To determine the time taken to reach the maximum height of a ball thrown vertically upward, we can use the kinematic equation for vertical motion.
The equation relating the final velocity (v), initial velocity (u), acceleration (a), and time (t) is given by:
v = u + at
In this case, the ball is thrown vertically upward, so the initial velocity (u) is 80 m/s, and the final velocity (v) at the maximum height is 0 m/s since the ball momentarily stops at its highest point.
Therefore, we have:
0 = 80 m/s - 9.8 m/s^2 * t
Solving for time (t), we can rearrange the equation:
9.8 m/s^2 * t = 80 m/s
t = 80 m/s / 9.8 m/s^2
t ≈ 8.16 seconds
So, the time taken to reach the maximum height is approximately 8.16 seconds.