Final answer:
The key factor determining the height reached by a baseball after being hit by a batter is the initial velocity of the ball. The initial velocity is composed of speed and direction and is more influential in the vertical motion of the ball than the mass of the ball, the speed of the pitch, or the angle of the bat swing.
Step-by-step explanation:
In a baseball game, when a batter hits the ball at a certain height, the key factor determining the height reached by the ball is the initial velocity of the ball (d). The initial velocity refers to both the speed and the direction of the ball just after being hit. For instance, a ball hit straight up with an initial velocity will have its trajectory determined by that velocity. The mass of the ball (b) and the speed of the pitch (a) could influence the initial velocity, but they are not directly responsible for the height reached. The angle of the bat swing (c) actually affects the direction of the initial velocity, and thus indirectly influences the height. However, if we only consider the options provided, the correct answer is (d), focusing primarily on the velocity aspect.
Considering an example where a ball is kicked with an initial velocity of 16 m/s in the horizontal direction and 12 m/s in the vertical direction, the maximum height that the ball reaches depends mainly on its vertical initial velocity and the acceleration due to gravity. We disregard the horizontal component because it does not affect the vertical motion, which determines the height.
The vertical motion of any projectile, including a baseball, is governed by the laws of kinematics, which links the initial velocity, acceleration due to gravity, and the height reached. Even for a ball thrown horizontally from a height, the key aspect determining how long the ball is in the air and the height it can reach involves its initial velocity and the constant acceleration due to gravity.