Respuesta :
Answer:
It takes approximately 2.13 seconds for the ball to hit the ground and its velocity before hitting the ground is approximately -4.23 m/s (negative sign indicates downward direction).
Explanation:
To solve this problem using the Gresa method, we can use the following equations:
1. The equation of motion for the ball when it is thrown vertically upward is given by:
h = ut - (1/2)gt^2
where h is the height of the ball, u is the initial velocity, g is the acceleration due to gravity, and t is the time.
2. The equation of motion for the ball when it is falling downward is given by:
h = (1/2)gt^2
where h is the height of the ball, g is the acceleration due to gravity, and t is the time.
Given:
- Initial velocity (u) = 15 m/s
- Height of the building (h) = 22 m
- Acceleration due to gravity (g) = 9.8 m/s^2
To find the time it takes for the ball to hit the ground, we can equate the height of the ball to zero in equation 2:
0 = (1/2)gt^2
Solving for t:
t = sqrt((2h)/g)
Substituting the given values:
t = sqrt((2*22)/9.8) ≈ 2.13 seconds
To find the velocity of the ball before it hits the ground, we can use the equation:
v = u - gt
where v is the final velocity, u is the initial velocity, g is the acceleration due to gravity, and t is the time.
Substituting the given values:
v = 15 - 9.8*2.13 ≈ -4.23 m/s
Therefore, it takes approximately 2.13 seconds for the ball to hit the ground and its velocity before hitting the ground is approximately -4.23 m/s (negative sign indicates downward direction).
