Answer:
the height of the rooftop is approximately 16.4 meters or about 54 feet high.
Step-by-step explanation:
To solve this problem, we need to use the kinematic equations of motion. We will assume that air resistance is negligible and that the acceleration due to gravity is -9.8 m/s^2.
First, we will use the initial velocity and angle of the kickball to find its horizontal and vertical components of velocity.
The horizontal component of velocity (Vx) can be found using the equation:
Vx = V * cos(theta)
where V is the initial velocity and theta is the angle of the kickball.
Vx = 15.2 m/s * cos(63 degrees)
Vx = 6.62 m/s
The vertical component of velocity (Vy) can be found using the equation:
Vy = V * sin(theta)
Vy = 15.2 m/s * sin(63 degrees)
Vy = 13.7 m/s
Next, we can use the vertical component of velocity to find the maximum height (h) reached by the kickball. We can use the following kinematic equation:
h = Vy^2 / (2 * g)
where g is the acceleration due to gravity.
h = (13.7 m/s)^2 / (2 * 9.8 m/s^2)
h = 9.47 meters
So, the maximum height reached by the kickball is 9.47 meters.
Finally, we can use the time it takes for the kickball to land on the rooftop to find the height (d) of the rooftop. We can use another kinematic equation:
d = Vy * t + 0.5 * g * t^2
where t is the time it takes for the kickball to land on the rooftop.
d = 13.7 m/s * 2.4 s + 0.5 * (-9.8 m/s^2) * (2.4 s)^2
d = 16.4 meters
Therefore, the height of the rooftop is approximately 16.4 meters or about 54 feet high.