To determine the time it takes for the ball to hit the ground, we can use the equations of motion. Since the ball is thrown vertically upwards and then falls back down, we can divide the motion into two parts: the upward motion and the downward motion.
First, let's calculate the time it takes for the ball to reach its maximum height during the upward motion. We can use the equation:
v = u + at
Where: v = final velocity (0 m/s at the highest point, as the ball momentarily stops) u = initial velocity (10 m/s upwards) a = acceleration (due to gravity, -9.8 m/s², negative because it opposes the upward motion) t = time
Using the equation:
0 = 10 - 9.8t
9.8t = 10
t = 10 / 9.8
t ≈ 1.02 seconds
It takes approximately 1.02 seconds for the ball to reach its maximum height during the upward motion.
Now, let's calculate the time it takes for the ball to fall back down and hit the ground. We can use the equation:
s = ut + (1/2)at²
Where: s = displacement (20 m, as the ball starts from a 20 m building and hits the ground) u = initial velocity (0 m/s at the highest point) a = acceleration (due to gravity, -9.8 m/s²) t = time
Using the equation:
20 = 0 × t + (1/2)(-9.8)t²
20 = -4.9t²
t² = -20 / -4.9
t² ≈ 4.08
t ≈ √(4.08)
t ≈ 2.02 seconds
It takes approximately 2.02 seconds for the ball to fall back down and hit the ground.
Therefore, the total time it takes for the ball to hit the ground is approximately 1.02 seconds (upward motion) + 2.02 seconds (falling back down) = 3.04 seconds.