Final answer:
The pull of gravity will change the magnitude of the velocity of the baseball when it reaches the batter. Using the kinematic equation, we can calculate the time it takes for the ball to reach the batter by rearranging the equation. The time is approximately 3.40 seconds.
Step-by-step explanation:
The magnitude of the velocity of the baseball will change due to the pull of gravity when it reaches the batter. The pull of gravity will act vertically downwards, causing the ball to accelerate in the vertical direction while maintaining a constant horizontal velocity.
First, we need to convert the velocity from km/h to m/s. We know that 1 km = 1000 m and 1 hour = 3600 s. Therefore, the initial velocity of the baseball is 120 km/h × (1000 m/1 km) / (3600 s/1 hour) = 33.33 m/s.
Next, we can use the kinematic equation:
vf = vi + at
Where vf is the final velocity, vi is the initial velocity, a is the acceleration, and t is the time. In this case, the final velocity is the magnitude of the velocity when the ball reaches the batter, and the initial velocity is 33.33 m/s. The acceleration is the acceleration due to gravity, which is approximately 9.8 m/s2. We are trying to find the time it takes for the ball to reach the batter, so we can rearrange the equation:
t = (vf - vi) / a
Substituting the known values:
t = (0 - 33.33) / -9.8
Simplifying the eqation:
t ≈ 3.40 s
Therefore, the pull of gravity will change the magnitude of the velocity over a time of approximately 3.40 seconds when the ball reaches the batter.