Student 1: The ball from the roof reaches the ground first, because its velocity in the same direction as its acceleration.
Student 2: Based on an experiment done in my dorm to recreate the movements of the two baseballs by tossing two identical guitar effects pedals (items of the same weight and shape), I have concluded that the two balls will most likely reach their destination at the same time. They have the same general motion pattern, just opposite of each other because one starts with initial velocity and the other ends with it, therefore they will arrive at approximately the same time. This is also proved with graphs of the velocity vs. time, where the two lines are parallel resulting in the same acceleration and area between them .
Student 1: Your wording is a bit confusing. I do believe that acceleration due to gravity is 9.8 meters per second squared. However, your wording makes me believe that gravity can be variable. Can you verify which one you meant in class?
Student 2: Disregarding air resistance, and falling object on earth has an acceleration of approximately 9.8m/s squared.
Student 1: Through experimentation, I found that the first gate opens at 1.26sec and closes at 1.6sec. The second gate opens at 2.96sec and closes at 3.18sec. The ball must move about 2.8cm in order to clear the first gate and 3.1cm to clear the second gate. The average velocity required to clear the first gate is therefore 2.8cm/(1.6-1.26)~=8cm/s and 3.1/(3.18-2.96)~=14cm/s to clear the second gate. The change in velocity from one gate to the next is (14cm/s-8cm/s)/(3s-1.45s)~=3.87cm/s^2, or approximately 3.9cm/s^2 (using intermediate gate timepoints). In order to achieve the required velocity for the first gate, I decided to use an initial velocity of 2.1cm/s so that the ball's velocity would be 2.1cm/s+(1.45s*3.9cm/s^2)=7.8cm/s at the center of the first gate and 2.1cm/s+(3.0s*3.9cm/s^2)=13.8cm/s at the center of the second gate. An initial velocity of 2.1cm/s and an acceleration of 3.9cm/s^2 was successful at sinking a hole in one.
Student 2: The final problem was conceptually fairly easy, but turned out to be very difficult because the position of the ball, the position of the windmills, and the time were all difficult to measure. I would enjoy/learn more from problems that are conceptually more challenging and mechanically or algebraically simpler, such as the first.