To determine the time the ball is in the air, we need to consider the ball's upward motion and its subsequent downward motion.
When the ball is thrown vertically upward, it reaches its maximum height and then falls back down to the initial position, where it is caught. At the highest point, the vertical velocity becomes zero.
Let's break down the problem into two parts: the upward motion and the downward motion.
- Upward motion: The initial velocity (v₀) is +15 m/s (positive because it's upward), and the final velocity (v) is 0 m/s at the highest point. The acceleration due to gravity (g) is -9.8 m/s² (negative because it acts downward).
Using the kinematic equation:
v = v₀ + at,
we can rearrange it to solve for time (t):
t = (v - v₀) / a.
Substituting the values:
t₁ = (0 - 15) / (-9.8) = 1.53 seconds (approx).
- Downward motion: The ball falls back down to the initial position, so the initial velocity (v₀) is 0 m/s, the final velocity (v) is also 0 m/s, and the acceleration (a) remains at -9.8 m/s².
Again, using the kinematic equation:
v = v₀ + at,
we can solve for time (t):
t₂ = (v - v₀) / a = (0 - 0) / (-9.8) = 0 seconds.
Since the total time in the air is the sum of the upward and downward times:
Total time = t₁ + t₂ = 1.53 + 0 = 1.53 seconds.
Therefore, the ball is in the air for approximately 1.53 seconds.