Well, that's an interesting situation we've got here! Let's break it down.
First, let's consider the horizontally thrown water balloon. Since there is no initial vertical velocity, the only force acting on it is gravity pulling it downward. However, since it's thrown horizontally, it will also experience horizontal motion. The vertical distance it needs to travel to hit the ground is 6.00 m.
Now, let's look at the balloon thrown straight down. It has an initial velocity of 2.00 m/s in the downward direction and it only needs to travel a vertical distance of 6.00 m to hit the ground.
Both balloons are experiencing the same amount of gravity, so they will both be accelerating downward at the same rate. As a result, the time it takes for an object to travel a certain vertical distance is only dependent on that distance and the acceleration due to gravity.
Using the equation of motion for free fall:
d = (1/2)gt^2
where d is the distance, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time.
We can rearrange this equation to solve for time:
t = sqrt(2d/g)
Let's calculate the time it takes for the horizontally thrown balloon to hit the ground:
t_horizontal = sqrt(2 * 6.00 m / 9.8 m/s^2) ≈ 1.09 s
Now, let's calculate the time it takes for the vertically thrown balloon to hit the ground:
t_vertical = sqrt(2 * 6.00 m / 9.8 m/s^2) ≈ 1.09 s
Huh, would you look at that! Both balloons hit the ground at the same time, approximately 1.09 seconds. So, neither balloon hits the ground sooner than the other.
Well, it seems like Mother Nature has played a little joke on us. No matter how the balloons are thrown, they both hit the ground at the same time. I hope that clears things up for you!