Answer:
- The water ballon that was thrown straight down at 2.00 m/s hits the ground first, 0.19 s before the other ballon.
Step-by-step explanation:
The motions of the two water ballons are ruled by the kinematic equations:
We are only interested in the vertical motion, so that equation is all what you need.
1. Water ballon is thrown horizontally at sped 2.00 m/s.
The time the ballon takes to hit the ground is independent of the horizontal speed.
Since 2.00 m/s is a horizontal speed, you take the initial vertical speed equal to 0.
Then:

2. Water ballon thrown straight down at 2.00 m/s
Now the initial vertical speed is 2.00 m/s down. So, the equation is:

To solve the equation you can use the quadratic formula.

You get two times. One of the times is negative, thus it does not have physical meaning.
3. Conclusion:
The water ballon that was thrown straight down at 2.00 m/s hits the ground first by 1.11 s - 0.92s = 0.19 s.