To find the total time of flight for the ball, we can use the kinematic equations of motion. We'll consider the motion in the vertical direction.
We know that the initial velocity of the ball is 30 m/s, and it is thrown upward. The final velocity at the highest point of the ball's trajectory will be 0 m/s since the ball momentarily comes to a stop before reversing direction.
We can use the following equation to relate the initial velocity, final velocity, acceleration, and time:
Final Velocity = Initial Velocity + (Acceleration × Time)
Since the final velocity is 0 m/s and the initial velocity is 30 m/s (upward), we have:
0 = 30 + (-9.8 × Time)
Simplifying the equation:
9.8 × Time = 30
Time = 30 / 9.8
Time ≈ 3.06 seconds (rounded to two decimal places)
This is the time it takes for the ball to reach its highest point.
Since the motion is symmetrical, the total time of flight is twice the time it takes to reach the highest point.
Total Time of Flight = 2 × 3.06 seconds
Total Time of Flight ≈ 6.12 seconds (rounded to two decimal places)
Therefore, the total time of flight for the ball is approximately 6.12 seconds.