Final answer:
To test the hypothesis that acceleration is independent of velocity, measurements of fall time, initial speeds, and time of contact with the ground for each ball are necessary. For the bouncing ball experiment, the drop height and rebound height are used to calculate the coefficient of restitution.
Step-by-step explanation:
To show that the acceleration of an object is independent of the object's velocity, a controlled experiment can be conducted using three balls as described. The information that would be crucial to collect for each ball includes the time taken for each ball to reach the ground, their initial speeds if applicable (Ball A and C), and the time of contact with the ground if possible. For Ball B, dropped from rest, only the time to hit the ground is needed as the initial speed is zero. These measurements will allow for the calculation of the acceleration of each ball due to gravity, expected to be approximately 9.81 m/s2 in the absence of air resistance, confirming if the initial velocity has an impact on the acceleration.
Meanwhile, in the bouncing ball experiment, students should measure the height from which the ball is dropped (H) and the height to which it bounces back (h). Using these values, they can determine the coefficient of restitution (c) using the formula c = (h/H)1/2. This coefficient reflects the elasticity of the collision. For a real-world context, they could compare this value with the standard coefficient of 0.85 for new tennis balls on a court.