Understanding the Physics

* Symmetry: When a ball is thrown vertically, its upward motion is symmetrical to its downward motion. This means the time it takes to go up is equal to the time it takes to come down.

* Acceleration due to gravity: The acceleration due to gravity (g) acts downwards, and its value is approximately 9.8 m/s².

Solution

1. Time of ascent: Since the total time is 6 seconds, the time taken for the ball to go up is 6 seconds / 2 = 3 seconds.

2. Final velocity at the highest point: At the highest point, the ball's velocity momentarily becomes zero before it starts falling back down.

3. Using the equation of motion: We can use the following equation of motion to find the initial velocity (u):

* 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 - negative since it acts downwards)

* t = time of ascent (3 seconds)

4. Substituting values:

* 0 = u + (-9.8 m/s²) * 3 s

* 0 = u - 29.4 m/s

5. Solving for initial velocity:

* u = 29.4 m/s

Therefore, the ball was thrown upwards with a velocity of 29.4 m/s.