To calculate the maximum height reached by the ball, we can use the equations of motion for vertical motion.
Given: Mass of the ball, m = 500 g = 0.5 kg Initial velocity, u = 20 m/s (thrown vertically upwards) Height of the building, h = 100 m
First, let's find the time taken for the ball to reach its maximum height. We can use the equation:
v = u + at
where: v is the final velocity (0 m/s at the maximum height), u is the initial velocity (20 m/s), a is the acceleration (due to gravity, -9.8 m/s²), and t is the time taken.
0 = 20 - 9.8t
Solving for t, we get: t = 20 / 9.8 ≈ 2.04 s
Now, we can calculate the maximum height reached using the equation:
h = u*t + (1/2)at²
where: h is the maximum height, u is the initial velocity (20 m/s), a is the acceleration (due to gravity, -9.8 m/s²), and t is the time taken (2.04 s).
h = 20 * 2.04 + (1/2) * (-9.8) * (2.04)² h ≈ 40.8 - 20.04 h ≈ 20.76 m
Therefore, the maximum height reached by the ball is approximately 20.76 meters.