Final answer:
The ball reaches its highest point at 3 seconds into its flight. By using the acceleration due to gravity and time taken to reach the apex, the initial velocity is found to be 29.4 m/s.
Step-by-step explanation:
The question involves the physics of projectile motion, specifically the time of flight and initial velocity of a ball thrown in a parabolic path. If a ball travels in the air for 6 seconds, the highest point of its trajectory, known as the apex, is reached at the halfway mark in time due to the symmetry of the trajectory under constant acceleration (due to gravity). Therefore, the time at which the ball reaches its highest point is 3 seconds (c).
To find the initial velocity of the ball, we use the kinematic equations for projectile motion. Given that the ball spends an equal amount of time ascending and descending, its initial vertical velocity must be zero at the apex. Therefore, the initial upward velocity is equal to the gravitational acceleration (approximately 9.8 m/s2) multiplied by the time taken to reach the apex. With a flight time of 6 seconds, the apex is reached at 3 seconds, thus the initial vertical velocity is:
Initial velocity = 9.8 m/s2 × 3 s = 29.4 m/s (d).