To determine the time taken to reach the maximum height of a ball thrown vertically upward, we need to use the kinematic equation for vertical motion.
The equation we will use is:
v = u + gt
where: v is the final velocity (which is 0 m/s at the maximum height), u is the initial velocity (80 m/s), g is the acceleration due to gravity (-9.8 m/s^2), and t is the time.
Since the ball reaches its maximum height when its velocity becomes zero, we can rearrange the equation as follows:
0 = 80 - 9.8t
Simplifying the equation, we have:
9.8t = 80
Dividing both sides of the equation by 9.8, we get:
t = 80 / 9.8
Calculating the value:
t ≈ 8.16 seconds
Therefore, it takes approximately 8.16 seconds for the ball to reach its maximum height.