Understanding the Physics

* Gravity: The projectile is constantly being pulled downwards by gravity (approximately 9.8 m/s²).

* Symmetry: The time it takes for the projectile to reach its highest point is equal to the time it takes to fall back down to its starting point.

Calculations

1. Find the time to reach the highest point:

* The projectile's upward velocity decreases at a rate of 9.8 m/s² due to gravity.

* At the highest point, the projectile's velocity is 0 m/s.

* We can use the following kinematic equation:

* v = u + at

* where:

* v = final velocity (0 m/s)

* u = initial velocity (30 m/s)

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

* t = time

* Solving for t:

* 0 = 30 - 9.8t

* t = 30 / 9.8 ≈ 3.06 seconds

2. Find the total time:

* Since the time to go up equals the time to come down, the total time is:

* Total time ≈ 3.06 seconds * 2 = 6.12 seconds

Therefore, the total time for the projectile to return to its starting point is approximately 6.12 seconds.