Problem 3

Description
A red ball slides horizontally off a table as shown in the animation (position is in meters and time is in seconds). Ignore air friction. At the SAME TIME that ball leaves the table, another ball is dropped from the SAME HEIGHT  straight down vertically  from the corner of the table on the right. (Remember to ALIGN, CLICK  and drag a little to  find the x and y coordinates.) The initial horizontal velocity of the ball coming from the left  is magnitude 6 m/s, but can be changed to 7 m/s or 8 m/s.

m/s (Change initial x-component of velocity)

(Hint: Review Ch. 3 ) 
Question 1
Will the horizontally launched  ball hit the vertically falling ball , or should it be launched at an angle below the horizontal to hit the falling ball? Predict your answer before you launch the ball on the left.
Question 2
How does your answer compare with what you see when you press play and run he simulation ?  Run it for initial horizontal velocity 6 m/s . Repeat the simulation for 7m/s and 8 m/s.  
Question 3
Prove mathematically that  the two balls will always collide independent of the initial horizontal velocity of the ball coming from the left. If you want you may want to label the ball from coming from the left "Ball A" and the vertically dropping ball on the right "Ball B." Prove Ball A and Ball B will always collide not matter what the value of Vx  for Ball A. 
Reference
See  Ch. 3