To determine the maximum height and initial velocity of the cricket ball, we can use the equations of motion for vertical motion.
Let's assume the upward direction as positive.
We know that the time taken for the ball to reach the highest point is half of the total time of flight. So, the time taken to reach the maximum height is 6 seconds divided by 2, which is 3 seconds.
At the maximum height, the vertical velocity becomes zero. Using this information, we can apply the following equation of motion:
v = u + at,
where: v = final velocity (0 m/s at the highest point), u = initial velocity (what we want to find), a = acceleration due to gravity (-9.8 m/s², assuming no air resistance), t = time (3 seconds).
Plugging in the values, we get:
0 = u - 9.8 * 3.
Simplifying the equation:
u = 9.8 * 3, u = 29.4 m/s.
Therefore, the initial velocity of the cricket ball is 29.4 m/s.
To find the maximum height, we can use the following equation of motion:
s = ut + (1/2)at²,
where: s = displacement (maximum height, what we want to find), u = initial velocity (29.4 m/s), a = acceleration due to gravity (-9.8 m/s²), t = time (3 seconds).
Plugging in the values, we get:
s = 29.4 * 3 + (1/2) * (-9.8) * (3²).
Simplifying the equation:
s = 88.2 - 44.1, s = 44.1 m.
Therefore, the maximum height reached by the cricket ball is 44.1 meters.