To determine how long the ball will stay in the air before it comes back to the person's hand, we need to analyze the ball's motion.
When the ball is thrown vertically upward, it experiences a constant downward acceleration due to gravity. We can assume the acceleration due to gravity to be approximately 9.8 m/s² (ignoring air resistance).
The ball reaches its maximum height when its vertical velocity becomes zero. At that point, it starts falling back down. The time taken to reach the maximum height is the same as the time taken to fall back to the initial position.
To find the time taken to reach the maximum height, we can use the following equation:
v = u + at
Where: v = 0 m/s (vertical velocity at maximum height, as it momentarily comes to rest) u = 15 m/s (initial velocity) a = -9.8 m/s² (acceleration due to gravity)
Rearranging the equation, we have:
t = (v - u) / a
Substituting the values, we get:
t = (0 - 15) / (-9.8)
t ≈ 1.53 seconds
Therefore, it takes approximately 1.53 seconds for the ball to reach its maximum height.
Since the total time in the air is the time to reach the maximum height plus the time to fall back down, the total time is approximately:
Total time = 1.53 seconds + 1.53 seconds = 3.06 seconds
Hence, the ball will stay in the air for approximately 3.06 seconds before it comes back to the person's hand.