To find the average speed of the ball, we need to calculate the total distance traveled by the ball and divide it by the total time taken.
When a ball is thrown vertically upward, it follows a parabolic trajectory. The time taken to reach the maximum height is equal to the time taken to return to the starting point. Since the initial velocity is 19.6 m/s and the final velocity is -19.6 m/s (opposite direction), the time of flight can be calculated using the equation:
v = u + at,
where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. In this case, the final velocity is -19.6 m/s, the initial velocity is 19.6 m/s, and the acceleration is the acceleration due to gravity (-9.8 m/s^2).
-19.6 = 19.6 + (-9.8)t,
-39.2 = -9.8t,
t = 4 seconds.
Since the time of flight is 4 seconds, the total time taken for the complete trip (up and down) is 2 times the time of flight, which is 8 seconds.
To calculate the total distance traveled by the ball, we need to find the distance covered during the upward journey and the downward journey.
The distance covered during the upward journey can be calculated using the equation:
s = ut + (1/2)at^2,
where s is the distance, u is the initial velocity, a is the acceleration, and t is the time.
s = (19.6)(4) + (1/2)(-9.8)(4)^2, s = 78.4 - 78.4, s = 0.
During the upward journey, the ball reaches a maximum height and then returns to the starting point, resulting in a net displacement of 0.
Therefore, the total distance traveled by the ball is 0 meters.
Finally, to calculate the average speed, we divide the total distance by the total time:
Average speed = Total distance / Total time, Average speed = 0 / 8, Average speed = 0 m/s.
Hence, the average speed of the ball is 0 m/s.