 when the stone reaches its peak), u is the initial velocity, g is the acceleration due to gravity (approximately 9.8 m/s^2).
Using the given values, we have: u = 9 m/s, v = 0 m/s, g = 9.8 m/s^2.
H = (0^2 - 9^2) / (2 * 9.8) H = (-81) / 19.6 H ≈ -4.13 meters.
Since the maximum height attained by the stone is negative, it indicates that the stone is projected downwards from its initial position.
- Time of Flight (T): The time of flight is the total time it takes for the stone to go up and come back down. It can be calculated using the formula: T = 2 * t where: T is the time of flight, t is the time it takes for the stone to reach its peak.
The time it takes for the stone to reach its peak can be found using the formula: v = u - g * t 0 = 9 - 9.8 * t 9.8 * t = 9 t ≈ 0.918 seconds.
Therefore, the time of flight is: T = 2 * 0.918 T ≈ 1.836 seconds.
To summarize: The stone reaches a maximum height of approximately -4.13 meters (indicating it is projected downwards) and has a time of flight of approximately 1.836 seconds.