Final answer:
The expression for the closest distance from the ceiling that the second ball will reach is given by the formula d = h - ½ gt², where h is the initial height, g is the acceleration due to gravity, and t is the time.
Step-by-step explanation:
To determine the expression for the magnitude of the closest distance from the ceiling that the second ball will reach, we must consider the ball's motion under the influence of gravity. Using the equations of motion for free fall, the distance d that the ball reaches closest to the ceiling can be expressed as:
d = h - ½ gt²,
where h is the initial height from which the ball is dropped, g is the acceleration due to gravity (9.8 m/s²), and t is the time in seconds. The initial velocity of the ball is zero since it is dropped, so the ½ in the formula accounts for the constant acceleration due to gravity over time. In the options provided, the correct choice for the expression is (c) d = h - ½ gt².