Understanding the Motion

* Upward Motion: The ball slows down as it goes up due to gravity. At the highest point, its velocity momentarily becomes zero.

* Downward Motion: The ball accelerates downwards due to gravity, gaining speed until it reaches the ground.

Key Concepts

* Acceleration due to gravity (g): Approximately 9.8 m/s² (downwards)

* Symmetry: The time it takes to go up is equal to the time it takes to come down.

Solution

1. Find the time to reach the highest point:

* We can use the following kinematic equation:

* v = u + at

* Where:

* v = final velocity (0 m/s at the highest point)

* u = initial velocity (45 m/s)

* a = acceleration due to gravity (-9.8 m/s²)

* t = time

* 0 = 45 - 9.8t

* t = 45 / 9.8 ≈ 4.59 seconds

2. Double the time to find the total time:

* Since the time up equals the time down, the total time in the air is:

* 2 * 4.59 seconds ≈ 9.18 seconds

Therefore, it takes approximately 9.18 seconds for the ball to return to the ground.